Regression with Graphics by Lawrence Hamilton Chapter 4: Regression Criticism

Correlation and Scatterplot Matrices

We will be using the concord1 data set. First, we need to change the variable retire from a string to a numeric variable.

data concy;
  set concord1;
  retired = .;
  if retire = 'yes' then retired = 1;
  if retire = 'no' then retired = 0;
run;

page 114 Table 4.2 Correlation matrix for 1981 household water use and predictors.

proc corr data = concy;
  var income water80 educat retired peop81 cpeop water81;
  with income water80 educat retired peop81 cpeop water81;
run;

The CORR Procedure

7 With Variables: income water80 educat retired peop81 cpeop water81 7 Variables: income water80 educat retired peop81 cpeop water81

Simple Statistics

Variable N Mean Std Dev Sum Minimum Maximum

income 496 23.07661 13.05784 11446 2.00000 100.00000 water80 496 2732 1764 1355100 200.00000 12700 educat 496 14.00403 3.09055 6946 6.00000 20.00000 retired 496 0.29435 0.45621 146.00000 0 1.00000 peop81 496 3.07258 1.65718 1524 1.00000 10.00000 cpeop 496 -0.03831 0.48466 -19.00000 -3.00000 3.00000 water81 496 2298 1486 1140000 100.00000 10100

Pearson Correlation Coefficients, N = 496 Prob > |r| under H0: Rho=0

income water80 educat retired peop81 cpeop water81

income 1.00000 0.33705 0.34625 -0.38056 0.31128 0.09112 0.41779 <.0001 <.0001 <.0001 <.0001 0.0425 <.0001

water80 0.33705 1.00000 0.09822 -0.29193 0.52510 -0.03117 0.76479 <.0001 0.0287 <.0001 <.0001 0.4885 <.0001

educat 0.34625 0.09822 1.00000 -0.17421 0.05872 0.00550 0.04038 <.0001 0.0287 <.0001 0.1917 0.9028 0.3695

retired -0.38056 -0.29193 -0.17421 1.00000 -0.37569 -0.05854 -0.27313 <.0001 <.0001 <.0001 <.0001 0.1930 <.0001

peop81 0.31128 0.52510 0.05872 -0.37569 1.00000 0.14433 0.61831 <.0001 <.0001 0.1917 <.0001 0.0013 <.0001

cpeop 0.09112 -0.03117 0.00550 -0.05854 0.14433 1.00000 0.06611 0.0425 0.4885 0.9028 0.1930 0.0013 0.1415

water81 0.41779 0.76479 0.04038 -0.27313 0.61831 0.06611 1.00000 <.0001 <.0001 0.3695 <.0001 <.0001 0.1415

page 115 Figure 4.1 Scatterplot matrix corresponding to Table 4.2 (household water use and predictors). The %include command tells SAS the a macro will be used. The macro is called scatter, so the %scatter is the command to use that macro.

proc insight data = concy;
  scatter income water80 educat retired peop81 cpeop water81 * 
  income water80 educat retired peop81 cpeop water81;
run;

page 115 Figure 4.2 Scatterplot matrix for data from 122 countries, using the nations data set.

proc insight data = nations;
 scatter encon85 popgro85 fert84 birthr85 * encon85 popgro85 fert84 birthr85;
run;

Residual Versus Predicted Y Plots

page 116 Figure 4.3 Residuals (e) versus predicted values (Y-hat) from regression of 1981 household water use on seven predictors.

proc reg data=concy;
 model water81 = income water80 educat retired peop81 cpeop peop80;
 output out=out1(keep=case e) residual=e;
run;
quit;

The REG Procedure Model: MODEL1 Dependent Variable: water81

Analysis of Variance

Sum of Mean Source DF Squares Square F Value Pr > F

Model 6 740477522 123412920 171.08 <.0001 Error 489 352761188 721393 Corrected Total 495 1093238710

Root MSE 849.34859 R-Square 0.6773 Dependent Mean 2298.38710 Adj R-Sq 0.6734 Coeff Var 36.95411

NOTE: Model is not full rank. Least-squares solutions for the parameters are not unique. Some statistics will be misleading. A reported DF of 0 or B means that the estimate is biased. NOTE: The following parameters have been set to 0, since the variables are a linear combination of other variables as shown.

peop80 = peop81 – cpeop

Parameter Estimates

Parameter Standard Variable DF Estimate Error t Value Pr > |t|

Intercept 1 242.22043 206.86382 1.17 0.2422 income 1 20.96699 3.46372 6.05 <.0001 water80 1 0.49194 0.02635 18.67 <.0001 educat 1 -41.86552 13.22031 -3.17 0.0016 retired 1 189.18433 95.02142 1.99 0.0470 peop81 B 248.19702 28.72480 8.64 <.0001 cpeop B 96.45360 80.51903 1.20 0.2315 peop80 0 0 . . .

proc reg data=concy;
 model water81 = income water80 educat retired peop81 cpeop peop80;
 output out=out2(keep=case yhat) predicted=yhat;
run;
quit;

The REG Procedure Model: MODEL1 Dependent Variable: water81

Analysis of Variance

Sum of Mean Source DF Squares Square F Value Pr > F

Model 6 740477522 123412920 171.08 <.0001 Error 489 352761188 721393 Corrected Total 495 1093238710

Root MSE 849.34859 R-Square 0.6773 Dependent Mean 2298.38710 Adj R-Sq 0.6734 Coeff Var 36.95411

peop80 = peop81 – cpeop

Parameter Estimates

Parameter Standard Variable DF Estimate Error t Value Pr > |t|

data concordall;
 merge concord1 out1 out2;
 by case;
 label e = . ;
 label yhat = . . ;
proc univariate data=concordall;
 var yhat e;
run;

The UNIVARIATE Procedure Variable: yhat (predicted value)

Moments

N 496 Sum Weights 496 Mean 2298.3871 Sum Observations 1140000 Std Deviation 1223.07571 Variance 1495914.19 Skewness 1.02246077 Kurtosis 1.53522546 Uncorrected SS 3360638812 Corrected SS 740477522 Coeff Variation 53.214522 Std Error Mean 54.9177205

Basic Statistical Measures

Location Variability

Mean 2298.387 Std Deviation 1223 Median 2024.846 Variance 1495914 Mode 1252.343 Range 7574 Interquartile Range 1643

Tests for Location: Mu0=0

Test -Statistic- —–p Value——

Student’s t t 41.85147 Pr > |t| <.0001 Sign M 248 Pr >= |M| <.0001 Signed Rank S 61628 Pr >= |S| <.0001

Quantiles (Definition 5)

Quantile Estimate

100% Max 7837.047 99% 6242.199 95% 4425.504 90% 3884.347 75% Q3 3036.301 50% Median 2024.846 25% Q1 1392.983 10% 902.298 5% 649.121 1% 359.403 0% Min 262.776

The UNIVARIATE Procedure Variable: yhat (predicted value)

Extreme Observations

——Lowest—– —–Highest—–

Value Obs Value Obs

262.776 100 6242.20 232 296.707 424 6697.20 194 345.901 375 6736.44 451 353.493 366 7321.02 62 359.403 330 7837.05 94

The UNIVARIATE Procedure Variable: e (residual)

Moments

N 496 Sum Weights 496 Mean 0 Sum Observations 0 Std Deviation 844.185326 Variance 712648.864 Skewness 1.18637008 Kurtosis 6.77888563 Uncorrected SS 352761188 Corrected SS 352761188 Coeff Variation . Std Error Mean 37.9050401

Basic Statistical Measures

Location Variability

Mean 0.0000 Std Deviation 844.18533 Median -69.4956 Variance 712649 Mode 22.7855 Range 9075 Interquartile Range 814.02638

Tests for Location: Mu0=0

Test -Statistic- —–p Value——

Student’s t t 0 Pr > |t| 1.0000 Sign M -18 Pr >= |M| 0.1160 Signed Rank S -4887 Pr >= |S| 0.1261

Quantiles (Definition 5)

Quantile Estimate

100% Max 5037.9871 99% 3315.5848 95% 1367.2257 90% 906.9871 75% Q3 365.3865 50% Median -69.4956 25% Q1 -448.6399 10% -828.8270 5% -1212.3343 1% -1870.9171 0% Min -4037.0471

The UNIVARIATE Procedure Variable: e (residual)

Extreme Observations

——Lowest—– —–Highest—–

Value Obs Value Obs

-4037.05 94 3315.58 118 -2224.40 494 3687.12 125 -1938.20 163 4112.44 124 -1883.80 133 4512.28 80 -1870.92 362 5037.99 85

To draw the horizontal boxplot, we need to use an annotated data set. The code below tells SAS where to draw each of the lines for the two boxplots. These numbers were obtained from the proc univariate immediately above this data step.

data anno_call1;
  length function color $8;
  retain xsys ysys '2' size 1 color 'green';
  function='move'; x=262.776; y=6000; output; * begin left line ; 
  function='draw'; x=1392.983; y=6000; output;  * end left line ; 
  function='poly'; x=1392.983; y=6100; output; * upper left corner of box ; 
  function='polycont'; x=1392.983; y=5900; output; * lower left corner ;
  function='polycont'; x=3036.301; y=5900; output; * lower right corner of box ;
  function='polycont'; x=3036.301; y=6100; output; * upper right corner of box ;
  function='polycont'; x=1392.983; y=6100; output; * back to upper left corner ;
  function='move'; x=2024.846; y=6100; output; * middle line of box ;
  function='draw'; x=2024.846; y=5900; output; 
  function='move'; x=3036.301; y=6000; output; * begin right line ;
  function='draw'; x=6242.199; y=6000; output; * end right line ;
  * to draw the vertical boxplot ;
  function='move'; x=8500; y=1586.42607; output; * begin top line ;
  function='draw'; x=8500; y=365.3865; output; * end top line ;
  function='poly'; x=8400; y=365.3865; output; * upper left corner of box ;
  function='polycont'; x=8600; y=365.3865; output; * upper right corner ;
  function='polycont'; x=8600; y=-448.6399; output; * lower right corner of box ;
  function='polycont'; x=8400; y=-448.6399; output; * lower left corner ;
  function='polycont'; x=8400; y=365.3865; output; * back to upper left ; 
  function='move'; x=8400; y=-69.4956; output; * middle line of box ; 
  function='draw'; x=8600; y=-69.4956; output; 
  function='move'; x=8500; y=-448.6399; output; * begin bottom line ; 
  function='draw'; x=8500; y=-1669.67947; output; * end bottom line ; 
run;
symbol1 color=black interpol=r value=circle height=0.5;
axis1 order=(-4000 to 8000 by 2000);
axis2 order=(0 to 10000 by 2000);
proc gplot data=concordall;
 plot e*yhat=1 / anno=anno_call1 vaxis=axis1 haxis=axis2; 
run;
quit;

Figure 4.3 The interpol=r option is used in the first symbol statement and tells SAS to include the regression line. Interpol can be shortened to i.

page 117 Figure 4.4 Absolute residuals |e| versus Y-hat, with band regression line indicating heteroscedasticity (household water-use regression).

data concordalla;
 set concordall;
 abse=abs(e);
proc means min max data=concordalla;
var yhat;
run;

The MEANS Procedure

Analysis Variable : yhat predicted value

Minimum Maximum —————————- 262.7759103 7837.05 —————————-

data newset;
  set concordalla;
  do i = 1 to 6;
  if  (i-1)*(7837.05-262.776)/6 + 262.776 <= yhat
     < i*(7837.05-262.776)/6 + 262.776 then do;
  a = i; output; end; 
  end; 
run;
proc means median data=newset nway; /*find the median for x and y*/
  class a;
  var yhat abse;
  output out=med median=ymed absemed;
run;

The MEANS Procedure

N a Obs Variable Label Median —————————————————————— 1 148 yhat predicted value 1122.77 abse 273.1849543

2 200 yhat predicted value 2033.12 abse 390.5594506

3 104 yhat predicted value 3367.23 abse 588.5223764

4 30 yhat predicted value 4292.81 abse 1084.30

5 9 yhat predicted value 5535.21 abse 1367.23

6 4 yhat predicted value 7028.73 abse 1721.27 ——————————————————————

proc sort data=med;
by a;
proc sort data=newset;
by a;
run;
data  outset; /* merge it back to the original dataset */
  merge newset med;
  by a;
run;
symbol1 color=black value=circle height=0.5;
symbol2 c=red v=none i=join l=2;
axis1 order=(0 to 6000 by 1000);
axis2 order=(0 to 8000 by 2000);
proc gplot data=outset;
 plot abse*yhat=1 absemed*ymed=2 / overlay vaxis=axis1 haxis=axis2;
run;
quit;

The line option (which can be abbreviated as l) tells SAS which type of line to use. SAS has approximately 50 different line types that can be selected, and each one has a number. To select a different type of line, simply replace the 2 with another line number.

Figure 4.4

Autocorrelation

page 119 Figure 4.5 Time plot of average daily water use by the city of Concord, 1970-1981, using the concord2 data set.

symbol1 color=black interpol=join value=none height=0.5;
axis1 order=(3.5 to 5.5 by 0.5);
axis2 order=(1 to 120 by 20);
proc gplot data=concord2;
 plot H2Ouse*time=1 / href=127 lhref=2;
run;
quit;

The href option tells SAS to put a horizontal reference line at 127. The lhref option tells SAS what kind of line to use. It is similar to the line option that was used above.

Figure 4.5

page 121 Figure 4.6 Correlogram showing autocorrelation of Concord water-use residuals, at monthly lags 0-25.

proc autoreg data=concord2;   
model H2Ouse = temp rain educ / nlag = 26;   
ods  output CorrGraph=concyautoreg;
run;
quit;

The AUTOREG Procedure

Dependent Variable H2Ouse

Ordinary Least Squares Estimates

SSE 17.2802336 DFE 133 MSE 0.12993 Root MSE 0.36045 SBC 124.821864 AIC 113.14194 Regress R-Square 0.3273 Total R-Square 0.3273 Durbin-Watson 0.5349

Standard Approx Variable DF Estimate Error t Value Pr > |t|

Intercept 1 3.8280 0.1006 38.03 <.0001 temp 1 0.0129 0.001698 7.57 <.0001 rain 1 -0.0474 0.0212 -2.23 0.0271 educ 1 -0.2470 0.1135 -2.18 0.0313

Estimates of Autocorrelations

Lag Covariance Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1

0 0.1261 1 0.0921 2 0.0597 3 0.0435 4 0.0580 5 0.0706 6 0.0744 7 0.0582 8 0.0354 9 0.0194 10 0.0302 11 0.0535 12 0.0612 13 0.0430 14 0.0193 15 0.0164 16 0.0272 17 0.0428 18 0.0466 19 0.0343 20 0.0108 21 -0.00238 22 0.00370 23 0.0250 24 0.0329 25 0.0204 26 -0.00063 1.000000 | |********************| 0.730231 | |*************** | 0.473521 | |********* | 0.345115 | |******* | 0.459549 | |********* | 0.559339 | |*********** | 0.589674 | |************ | 0.461684 | |********* | 0.280885 | |****** | 0.153916 | |*** | 0.239722 | |***** | 0.424193 | |******** | 0.485392 | |********** | 0.340738 | |******* | 0.152932 | |*** | 0.129701 | |*** | 0.215724 | |**** | 0.339531 | |******* | 0.369486 | |******* | 0.271671 | |***** | 0.085549 | |** | -0.018880 | | | 0.029327 | |* | 0.198215 | |**** | 0.260869 | |***** | 0.161734 | |*** | -0.004964 | | |

The AUTOREG Procedure

Preliminary MSE 0.0348

Estimates of Autoregressive Parameters

Standard Lag Coefficient Error t Value

1 -0.633558 0.096645 -6.56 2 -0.043799 0.114254 -0.38 3 0.093387 0.113960 0.82 4 -0.335057 0.114273 -2.93 5 0.016375 0.117644 0.14 6 -0.048498 0.117465 -0.41 7 0.025855 0.117467 0.22 8 0.048794 0.117482 0.42 9 0.166974 0.117203 1.42 10 -0.039854 0.118284 -0.34 11 -0.164261 0.118311 -1.39 12 -0.062547 0.118359 -0.53 13 0.079678 0.117840 0.68 14 0.130513 0.117840 1.11 15 -0.160535 0.118359 -1.36 16 0.029807 0.118311 0.25 17 -0.025415 0.118284 -0.21 18 -0.096891 0.117203 -0.83 19 0.017487 0.117482 0.15 20 0.047749 0.117467 0.41 21 0.069170 0.117465 0.59 22 0.169159 0.117644 1.44 23 -0.032654 0.114273 -0.29 24 -0.095382 0.113960 -0.84 25 -0.063571 0.114254 -0.56 26 0.024134 0.096645 0.25

Yule-Walker Estimates

SSE 4.4304032 DFE 107 MSE 0.04141 Root MSE 0.20348 SBC 71.6729358 AIC -15.926492 Regress R-Square 0.6497 Total R-Square 0.8275 Durbin-Watson 2.0353

The AUTOREG Procedure

Standard Approx Variable DF Estimate Error t Value Pr > |t|

Intercept 1 3.7674 0.1455 25.89 <.0001 temp 1 0.0133 0.000971 13.73 <.0001 rain 1 -0.0406 0.009274 -4.37 <.0001 educ 1 -0.2134 0.1642 -1.30 0.1966

axis1 order =(-.2 to 1 by .2) label=(r=0 a=90); 
axis2 order = (0 to 26 by 2); 
symbol1 color=green i=needle v=none width=20; 
title 'Figure 4.6'; 
proc gplot data=concyautoreg;   
format Autocorr 4.2;   
plot Autocorr*Lag=1/ haxis=axis2 vaxis=axis1 hminor=0 vminor=0 vref=.16 lvref=2; 
label Autocorr='Autocorrelation';     
run; 
quit;

The hminor and vminor options instruct SAS regarding tick marks. The hminor=0 option means that no tick marks are to appear on the horizontal axis, and the vminor=0 option means that no tick marks are to appear on the vertical axis. In the axis1 order statement, the label=(r=0 a=90) means that the axis label will be turned 90 degrees. This greatly improves the appearance of the graph.

page 122 Figure 4.7 Time plot of Concord water-use residuals.

proc reg data=concord2;
 model H2Ouse = temp rain educ;
 output out=outx(keep=time e) residual=e;
run;
quit;

The REG Procedure Model: MODEL1 Dependent Variable: H2Ouse

Analysis of Variance

Sum of Mean Source DF Squares Square F Value Pr > F

Model 3 8.40906 2.80302 21.57 <.0001 Error 133 17.28023 0.12993 Corrected Total 136 25.68929

Root MSE 0.36045 R-Square 0.3273 Dependent Mean 4.23496 Adj R-Sq 0.3122 Coeff Var 8.51138

Parameter Estimates

Parameter Standard Variable DF Estimate Error t Value Pr > |t|

Intercept 1 3.82800 0.10064 38.03 <.0001 temp 1 0.01286 0.00170 7.57 <.0001 rain 1 -0.04743 0.02123 -2.23 0.0271 educ 1 -0.24698 0.11348 -2.18 0.0313

symbol1 color=black interpol=join value=none;
axis1 order=(-.8 to .8 by 0.2);
axis2 order=(0 to 140 by 20);
proc gplot data=outx;
 plot e*time=1 / haxis=axis2 vaxis=axis1 vref=0 hminor=1 vminor=0;
run;
quit;

Figure 4.7

page 122 Figure 4.8 Time plots of Concord water-use residuals, showing effects of repeated smoothing by running means of span 3. Note that the first of the four graphs is the same as the graph above.

proc reg data=concord2;
 model H2Ouse = temp rain educ;
 output out=outx(keep=time e) residual=e;
run;
quit;

The REG Procedure Model: MODEL1 Dependent Variable: H2Ouse

Analysis of Variance

Sum of Mean Source DF Squares Square F Value Pr > F

Model 3 8.40906 2.80302 21.57 <.0001 Error 133 17.28023 0.12993 Corrected Total 136 25.68929

Root MSE 0.36045 R-Square 0.3273 Dependent Mean 4.23496 Adj R-Sq 0.3122 Coeff Var 8.51138

Parameter Estimates

Parameter Standard Variable DF Estimate Error t Value Pr > |t|

Intercept 1 3.82800 0.10064 38.03 <.0001 temp 1 0.01286 0.00170 7.57 <.0001 rain 1 -0.04743 0.02123 -2.23 0.0271 educ 1 -0.24698 0.11348 -2.18 0.0313

symbol1 color=black interpol=join value=none;
axis1 order=(-.8 to .8 by 0.2);
axis2 order=(0 to 140 by 20);
proc gplot data=outx;
 plot e*time=1 / haxis=axis2 vaxis=axis1 vref=0 hminor=1 vminor=0;
run;
quit;

proc reg data=concord2;
 model H2Ouse = temp rain educ;
 output out=outx(keep= e) residual=e;
run;
quit;

The REG Procedure Model: MODEL1 Dependent Variable: H2Ouse

Analysis of Variance

Sum of Mean Source DF Squares Square F Value Pr > F

Model 3 8.40906 2.80302 21.57 <.0001 Error 133 17.28023 0.12993 Corrected Total 136 25.68929

Root MSE 0.36045 R-Square 0.3273 Dependent Mean 4.23496 Adj R-Sq 0.3122 Coeff Var 8.51138

Parameter Estimates

Parameter Standard Variable DF Estimate Error t Value Pr > |t|

Intercept 1 3.82800 0.10064 38.03 <.0001 temp 1 0.01286 0.00170 7.57 <.0001 rain 1 -0.04743 0.02123 -2.23 0.0271 educ 1 -0.24698 0.11348 -2.18 0.0313

data outx1;
set outx;
id=_n_;
run;
proc loess data=outx1;
model e=id / direct smooth=0.05;
ods output OutputStatistics=ENSOstats;
run;

The LOESS Procedure

Independent Variable Scaling

Scaling applied: None

Statistic id

Minimum Value 1.00000 Maximum Value 137.00000

The LOESS Procedure Smoothing Parameter: 0.05 Dependent Variable: e

Fit Summary

Fit Method Direct Number of Observations 137 Degree of Local Polynomials 1 Smoothing Parameter 0.05000 Points in Local Neighborhood 6 Residual Sum of Squares 2.98454

symbol1 color=black interpol=join value=none width=2;
proc gplot data=ENSOstats;
 plot  pred*id=1;
run;
quit;

data concord21;
 set outx;
 time=_n_;
 a1=lag(e);
 a2=lag(a1);
 
e1=mean(a2, a1, e);
b1=lag(e1);
b2=lag(b1);
e2=mean(b2, b1, e1);
 
c1=lag(e2);
c2=lag(c1);
e3=mean(c2, c1, e2);
 
d1=lag(e3);
d2=lag(d1);
e4=mean(d2, d1, e3);
 
f1=lag(e4);
f2=lag(f1);
e5=mean(f2, f1, e4);
 
run;
 
goptions reset=all;
filename outfile 'e:https://stats.idre.ucla.edu/wp-content/uploads/2016/02/rwgsas4j.gif'; 
goptions gsfmode=replace gsfname=outfile device=gif373;
 
symbol1 color=black interpol=join value=none;
axis1 order=(-.8 to .8 by 0.2);
axis2 order=(0 to 140 by 20);
proc gplot data=concord21;
 plot e1*time=1 / haxis=axis2 vaxis=axis1 vref=0 hminor=1 vminor=0;
run;
quit;

proc gplot data=concord21;
 plot e2*time=1 / haxis=axis2 vaxis=axis1 vref=0 hminor=1 vminor=0;
run;
quit;

proc gplot data=concord21;
 plot e5*time=1 / haxis=axis2 vaxis=axis1 vref=0 hminor=1 vminor=0;
run;
quit;

4Nonnormality

page 124 Figure 4.9 Four views showing nonnormality of residuals from regression of 1981 household water use on six predictors.

proc reg data=concy;
 model water81 = income water80 educat retired peop81 cpeop;
 output out=out3(keep=case e) residual=e;
run;
quit;

The REG Procedure Model: MODEL1 Dependent Variable: water81

Analysis of Variance

Sum of Mean Source DF Squares Square F Value Pr > F

Model 6 740477522 123412920 171.08 <.0001 Error 489 352761188 721393 Corrected Total 495 1093238710

Root MSE 849.34859 R-Square 0.6773 Dependent Mean 2298.38710 Adj R-Sq 0.6734 Coeff Var 36.95411

Parameter Estimates

Parameter Standard Variable DF Estimate Error t Value Pr > |t|

Intercept 1 242.22043 206.86382 1.17 0.2422 income 1 20.96699 3.46372 6.05 <.0001 water80 1 0.49194 0.02635 18.67 <.0001 educat 1 -41.86552 13.22031 -3.17 0.0016 retired 1 189.18433 95.02142 1.99 0.0470 peop81 1 248.19702 28.72480 8.64 <.0001 cpeop 1 96.45360 80.51903 1.20 0.2315

proc univariate data=out3 noprint;
 var e;
 histogram / noframe normal(color=red) cfill=grey midpoints=-4000 to 5000 by 750;
run;

The UNIVARIATE Procedure Fitted Distribution for e

Parameters for Normal Distribution

Parameter Symbol Estimate

Mean Mu 0 Std Dev Sigma 844.1853

Goodness-of-Fit Tests for Normal Distribution

Test —Statistic—- —–p Value—–

Kolmogorov-Smirnov D 0.09008163 Pr > D <0.010 Cramer-von Mises W-Sq 1.34942807 Pr > W-Sq <0.005 Anderson-Darling A-Sq 8.06505238 Pr > A-Sq <0.005

Quantiles for Normal Distribution

———Quantile——– Percent Observed Estimated

1.0 -1870.9171 -1963.868737 5.0 -1212.3343 -1388.561295 10.0 -828.8270 -1081.867026 25.0 -448.6399 -569.394349 50.0 -69.4956 -0.000000 75.0 365.3865 569.394349 90.0 906.9871 1081.867026 95.0 1367.2257 1388.561295 99.0 3315.5848 1963.868737

Unlike Stata that uses the bin option to determine the size of the bins of the histogram SAS asks for the midpoints of the bins. That is the purpose of the midpoints option shown above.

Figure 4.9 histogram

data concz;
 set out3;
cvar=2;
proc boxplot data=concz; 
 plot e*cvar / boxstyle=schematic 
 cboxes=green idsymbol=circle noframe boxwidth=15 vaxis=-4100 to 5100 by 2300;
run;
quit;

Figure 4.9 boxplot

Below is the code for a symmetry plot – SAS does not have a symmetry plot feature, so you have to do it by hand.

proc reg data=concy;
 model water81 = income water80 educat retired peop81 cpeop;
 output out=outa (keep=case water81 e) residual=e;
run;
quit;

The REG Procedure Model: MODEL1 Dependent Variable: water81

Analysis of Variance

Sum of Mean Source DF Squares Square F Value Pr > F

Model 6 740477522 123412920 171.08 <.0001 Error 489 352761188 721393 Corrected Total 495 1093238710

Root MSE 849.34859 R-Square 0.6773 Dependent Mean 2298.38710 Adj R-Sq 0.6734 Coeff Var 36.95411

Parameter Estimates

Parameter Standard Variable DF Estimate Error t Value Pr > |t|

Intercept 1 242.22043 206.86382 1.17 0.2422 income 1 20.96699 3.46372 6.05 <.0001 water80 1 0.49194 0.02635 18.67 <.0001 educat 1 -41.86552 13.22031 -3.17 0.0016 retired 1 189.18433 95.02142 1.99 0.0470 peop81 1 248.19702 28.72480 8.64 <.0001 cpeop 1 96.45360 80.51903 1.20 0.2315

proc univariate data=outa noprint; 
var e; 
output out = stats1 median = med81 n = n81 ;
data stats2; 
set stats1; evodd81 = mod(n81,2); 
/* even/odd flag */
call symput('evodd81',evodd81); 
call symput('med81',med81); 
call symput('n81',n81);
proc sort data=outa 
out=sorted81(keep=e); 
by e;
data above81(drop=b) below81(drop=a); 
set sorted81; i = _n_; 
/* n is even */
if evodd81 = 0 then do; 
if i <= &n81 / 2 then do; 
b = &med81 - e; output below81; 
end; 
else do; 
a = e - &med81; 
output above81; 
end; 
end;
/* n is odd */
else do; 
if i <= (&n81 + 1)/2 then do; 
b = &med81 - e; output below81; 
end; 
if i >= (&n81 + 1)/2 then do; 
a = e - &med81; output above81; 
end; 
end;
proc sort data=above81; 
by descending i; 
data ab; 
merge above81 below81; 
/* n is even */
if &evodd81 = 0 then do; 
if i = 1 then x = min(a,b); 
else if i = &n81 / 2 then x = max(a,b); y=x; 
end;
/* n is odd */
else do; 
if i = 1 then x = min(a,b); 
else if i = (&n81 + 1)/2 then x = max(a,b); 
y=x; 
end; 
axis1 order=(0 to 6000 by 2000) label=(angle=90 height=.75 'Distance above median'); 
axis2 order=(0,2000,4000) label=('Distance below median'); 
symbol1 interpol=none value=circle color=black height=.5; symbol2 interpol=join value=none color=red; 
proc gplot data=ab; plot a*b y*x / 
vaxis=axis1 vminor=0
haxis=axis2 hminor=0
noframe overlay; 
run;
quit;

Figure 4.9 symmetry plot

proc univariate data=outa noprint;
  var e;
  probplot / normal(mu=est sigma=est color=red) noframe;
run;
quit;

Figure 4.9 quantile-normal plot

Influence Analysis

page 127 Table 4.3 Summary statistics for DFBETAS of coefficients in household water-use regression of Equation [4.3].

proc reg data=concy;
  model water81 = income water80 educat retired peop81 cpeop /influence;
  ods output OutputStatistics=cydfbetas;
run;
quit;
proc means data=cydfbetas;
  var  DFB_income DFB_water80 DFB_educat DFB_retired DFB_peop81 DFB_cpeop;
run;

The REG Procedure Model: MODEL1 Dependent Variable: water81

Analysis of Variance

Sum of Mean Source DF Squares Square F Value Pr > F

Model 6 740477522 123412920 171.08 <.0001 Error 489 352761188 721393 Corrected Total 495 1093238710

Root MSE 849.34859 R-Square 0.6773 Dependent Mean 2298.38710 Adj R-Sq 0.6734 Coeff Var 36.95411

Parameter Estimates

Parameter Standard Variable DF Estimate Error t Value Pr > |t|

Intercept 1 242.22043 206.86382 1.17 0.2422 income 1 20.96699 3.46372 6.05 <.0001 water80 1 0.49194 0.02635 18.67 <.0001 educat 1 -41.86552 13.22031 -3.17 0.0016 retired 1 189.18433 95.02142 1.99 0.0470 peop81 1 248.19702 28.72480 8.64 <.0001 cpeop 1 96.45360 80.51903 1.20 0.2315

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

Hat Diag Cov Obs Residual RStudent H Ratio DFFITS

1 -388.8667 -0.4590 0.0066 1.0180 -0.0373 2 -1667 -1.9899 0.0215 0.9797 -0.2948 3 343.6106 0.4076 0.0165 1.0290 0.0528 4 -779.8772 -0.9262 0.0174 1.0198 -0.1234 5 1335 1.5897 0.0193 0.9977 0.2232 6 -154.2695 -0.1824 0.0108 1.0250 -0.0191 7 764.1568 0.9038 0.0093 1.0121 0.0878 8 488.5489 0.5799 0.0174 1.0274 0.0771 9 318.2554 0.3759 0.0083 1.0208 0.0343 10 439.8363 0.5205 0.0117 1.0225 0.0567 11 1078 1.2744 0.0073 0.9984 0.1093 12 800.0813 0.9481 0.0130 1.0146 0.1087 13 -367.3797 -0.4335 0.0059 1.0177 -0.0333 14 1052 1.2594 0.0316 1.0240 0.2276 15 -523.4685 -0.6250 0.0289 1.0388 -0.1078 16 -143.1716 -0.1690 0.0075 1.0217 -0.0147 17 -165.9163 -0.1960 0.0091 1.0232 -0.0188 18 -738.2989 -0.8745 0.0124 1.0160 -0.0981 19 557.5599 0.6607 0.0140 1.0224 0.0787 20 -55.1810 -0.0652 0.0087 1.0233 -0.0061 21 -694.7070 -0.8207 0.0074 1.0121 -0.0707 22 423.7686 0.4996 0.0040 1.0149 0.0317 23 -243.7578 -0.2875 0.0054 1.0187 -0.0212 24 -450.8112 -0.5349 0.0167 1.0275 -0.0698 25 2390 2.8678 0.0232 0.9238 0.4415 26 -431.9259 -0.5101 0.0077 1.0185 -0.0451 27 500.0761 0.5906 0.0075 1.0170 0.0514 28 348.6592 0.4125 0.0115 1.0237 0.0445 29 -782.9470 -0.9236 0.0041 1.0062 -0.0592 30 -642.0676 -0.7609 0.0138 1.0201 -0.0899 31 -1441 -1.7189 0.0222 0.9945 -0.2590 32 939.7894 1.1136 0.0122 1.0089 0.1240 33 11.9625 0.0142 0.0132 1.0280 0.0016 34 668.9890 0.7957 0.0210 1.0268 0.1164 35 199.3090 0.2351 0.0053 1.0190 0.0171 36 1379 1.6419 0.0187 0.9946 0.2264 37 99.2552 0.1176 0.0139 1.0285 0.0140 38 -1224 -1.4555 0.0180 1.0021 -0.1968 39 196.4742 0.2324 0.0110 1.0249 0.0245 40 -427.0224 -0.5044 0.0080 1.0188 -0.0452 41 -153.3359 -0.1817 0.0153 1.0297 -0.0226 42 22.7855 0.0269 0.0095 1.0241 0.0026 43 527.2992 0.6253 0.0155 1.0246 0.0785 44 327.0076 0.3861 0.0075 1.0199 0.0336 45 1077 1.2745 0.0089 1.0000 0.1207

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

————————————-DFBETAS————————————- Obs Intercept income water80 educat retired peop81 cpeop

1 0.0146 -0.0077 -0.0067 -0.0206 0.0073 0.0102 -0.0022 2 0.1725 -0.1941 0.0024 -0.0976 -0.0588 -0.0455 0.0183 3 -0.0142 -0.0051 -0.0021 0.0116 0.0006 0.0242 0.0349 4 -0.0333 -0.0393 0.0115 0.0409 -0.0504 0.0192 0.0792 5 -0.0811 0.1069 0.0693 0.0882 -0.0085 -0.1138 0.0158 6 -0.0033 0.0042 0.0120 0.0014 0.0048 -0.0138 0.0021 7 -0.0233 0.0206 0.0260 0.0026 0.0742 0.0037 0.0061 8 -0.0508 -0.0077 0.0076 0.0580 0.0433 -0.0041 0.0063 9 0.0203 -0.0124 -0.0128 -0.0129 -0.0152 0.0134 -0.0011 10 -0.0222 -0.0023 0.0014 0.0420 -0.0150 -0.0200 0.0044 11 0.0777 -0.0487 0.0319 -0.0464 -0.0585 -0.0230 0.0113 12 -0.0733 -0.0164 -0.0236 0.0825 -0.0034 0.0523 -0.0057 13 0.0125 -0.0083 0.0044 -0.0078 0.0007 -0.0177 0.0027 14 -0.0668 -0.0782 -0.0496 0.0581 -0.0074 0.1685 -0.1357 15 0.0046 -0.0127 0.0213 0.0230 -0.0117 -0.0749 -0.0453 16 -0.0050 0.0055 0.0081 0.0010 0.0063 -0.0072 0.0008 17 -0.0057 -0.0054 0.0015 0.0049 -0.0105 0.0061 -0.0018 18 -0.0654 -0.0579 0.0366 0.0702 0.0244 0.0040 0.0049 19 -0.0361 0.0041 0.0438 0.0226 0.0572 -0.0073 0.0084 20 -0.0021 0.0013 0.0011 0.0015 -0.0031 -0.0005 -0.0004 21 -0.0332 -0.0111 0.0456 0.0279 0.0230 -0.0311 0.0068 22 0.0117 0.0087 -0.0091 -0.0117 -0.0103 0.0095 -0.0018 23 -0.0025 0.0004 -0.0016 -0.0066 0.0106 0.0117 -0.0024 24 0.0308 -0.0245 0.0318 -0.0305 -0.0416 -0.0093 0.0010 25 -0.0747 -0.1338 0.0144 -0.0103 0.0201 0.3549 -0.0364 26 -0.0031 -0.0064 0.0141 0.0025 -0.0308 -0.0038 -0.0019 27 0.0357 0.0223 -0.0096 -0.0263 -0.0226 -0.0222 0.0019 28 -0.0008 -0.0019 -0.0077 0.0221 -0.0191 -0.0223 0.0039 29 -0.0236 0.0190 0.0184 -0.0025 0.0360 -0.0009 -0.0020 30 -0.0551 0.0080 0.0212 0.0517 -0.0323 -0.0086 -0.0036 31 0.0389 -0.0404 0.1013 0.0111 -0.1391 -0.1440 0.1759 32 0.1150 -0.0297 -0.0184 -0.0737 -0.0698 -0.0290 0.0073 33 0.0010 -0.0002 -0.0002 -0.0010 0.0006 0.0001 0.0001 34 -0.0199 -0.0249 -0.0201 0.0413 0.0452 0.0029 0.0798 35 0.0063 -0.0084 -0.0054 0.0018 -0.0102 0.0012 0.0006 36 -0.0007 0.1695 -0.0287 -0.0338 0.1275 -0.0656 0.0068 37 0.0022 0.0034 -0.0038 -0.0031 -0.0023 0.0041 -0.0117 38 0.0922 -0.1087 -0.0512 -0.0782 -0.0092 0.0623 -0.0066 39 -0.0123 -0.0065 -0.0021 0.0207 -0.0060 -0.0006 0.0010 40 -0.0100 0.0057 0.0112 0.0058 -0.0263 -0.0046 -0.0029 41 0.0111 0.0086 0.0083 -0.0178 0.0044 -0.0081 0.0006 42 0.0009 -0.0007 -0.0004 -0.0002 0.0010 -0.0005 0.0003 43 0.0159 -0.0154 0.0015 -0.0058 0.0253 -0.0097 -0.0499 44 0.0071 -0.0055 -0.0026 -0.0045 0.0205 0.0008 0.0031 45 0.0173 -0.0143 0.0521 -0.0195 0.0753 -0.0277 0.0178

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

Hat Diag Cov Obs Residual RStudent H Ratio DFFITS

46 22.7855 0.0269 0.0095 1.0241 0.0026 47 -914.4225 -1.0854 0.0157 1.0134 -0.1371 48 395.6209 0.4684 0.0126 1.0241 0.0529 49 517.8713 0.6131 0.0123 1.0215 0.0684 50 231.4842 0.2732 0.0067 1.0202 0.0224 51 -1045 -1.2369 0.0104 1.0029 -0.1267 52 -372.9229 -0.4405 0.0080 1.0198 -0.0397 53 -586.0330 -0.6912 0.0046 1.0122 -0.0470 54 -321.0289 -0.3789 0.0067 1.0191 -0.0310 55 0.5991 0.000707 0.0067 1.0213 0.0001 56 -349.1211 -0.4127 0.0099 1.0221 -0.0413 57 77.2007 0.0912 0.0082 1.0227 0.0083 58 -313.8129 -0.3722 0.0164 1.0293 -0.0480 59 -786.5014 -0.9309 0.0108 1.0129 -0.0973 60 157.7162 0.1862 0.0079 1.0220 0.0166 61 361.7777 0.4286 0.0142 1.0263 0.0514 62 2079 2.5265 0.0510 0.9760 0.5859 63 -721.8686 -0.8556 0.0138 1.0179 -0.1013 64 919.1880 1.0897 0.0132 1.0107 0.1262 65 -968.1694 -1.1786 0.0638 1.0622 -0.3077 66 103.3428 0.1221 0.0088 1.0232 0.0115 67 -883.5449 -1.0443 0.0076 1.0064 -0.0914 68 2003 2.4177 0.0391 0.9713 0.4875 69 -1074 -1.2761 0.0170 1.0082 -0.1679 70 1529 1.8436 0.0424 1.0091 0.3878 71 635.0666 0.7506 0.0086 1.0150 0.0699 72 321.9857 0.3818 0.0156 1.0284 0.0481 73 955.8874 1.1364 0.0187 1.0148 0.1568 74 149.2690 0.1762 0.0074 1.0215 0.0152 75 65.9999 0.0781 0.0130 1.0277 0.0090 76 -331.3901 -0.3914 0.0080 1.0204 -0.0352 77 -59.5560 -0.0702 0.0053 1.0198 -0.0051 78 357.6185 0.4245 0.0178 1.0302 0.0572 79 2565 3.0761 0.0197 0.9046 0.4357 80 4512 5.4938 0.0091 0.6726 0.5256 81 409.9462 0.4842 0.0079 1.0191 0.0432 82 1506 1.7846 0.0079 0.9770 0.1596 83 -78.7396 -0.0936 0.0220 1.0372 -0.0141 84 -456.0644 -0.5384 0.0066 1.0170 -0.0440 85 5038 6.1889 0.0114 0.6046 0.6632 86 -494.4666 -0.5851 0.0112 1.0209 -0.0623 87 -1216 -1.4516 0.0253 1.0099 -0.2340 88 -113.8159 -0.1348 0.0143 1.0289 -0.0162 89 237.8361 0.2805 0.0051 1.0185 0.0200 90 952.0715 1.1270 0.0101 1.0063 0.1140

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

————————————-DFBETAS————————————- Obs Intercept income water80 educat retired peop81 cpeop

46 0.0009 -0.0007 -0.0004 -0.0002 0.0010 -0.0005 0.0003 47 0.0894 -0.0666 0.0235 -0.0669 -0.0192 -0.0427 0.0108 48 -0.0114 0.0330 -0.0062 -0.0047 0.0423 0.0075 -0.0006 49 0.0490 -0.0388 -0.0125 -0.0159 -0.0418 -0.0106 0.0050 50 -0.0107 -0.0015 -0.0066 0.0149 -0.0043 0.0073 -0.0008 51 -0.0280 -0.0774 0.0405 0.0631 0.0025 -0.0540 0.0147 52 -0.0128 0.0002 -0.0043 0.0136 -0.0247 0.0038 -0.0041 53 -0.0347 0.0055 0.0101 0.0205 0.0275 0.0029 -0.0014 54 -0.0139 -0.0120 0.0132 0.0050 0.0141 0.0103 -0.0005 55 0.0000 -0.0000 -0.0000 0.0000 -0.0000 -0.0000 0.0000 56 -0.0279 0.0056 0.0238 0.0106 0.0234 0.0033 -0.0003 57 0.0003 0.0016 0.0001 -0.0020 0.0067 0.0017 0.0003 58 0.0223 0.0084 0.0265 -0.0340 0.0077 -0.0197 0.0030 59 -0.0073 -0.0260 0.0481 0.0207 -0.0652 -0.0393 0.0038 60 -0.0028 -0.0024 -0.0011 0.0103 -0.0068 -0.0061 0.0014 61 -0.0253 -0.0213 0.0067 0.0237 0.0329 0.0214 0.0022 62 -0.1215 -0.1304 0.2451 -0.0547 0.0885 0.3393 -0.0218 63 0.0572 -0.0441 0.0367 -0.0563 -0.0019 -0.0218 0.0071 64 -0.0242 -0.0808 -0.0312 0.0838 -0.0490 0.0166 0.0046 65 0.0596 -0.2482 0.0490 0.0616 -0.1752 -0.0553 -0.0887 66 -0.0043 -0.0011 0.0012 0.0051 0.0080 -0.0008 0.0012 67 -0.0070 0.0180 0.0167 -0.0043 -0.0560 -0.0075 -0.0072 68 -0.0978 0.1264 0.2491 -0.0952 0.2785 0.0635 -0.2118 69 0.0093 -0.1104 0.0850 0.0155 -0.1000 -0.0167 0.0067 70 0.0440 -0.1120 0.0249 0.0007 -0.0493 0.0409 0.3507 71 0.0137 -0.0277 0.0072 -0.0039 0.0367 -0.0014 0.0085 72 0.0141 0.0370 -0.0273 -0.0176 -0.0061 0.0017 -0.0042 73 0.0496 -0.0694 0.0108 0.0161 -0.0647 -0.0490 0.1201 74 0.0111 0.0038 -0.0060 -0.0067 -0.0079 -0.0045 0.0003 75 0.0061 -0.0045 -0.0005 -0.0012 -0.0057 -0.0040 0.0011 76 -0.0250 0.0170 0.0015 0.0075 0.0230 0.0113 -0.0036 77 -0.0019 0.0009 0.0030 -0.0001 0.0028 -0.0007 0.0001 78 0.0308 -0.0123 -0.0101 -0.0099 -0.0290 -0.0157 -0.0355 79 0.0135 0.0212 0.1790 -0.1612 0.0361 0.1896 -0.0149 80 -0.0907 0.3825 -0.2014 0.0170 -0.0093 0.1030 -0.0475 81 0.0226 0.0290 -0.0089 -0.0249 -0.0107 -0.0071 -0.0010 82 0.0665 -0.1002 0.0208 0.0216 -0.0993 -0.0605 0.0216 83 0.0004 -0.0094 0.0047 -0.0020 0.0021 0.0054 0.0000 84 -0.0142 -0.0151 0.0286 0.0133 0.0116 -0.0184 0.0047 85 0.3854 0.3939 -0.2980 -0.3158 -0.2167 -0.1655 -0.0142 86 0.0417 0.0014 -0.0196 -0.0459 0.0023 0.0012 -0.0027 87 0.0669 -0.0073 -0.1522 -0.0633 0.0145 0.0775 0.1111 88 -0.0099 -0.0090 0.0044 0.0072 0.0058 0.0082 -0.0005 89 0.0101 0.0023 -0.0043 -0.0019 -0.0116 -0.0091 0.0014 90 0.0971 -0.0229 0.0265 -0.0792 -0.0519 -0.0234 0.0085

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

Hat Diag Cov Obs Residual RStudent H Ratio DFFITS

91 267.5371 0.3157 0.0063 1.0194 0.0252 92 -1367 -1.6233 0.0135 0.9903 -0.1901 93 58.2736 0.0688 0.0084 1.0230 0.0064 94 -4037 -5.0846 0.0817 0.7697 -1.5170 95 611.3653 0.7241 0.0127 1.0198 0.0822 96 99.2229 0.1177 0.0166 1.0313 0.0153 97 -1038 -1.2346 0.0187 1.0115 -0.1706 98 -390.0230 -0.4607 0.0079 1.0194 -0.0412 99 62.4404 0.0751 0.0442 1.0613 0.0162 100 337.2241 0.4006 0.0194 1.0321 0.0563 101 2178 2.5944 0.0117 0.9325 0.2818 102 71.1612 0.0840 0.0082 1.0227 0.0076 103 -1448 -1.7310 0.0263 0.9982 -0.2846 104 197.6948 0.2336 0.0093 1.0232 0.0227 105 -694.4760 -0.8216 0.0101 1.0149 -0.0831 106 63.2446 0.0753 0.0253 1.0407 0.0121 107 -101.5297 -0.1201 0.0121 1.0267 -0.0133 108 1367 1.6647 0.0615 1.0389 0.4262 109 134.0003 0.1581 0.0067 1.0209 0.0130 110 509.3545 0.6036 0.0142 1.0237 0.0725 111 -176.0944 -0.2077 0.0058 1.0197 -0.0159 112 -64.8879 -0.0772 0.0218 1.0369 -0.0115 113 251.3355 0.2971 0.0099 1.0233 0.0297 114 -295.3202 -0.3504 0.0173 1.0305 -0.0466 115 -767.2320 -0.9110 0.0171 1.0198 -0.1200 116 150.6509 0.1787 0.0172 1.0317 0.0236 117 -297.5814 -0.3510 0.0054 1.0181 -0.0258 118 3316 4.0942 0.0616 0.8534 1.0491 119 111.3602 0.1315 0.0080 1.0224 0.0118 120 490.2967 0.5808 0.0134 1.0233 0.0678 121 205.7678 0.2431 0.0091 1.0229 0.0233 122 582.5822 0.6898 0.0123 1.0201 0.0771 123 -295.6879 -0.3495 0.0096 1.0225 -0.0345 124 4112 5.0286 0.0268 0.7319 0.8348 125 3687 4.6465 0.0904 0.8237 1.4646 126 -252.3430 -0.2980 0.0079 1.0212 -0.0265 127 43.9022 0.0518 0.0060 1.0205 0.0040 128 -1156 -1.3830 0.0301 1.0177 -0.2436 129 -617.4949 -0.7295 0.0076 1.0145 -0.0639 130 149.0392 0.1764 0.0126 1.0269 0.0199 131 393.4716 0.4657 0.0122 1.0238 0.0518 132 171.7592 0.2025 0.0042 1.0181 0.0132 133 -1884 -2.2430 0.0142 0.9577 -0.2689 134 -223.7984 -0.2642 0.0076 1.0211 -0.0231 135 1551 1.8432 0.0131 0.9792 0.2124

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

————————————-DFBETAS————————————- Obs Intercept income water80 educat retired peop81 cpeop

91 0.0039 0.0005 -0.0098 0.0077 -0.0127 -0.0074 0.0011 92 0.0337 0.0513 -0.1129 -0.0026 0.0013 -0.0603 -0.0046 93 0.0021 0.0003 -0.0006 -0.0012 0.0033 -0.0018 0.0007 94 0.5610 0.0630 -1.3879 -0.3601 -0.1538 0.4554 -0.1647 95 -0.0588 -0.0184 0.0136 0.0630 -0.0008 0.0256 0.0001 96 -0.0045 -0.0006 0.0047 0.0026 -0.0004 0.0038 -0.0108 97 0.0491 -0.1034 0.0846 -0.0011 -0.0243 -0.1035 0.0264 98 -0.0070 0.0287 0.0088 -0.0075 0.0182 -0.0157 -0.0003 99 -0.0018 0.0035 -0.0050 0.0009 -0.0009 0.0045 -0.0151 100 -0.0096 -0.0208 -0.0119 0.0392 -0.0223 -0.0161 0.0043 101 -0.0979 0.0539 -0.1311 0.0520 0.0125 0.2238 -0.0404 102 -0.0018 0.0014 -0.0015 0.0018 0.0056 0.0002 0.0004 103 0.0968 0.1028 -0.1896 -0.1403 -0.1002 0.1248 -0.0517 104 -0.0084 -0.0044 0.0048 0.0104 0.0150 -0.0024 0.0028 105 -0.0628 0.0126 0.0142 0.0227 0.0519 0.0438 -0.0081 106 -0.0037 0.0089 -0.0008 0.0032 0.0002 -0.0041 0.0000 107 0.0095 -0.0001 0.0020 -0.0097 -0.0003 -0.0057 0.0007 108 -0.1422 -0.0402 -0.0009 -0.0126 0.2316 0.3556 -0.0373 109 0.0031 0.0095 -0.0013 -0.0038 -0.0026 -0.0031 -0.0001 110 0.0482 0.0043 0.0090 -0.0461 0.0250 -0.0234 0.0080 111 -0.0103 -0.0022 0.0031 0.0103 0.0056 -0.0038 0.0006 112 -0.0017 -0.0023 0.0005 0.0041 -0.0063 -0.0027 -0.0071 113 0.0129 -0.0081 0.0029 -0.0108 0.0139 -0.0011 0.0032 114 0.0300 0.0048 0.0017 -0.0355 -0.0254 -0.0006 -0.0030 115 0.0583 -0.0670 0.0069 -0.0157 -0.0976 -0.0353 0.0041 116 -0.0155 0.0011 -0.0010 0.0170 0.0139 -0.0003 0.0013 117 -0.0164 -0.0029 -0.0033 0.0079 0.0144 0.0156 -0.0029 118 -0.2691 0.9804 -0.1809 -0.0870 0.2371 0.0765 -0.0931 119 0.0074 0.0039 0.0036 -0.0059 -0.0047 -0.0075 0.0012 120 -0.0345 -0.0221 0.0044 0.0464 0.0363 -0.0000 0.0066 121 -0.0088 0.0049 0.0003 0.0081 0.0177 -0.0019 0.0018 122 -0.0277 0.0005 -0.0175 0.0556 -0.0210 -0.0177 0.0031 123 -0.0157 -0.0013 0.0081 0.0107 -0.0151 0.0067 -0.0030 124 -0.2240 0.1597 0.6845 0.0277 0.0880 -0.1629 0.0605 125 -0.1195 1.3404 0.2510 -0.3333 0.2546 -0.4263 -0.0218 126 -0.0190 -0.0067 0.0120 0.0114 0.0134 0.0069 -0.0003 127 -0.0014 -0.0012 0.0002 0.0016 -0.0006 0.0022 -0.0001 128 0.1349 -0.1338 -0.0612 -0.0878 -0.1492 0.0586 -0.0125 129 -0.0320 0.0156 -0.0416 0.0216 0.0260 0.0267 -0.0089 130 0.0044 0.0119 -0.0102 -0.0090 -0.0006 0.0097 -0.0027 131 -0.0089 -0.0224 -0.0014 0.0258 0.0203 -0.0090 0.0067 132 -0.0004 0.0027 -0.0045 0.0041 -0.0052 -0.0008 0.0000 133 0.1805 0.1032 -0.0508 -0.2097 0.0137 -0.0835 -0.0038 134 -0.0050 0.0036 0.0026 0.0031 -0.0140 -0.0009 -0.0020 135 0.0399 -0.1341 0.1030 -0.0236 -0.0525 0.0463 0.0130

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

Hat Diag Cov Obs Residual RStudent H Ratio DFFITS

136 389.9307 0.4617 0.0127 1.0244 0.0524 137 -69.2229 -0.0818 0.0090 1.0235 -0.0078 138 90.4051 0.1069 0.0105 1.0251 0.0110 139 -246.9667 -0.2922 0.0118 1.0253 -0.0320 140 1841 2.2223 0.0405 0.9853 0.4568 141 -484.4968 -0.5721 0.0071 1.0169 -0.0485 142 -152.5721 -0.1811 0.0177 1.0323 -0.0243 143 592.5429 0.7020 0.0133 1.0208 0.0814 144 -525.5644 -0.6202 0.0058 1.0148 -0.0475 145 -283.5739 -0.3345 0.0057 1.0186 -0.0254 146 -500.6267 -0.5909 0.0064 1.0159 -0.0474 147 894.3988 1.0676 0.0268 1.0254 0.1770 148 163.7760 0.1932 0.0061 1.0201 0.0151 149 330.9084 0.3925 0.0166 1.0293 0.0511 150 -342.1771 -0.4252 0.1038 1.1289 -0.1447 151 413.0855 0.4871 0.0047 1.0158 0.0336 152 -304.7599 -0.3600 0.0085 1.0212 -0.0332 153 -398.0820 -0.4699 0.0066 1.0179 -0.0382 154 502.9212 0.5955 0.0125 1.0221 0.0671 155 692.6423 0.8293 0.0336 1.0394 0.1546 156 -837.2812 -0.9931 0.0147 1.0152 -0.1215 157 -767.9189 -0.9070 0.0067 1.0093 -0.0744 158 -652.0787 -0.7718 0.0113 1.0173 -0.0824 159 -245.9645 -0.2902 0.0062 1.0195 -0.0229 160 -78.3371 -0.0932 0.0221 1.0372 -0.0140 161 -96.6999 -0.1142 0.0073 1.0217 -0.0098 162 -341.7275 -0.4039 0.0092 1.0215 -0.0390 163 -1938 -2.3278 0.0303 0.9683 -0.4116 164 -48.9875 -0.0579 0.0094 1.0240 -0.0056 165 -18.0317 -0.0213 0.0113 1.0261 -0.0023 166 -314.0228 -0.3723 0.0153 1.0282 -0.0464 167 207.9017 0.2471 0.0206 1.0349 0.0358 168 -413.1968 -0.4888 0.0111 1.0223 -0.0518 169 -520.7958 -0.6140 0.0040 1.0130 -0.0387 170 1478 1.7585 0.0164 0.9867 0.2269 171 -120.6418 -0.1428 0.0131 1.0276 -0.0165 172 -627.5333 -0.7447 0.0167 1.0235 -0.0969 173 -315.6008 -0.3756 0.0229 1.0361 -0.0575 174 173.5915 0.2051 0.0094 1.0234 0.0200 175 -1300 -1.5414 0.0109 0.9913 -0.1617 176 27.8590 0.0329 0.0057 1.0202 0.0025 177 -881.0514 -1.0415 0.0078 1.0066 -0.0921 178 154.6453 0.1830 0.0115 1.0258 0.0198 179 -557.1758 -0.6596 0.0119 1.0203 -0.0723 180 -104.6759 -0.1244 0.0206 1.0355 -0.0180

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

————————————-DFBETAS————————————- Obs Intercept income water80 educat retired peop81 cpeop

136 0.0148 -0.0025 -0.0101 -0.0012 -0.0214 -0.0074 -0.0407 137 -0.0014 0.0024 -0.0012 -0.0005 -0.0035 0.0026 -0.0013 138 0.0066 0.0066 -0.0041 -0.0055 -0.0037 -0.0033 -0.0001 139 -0.0022 -0.0234 0.0081 0.0003 0.0056 0.0115 0.0001 140 -0.0213 0.3854 0.0812 -0.1340 0.2470 -0.1182 0.0078 141 0.0072 -0.0191 0.0308 -0.0090 0.0076 -0.0193 0.0051 142 0.0160 -0.0046 0.0006 -0.0160 -0.0151 0.0011 -0.0012 143 0.0094 0.0295 0.0073 -0.0137 -0.0138 -0.0101 -0.0635 144 -0.0014 0.0064 0.0296 -0.0095 0.0165 -0.0239 0.0036 145 -0.0035 0.0167 -0.0069 -0.0033 0.0107 -0.0041 -0.0017 146 0.0100 -0.0300 0.0125 -0.0048 0.0029 -0.0086 0.0033 147 -0.0060 -0.0684 0.1412 0.0260 0.0530 -0.0883 0.0351 148 0.0117 -0.0012 0.0014 -0.0061 -0.0092 -0.0079 0.0017 149 -0.0016 0.0079 0.0063 -0.0095 0.0295 0.0084 -0.0347 150 0.0297 0.0249 0.0071 -0.0186 0.0012 -0.0634 0.1296 151 0.0183 -0.0170 -0.0007 -0.0038 -0.0210 -0.0027 0.0026 152 -0.0224 -0.0149 0.0126 0.0161 0.0142 0.0105 -0.0002 153 -0.0073 0.0185 0.0166 -0.0047 0.0166 -0.0178 0.0013 154 -0.0313 -0.0297 0.0007 0.0569 -0.0182 -0.0021 0.0041 155 0.0187 -0.0550 0.1400 0.0050 -0.0346 -0.0906 0.0276 156 -0.0098 -0.0091 -0.0071 0.0063 -0.0520 0.0238 0.0804 157 -0.0211 0.0223 -0.0097 0.0231 0.0186 -0.0347 0.0013 158 -0.0025 -0.0495 0.0218 0.0165 -0.0572 0.0013 -0.0007 159 -0.0148 -0.0012 0.0092 0.0055 0.0135 0.0069 -0.0009 160 0.0027 -0.0084 -0.0006 0.0005 -0.0018 -0.0008 -0.0080 161 -0.0068 -0.0040 0.0004 0.0051 0.0043 0.0049 -0.0006 162 -0.0133 0.0052 0.0097 0.0045 -0.0166 0.0063 -0.0038 163 -0.0078 0.2086 -0.1196 0.0155 0.0276 -0.1679 -0.2179 164 -0.0019 0.0013 0.0011 0.0005 -0.0023 0.0009 -0.0006 165 0.0011 -0.0004 0.0008 -0.0016 0.0004 -0.0000 0.0000 166 -0.0164 -0.0158 0.0145 0.0115 0.0141 0.0061 0.0347 167 -0.0203 -0.0124 -0.0055 0.0282 0.0151 0.0042 0.0021 168 0.0254 0.0020 0.0154 -0.0404 0.0107 -0.0020 -0.0001 169 0.0091 -0.0039 0.0097 -0.0136 0.0100 -0.0123 0.0015 170 -0.0503 -0.0496 0.1422 0.0775 0.1020 -0.1122 0.0426 171 0.0056 -0.0004 0.0054 -0.0115 0.0045 0.0029 -0.0004 172 0.0182 -0.0415 0.0149 -0.0054 -0.0055 -0.0211 -0.0624 173 -0.0137 -0.0377 0.0033 0.0190 0.0029 0.0141 -0.0341 174 0.0067 -0.0055 -0.0025 -0.0015 0.0079 -0.0039 0.0024 175 -0.0881 -0.0025 0.0200 0.0902 -0.0765 -0.0030 -0.0094 176 0.0012 -0.0012 0.0001 -0.0007 -0.0012 0.0006 0.0001 177 -0.0196 -0.0090 0.0239 0.0187 -0.0598 -0.0060 -0.0047 178 0.0013 0.0144 -0.0039 -0.0002 -0.0034 -0.0077 0.0001 179 -0.0384 -0.0509 0.0096 0.0378 0.0183 0.0301 -0.0009 180 -0.0095 -0.0010 0.0008 0.0095 -0.0048 0.0022 0.0103

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

Hat Diag Cov Obs Residual RStudent H Ratio DFFITS

181 -654.2538 -0.7738 0.0099 1.0158 -0.0775 182 -69.7684 -0.0824 0.0075 1.0220 -0.0072 183 -337.9932 -0.4007 0.0156 1.0282 -0.0505 184 -96.2014 -0.1135 0.0068 1.0212 -0.0094 185 -68.2045 -0.0806 0.0103 1.0249 -0.0082 186 -211.9686 -0.2506 0.0099 1.0237 -0.0251 187 -615.5789 -0.7291 0.0128 1.0198 -0.0832 188 311.9113 0.3701 0.0172 1.0301 0.0489 189 -532.6704 -0.6293 0.0079 1.0167 -0.0562 190 -105.9870 -0.1252 0.0089 1.0233 -0.0118 191 -657.4362 -0.7799 0.0156 1.0216 -0.0983 192 241.5939 0.2869 0.0186 1.0325 0.0395 193 40.3755 0.0478 0.0135 1.0283 0.0056 194 502.8014 0.6013 0.0320 1.0426 0.1093 195 547.6570 0.6470 0.0079 1.0163 0.0576 196 -92.6362 -0.1098 0.0161 1.0308 -0.0140 197 -34.9928 -0.0413 0.0056 1.0201 -0.0031 198 -335.9020 -0.4005 0.0268 1.0400 -0.0665 199 225.2630 0.2657 0.0056 1.0191 0.0200 200 -285.4190 -0.3369 0.0066 1.0196 -0.0275 201 -376.0955 -0.4439 0.0066 1.0183 -0.0361 202 -668.1564 -0.7894 0.0076 1.0131 -0.0691 203 855.1841 1.0118 0.0097 1.0095 0.1002 204 497.7022 0.5911 0.0186 1.0285 0.0814 205 -525.1719 -0.6198 0.0061 1.0150 -0.0484 206 -555.8710 -0.6566 0.0075 1.0158 -0.0572 207 486.6448 0.5771 0.0155 1.0255 0.0723 208 618.4105 0.7326 0.0132 1.0201 0.0846 209 -578.9656 -0.6871 0.0170 1.0250 -0.0903 210 -443.9010 -0.5241 0.0070 1.0176 -0.0441 211 -923.9450 -1.0918 0.0069 1.0042 -0.0908 212 -552.2264 -0.6512 0.0044 1.0128 -0.0434 213 207.9884 0.2465 0.0153 1.0293 0.0307 214 551.6115 0.6508 0.0054 1.0137 0.0477 215 -422.2622 -0.4998 0.0121 1.0231 -0.0552 216 -343.7448 -0.4061 0.0086 1.0208 -0.0379 217 -9.4951 -0.0113 0.0185 1.0335 -0.0015 218 289.0283 0.3414 0.0085 1.0214 0.0317 219 115.6526 0.1378 0.0252 1.0403 0.0221 220 -1002 -1.1842 0.0069 1.0012 -0.0986 221 1240 1.4794 0.0244 1.0078 0.2341 222 100.6099 0.1193 0.0158 1.0305 0.0151 223 77.8125 0.0919 0.0088 1.0233 0.0087 224 668.6121 0.7895 0.0067 1.0122 0.0648 225 -696.6999 -0.8230 0.0073 1.0120 -0.0704

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

————————————-DFBETAS————————————- Obs Intercept income water80 educat retired peop81 cpeop

181 -0.0039 0.0279 -0.0490 -0.0238 0.0309 0.0484 -0.0138 182 -0.0014 0.0014 -0.0005 0.0009 -0.0044 0.0003 -0.0008 183 -0.0373 0.0211 0.0087 0.0286 0.0207 -0.0133 0.0002 184 -0.0014 -0.0022 0.0043 0.0026 0.0013 -0.0061 0.0011 185 -0.0045 0.0007 -0.0003 0.0034 -0.0033 0.0024 -0.0010 186 -0.0040 -0.0186 -0.0056 0.0076 0.0023 0.0093 -0.0006 187 0.0256 0.0130 0.0403 -0.0239 0.0044 -0.0698 0.0103 188 0.0077 -0.0255 -0.0045 0.0068 -0.0149 0.0077 0.0353 189 -0.0122 0.0133 0.0071 0.0057 -0.0319 -0.0035 -0.0048 190 -0.0041 0.0023 0.0025 0.0029 -0.0060 -0.0012 -0.0008 191 -0.0093 -0.0209 0.0182 0.0079 -0.0419 0.0096 0.0670 192 -0.0210 0.0042 -0.0052 0.0266 0.0195 -0.0066 0.0026 193 0.0027 -0.0004 0.0005 -0.0034 0.0028 0.0009 0.0003 194 -0.0150 -0.0049 0.0614 -0.0216 0.0153 0.0420 -0.0013 195 0.0413 0.0146 -0.0261 -0.0247 -0.0291 -0.0149 0.0006 196 -0.0012 -0.0036 -0.0052 0.0063 -0.0097 -0.0021 -0.0005 197 0.0002 0.0007 -0.0009 0.0000 0.0005 -0.0013 0.0000 198 0.0036 0.0239 0.0112 0.0047 0.0010 -0.0570 0.0066 199 0.0136 0.0032 -0.0096 -0.0093 -0.0098 0.0008 -0.0005 200 -0.0212 0.0079 0.0016 0.0086 0.0180 0.0108 -0.0027 201 -0.0231 0.0027 0.0133 0.0192 0.0146 -0.0128 0.0017 202 -0.0133 0.0139 -0.0095 0.0091 -0.0428 0.0051 -0.0083 203 -0.0272 -0.0659 0.0180 0.0439 -0.0214 0.0432 0.0019 204 -0.0163 -0.0353 0.0065 0.0579 -0.0315 -0.0346 0.0098 205 -0.0145 0.0015 0.0015 0.0197 0.0099 -0.0252 0.0027 206 -0.0397 0.0066 -0.0110 0.0386 0.0205 -0.0044 -0.0015 207 -0.0498 -0.0110 0.0064 0.0427 0.0515 0.0269 0.0018 208 0.0504 -0.0133 0.0093 -0.0497 0.0329 -0.0052 0.0077 209 0.0237 -0.0181 -0.0314 0.0106 -0.0155 -0.0442 0.0050 210 -0.0210 -0.0068 0.0275 0.0178 0.0146 -0.0191 0.0041 211 -0.0557 0.0553 -0.0027 0.0186 0.0539 0.0051 -0.0072 212 -0.0246 -0.0065 0.0201 0.0133 0.0224 -0.0004 0.0006 213 0.0060 0.0068 0.0228 -0.0048 -0.0061 -0.0219 0.0045 214 0.0321 -0.0052 -0.0055 -0.0105 -0.0308 -0.0214 0.0044 215 0.0221 -0.0139 0.0246 -0.0170 -0.0398 -0.0207 0.0018 216 -0.0046 -0.0177 0.0182 -0.0047 0.0124 0.0099 0.0002 217 0.0007 0.0002 -0.0002 -0.0009 0.0002 0.0001 0.0010 218 0.0018 0.0245 0.0013 -0.0096 -0.0005 -0.0005 -0.0012 219 -0.0047 -0.0092 0.0053 0.0005 0.0120 0.0129 0.0002 220 -0.0019 0.0053 0.0508 0.0008 0.0193 -0.0722 0.0112 221 0.0012 0.0486 0.1295 -0.0483 0.1123 -0.0615 -0.1126 222 -0.0057 0.0056 -0.0038 0.0065 0.0084 -0.0027 0.0007 223 0.0019 -0.0029 -0.0017 -0.0005 0.0043 0.0010 0.0007 224 0.0466 -0.0076 0.0203 -0.0251 -0.0366 -0.0390 0.0089 225 -0.0488 -0.0292 0.0031 0.0366 0.0309 0.0356 -0.0041

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

Hat Diag Cov Obs Residual RStudent H Ratio DFFITS

226 -1216 -1.4754 0.0565 1.0422 -0.3609 227 -699.2514 -0.8300 0.0167 1.0215 -0.1080 228 54.0732 0.0649 0.0409 1.0576 0.0134 229 -498.0788 -0.5870 0.0034 1.0129 -0.0342 230 -499.6919 -0.5889 0.0033 1.0127 -0.0339 231 -243.2860 -0.2869 0.0051 1.0185 -0.0206 232 257.8006 0.3073 0.0260 1.0401 0.0502 233 -820.4971 -0.9766 0.0216 1.0228 -0.1451 234 -643.6198 -0.7596 0.0055 1.0117 -0.0567 235 644.8212 0.7621 0.0084 1.0146 0.0702 236 -744.5117 -0.8818 0.0123 1.0157 -0.0985 237 -68.1574 -0.0805 0.0085 1.0230 -0.0075 238 -867.8866 -1.0286 0.0130 1.0124 -0.1182 239 59.1742 0.0697 0.0037 1.0181 0.0042 240 -238.0672 -0.2826 0.0184 1.0322 -0.0387 241 219.3422 0.2586 0.0048 1.0184 0.0180 242 -312.9688 -0.3692 0.0055 1.0180 -0.0274 243 -445.3954 -0.5257 0.0066 1.0171 -0.0428 244 453.4016 0.5418 0.0308 1.0422 0.0966 245 -744.1675 -0.8777 0.0039 1.0072 -0.0551 246 142.0571 0.1674 0.0035 1.0176 0.0100 247 -173.5091 -0.2051 0.0103 1.0243 -0.0209 248 -733.0736 -0.8666 0.0085 1.0122 -0.0803 249 584.2690 0.6918 0.0124 1.0201 0.0774 250 -99.7239 -0.1178 0.0092 1.0236 -0.0114 251 -588.7261 -0.7011 0.0236 1.0317 -0.1091 252 -43.1545 -0.0510 0.0086 1.0232 -0.0047 253 48.6518 0.0575 0.0084 1.0229 0.0053 254 674.9778 0.7995 0.0127 1.0181 0.0905 255 -466.0008 -0.5497 0.0052 1.0153 -0.0396 256 -380.8887 -0.4514 0.0147 1.0265 -0.0551 257 -468.3854 -0.5563 0.0186 1.0291 -0.0767 258 -254.1862 -0.3018 0.0188 1.0326 -0.0418 259 228.0087 0.2705 0.0166 1.0305 0.0351 260 -499.8074 -0.5893 0.0041 1.0135 -0.0378 261 536.4132 0.6368 0.0175 1.0265 0.0849 262 56.0987 0.0667 0.0206 1.0357 0.0097 263 989.5682 1.1758 0.0173 1.0121 0.1561 264 -516.0408 -0.6122 0.0162 1.0256 -0.0786 265 -177.5158 -0.2112 0.0231 1.0377 -0.0325 266 -1437 -1.7102 0.0177 0.9904 -0.2296 267 -1066 -1.2824 0.0410 1.0332 -0.2652 268 854.7948 1.0142 0.0152 1.0150 0.1261 269 -82.9940 -0.0979 0.0062 1.0206 -0.0077 270 -400.3069 -0.4724 0.0064 1.0177 -0.0379

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

————————————-DFBETAS————————————- Obs Intercept income water80 educat retired peop81 cpeop

226 0.0253 0.0803 0.0038 0.0820 -0.1624 -0.2842 0.0254 227 -0.0407 -0.0055 0.0545 0.0265 0.0350 -0.0240 0.0820 228 0.0043 -0.0003 -0.0015 -0.0021 -0.0041 -0.0021 -0.0117 229 -0.0048 -0.0067 -0.0053 0.0053 0.0099 -0.0040 -0.0002 230 -0.0066 0.0026 0.0070 0.0016 0.0137 -0.0117 0.0009 231 -0.0144 -0.0041 0.0080 0.0103 0.0101 0.0005 0.0002 232 -0.0172 0.0155 0.0339 0.0004 0.0093 0.0009 0.0012 233 0.0233 -0.1139 0.0450 0.0223 -0.0970 -0.0231 0.0079 234 -0.0245 -0.0067 -0.0179 0.0072 0.0281 0.0391 -0.0077 235 0.0212 0.0112 0.0098 -0.0275 0.0462 -0.0098 0.0067 236 -0.0178 -0.0702 0.0158 0.0506 -0.0036 -0.0294 0.0096 237 -0.0016 0.0028 0.0002 0.0004 -0.0039 -0.0003 -0.0008 238 -0.0826 -0.0096 0.0631 0.0769 0.0380 -0.0423 0.0092 239 0.0006 -0.0008 0.0016 -0.0002 -0.0015 0.0003 0.0002 240 0.0242 0.0102 -0.0024 -0.0304 -0.0192 0.0002 -0.0033 241 -0.0009 0.0083 -0.0043 0.0035 -0.0052 -0.0026 -0.0000 242 -0.0125 -0.0095 0.0014 0.0049 0.0131 0.0152 -0.0021 243 -0.0065 -0.0097 0.0180 0.0119 0.0061 -0.0276 0.0051 244 -0.0281 -0.0526 -0.0226 0.0616 -0.0262 0.0200 -0.0489 245 -0.0329 0.0112 0.0127 0.0124 0.0340 0.0028 -0.0021 246 0.0041 0.0006 -0.0036 -0.0008 -0.0055 -0.0004 0.0001 247 -0.0157 0.0040 0.0034 0.0054 0.0132 0.0109 -0.0021 248 0.0067 -0.0589 -0.0032 -0.0009 0.0071 0.0230 -0.0005 249 0.0168 -0.0415 0.0080 0.0286 -0.0433 -0.0408 0.0113 250 -0.0052 0.0009 0.0007 0.0033 -0.0050 0.0030 -0.0013 251 0.0360 0.0347 -0.0397 -0.0645 0.0249 0.0321 0.0531 252 -0.0010 0.0014 0.0010 0.0003 -0.0025 -0.0005 -0.0004 253 -0.0006 0.0021 -0.0005 0.0000 0.0041 -0.0003 0.0003 254 -0.0472 -0.0192 -0.0033 0.0608 0.0520 0.0025 0.0073 255 -0.0122 -0.0237 0.0126 0.0096 0.0123 0.0050 0.0009 256 0.0179 -0.0277 0.0249 -0.0033 -0.0068 -0.0367 0.0083 257 0.0372 0.0360 0.0171 -0.0507 -0.0345 -0.0275 -0.0022 258 0.0250 0.0022 0.0119 -0.0306 -0.0213 -0.0052 -0.0011 259 -0.0121 -0.0158 0.0001 0.0235 0.0124 -0.0051 0.0042 260 -0.0204 -0.0148 0.0039 0.0158 0.0164 0.0082 -0.0008 261 -0.0183 -0.0309 0.0095 0.0599 -0.0317 -0.0398 0.0104 262 -0.0047 -0.0031 -0.0004 0.0075 0.0035 -0.0012 0.0009 263 0.0612 -0.0293 0.1261 -0.0374 -0.0492 -0.1018 0.0268 264 -0.0360 -0.0617 0.0209 0.0391 0.0145 0.0248 0.0015 265 0.0021 -0.0171 0.0223 0.0051 -0.0021 -0.0216 0.0055 266 0.1539 -0.0285 0.0811 -0.1331 -0.0231 -0.1472 0.0252 267 -0.0278 -0.0632 0.0404 0.0234 0.0136 0.0027 -0.2337 268 -0.0145 -0.0212 0.0721 -0.0138 0.0822 0.0175 0.0108 269 -0.0061 -0.0006 0.0013 0.0034 0.0046 0.0032 -0.0005 270 -0.0005 0.0027 0.0173 0.0003 0.0075 -0.0275 0.0040

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

Hat Diag Cov Obs Residual RStudent H Ratio DFFITS

271 1025 1.2134 0.0090 1.0023 0.1155 272 374.8041 0.4467 0.0258 1.0383 0.0726 273 -815.2700 -0.9653 0.0114 1.0125 -0.1036 274 157.3280 0.1856 0.0063 1.0204 0.0148 275 -594.0909 -0.7010 0.0054 1.0128 -0.0516 276 17.5792 0.0207 0.0065 1.0210 0.0017 277 906.9871 1.0743 0.0117 1.0096 0.1169 278 264.3152 0.3120 0.0068 1.0200 0.0258 279 -335.5327 -0.3981 0.0169 1.0296 -0.0522 280 364.4100 0.4349 0.0282 1.0411 0.0741 281 -1332 -1.5945 0.0291 1.0076 -0.2763 282 7.7521 0.009147 0.0064 1.0209 0.0007 283 -723.8636 -0.8578 0.0134 1.0174 -0.1000 284 -196.8353 -0.2342 0.0229 1.0374 -0.0359 285 -253.3283 -0.2994 0.0092 1.0226 -0.0289 286 -944.7845 -1.1226 0.0176 1.0141 -0.1501 287 -670.3834 -0.7924 0.0087 1.0141 -0.0741 288 335.5834 0.3986 0.0191 1.0319 0.0557 289 -1249 -1.4830 0.0143 0.9972 -0.1785 290 -146.3934 -0.1726 0.0044 1.0185 -0.0115 291 -1159 -1.3716 0.0078 0.9953 -0.1219 292 -618.2475 -0.7406 0.0349 1.0428 -0.1407 293 338.8361 0.4024 0.0190 1.0317 0.0560 294 1167 1.3797 0.0070 0.9942 0.1162 295 -1507 -1.7815 0.0035 0.9728 -0.1053 296 354.6217 0.4189 0.0084 1.0204 0.0385 297 804.0285 0.9495 0.0063 1.0077 0.0754 298 106.0794 0.1257 0.0147 1.0293 0.0153 299 -284.0401 -0.3362 0.0123 1.0254 -0.0375 300 -745.0075 -0.8887 0.0262 1.0300 -0.1457 301 -357.9988 -0.4247 0.0165 1.0288 -0.0550 302 -1008 -1.1970 0.0164 1.0104 -0.1544 303 532.9129 0.6313 0.0135 1.0225 0.0738 304 -252.6105 -0.2986 0.0095 1.0229 -0.0293 305 294.5706 0.3500 0.0199 1.0332 0.0499 306 402.3062 0.4766 0.0138 1.0253 0.0563 307 -222.0259 -0.2624 0.0095 1.0232 -0.0257 308 -572.1399 -0.6749 0.0049 1.0127 -0.0471 309 -257.7856 -0.3050 0.0117 1.0251 -0.0332 310 320.2138 0.3861 0.0480 1.0633 0.0867 311 134.2291 0.1586 0.0096 1.0239 0.0156 312 832.2351 0.9821 0.0047 1.0052 0.0676 313 651.7237 0.7710 0.0104 1.0164 0.0789 314 -285.9175 -0.3373 0.0056 1.0185 -0.0254 315 -298.0905 -0.3539 0.0184 1.0315 -0.0484

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

————————————-DFBETAS————————————- Obs Intercept income water80 educat retired peop81 cpeop

271 -0.0095 -0.0296 0.0764 -0.0006 -0.0122 0.0157 0.0066 272 0.0075 0.0229 -0.0156 -0.0272 0.0062 0.0394 0.0333 273 -0.0565 0.0534 -0.0564 0.0184 0.0532 0.0551 -0.0175 274 0.0117 -0.0003 -0.0033 -0.0059 -0.0091 -0.0055 0.0010 275 -0.0337 -0.0223 0.0112 0.0297 0.0206 0.0075 0.0002 276 -0.0006 -0.0005 0.0002 0.0012 -0.0006 -0.0003 0.0001 277 0.0483 -0.0407 0.0552 0.0040 -0.0613 -0.0887 0.0217 278 0.0026 0.0118 -0.0043 0.0036 -0.0089 -0.0120 0.0012 279 -0.0128 -0.0440 0.0126 0.0155 0.0064 0.0172 0.0010 280 0.0582 -0.0146 0.0104 -0.0417 -0.0332 -0.0261 -0.0339 281 0.1254 -0.2091 -0.0381 -0.0588 -0.0488 0.0343 0.0062 282 0.0000 -0.0003 -0.0002 0.0001 -0.0002 0.0005 -0.0000 283 0.0368 -0.0339 0.0177 -0.0583 0.0169 0.0301 -0.0026 284 0.0139 -0.0109 0.0127 -0.0096 -0.0039 -0.0171 -0.0179 285 -0.0094 -0.0070 -0.0098 0.0169 0.0023 -0.0056 0.0004 286 0.0387 -0.1239 0.0103 0.0127 -0.0254 -0.0269 0.0125 287 -0.0057 0.0141 0.0150 0.0075 -0.0486 -0.0274 -0.0021 288 -0.0319 0.0301 -0.0217 0.0236 0.0071 0.0211 -0.0060 289 -0.0449 0.0017 0.0220 0.0464 0.0246 -0.0530 -0.1294 290 -0.0044 -0.0007 0.0053 0.0032 0.0044 -0.0047 0.0008 291 0.0333 0.0516 0.0322 -0.0507 0.0251 -0.0792 0.0068 292 0.0599 0.0344 0.0358 -0.0526 -0.0102 -0.1036 -0.0554 293 -0.0099 -0.0214 -0.0094 0.0394 -0.0223 -0.0173 0.0047 294 0.0615 0.0068 0.0511 -0.0701 -0.0312 -0.0081 0.0058 295 -0.0385 -0.0351 0.0063 0.0199 0.0472 0.0256 -0.0038 296 0.0015 0.0097 -0.0023 -0.0098 0.0309 0.0086 0.0009 297 0.0484 -0.0253 -0.0133 -0.0094 -0.0502 -0.0254 0.0068 298 0.0038 -0.0058 0.0003 0.0012 -0.0054 -0.0021 0.0126 299 -0.0106 0.0101 0.0224 0.0065 0.0102 -0.0259 0.0038 300 0.0280 -0.0068 -0.1312 -0.0110 -0.0015 0.0531 -0.0167 301 -0.0090 -0.0146 0.0257 0.0114 0.0090 -0.0202 0.0439 302 0.0582 -0.0528 0.1066 -0.0514 -0.0012 -0.0900 0.0214 303 -0.0156 0.0162 0.0087 0.0088 -0.0053 0.0083 -0.0587 304 -0.0190 0.0060 0.0052 0.0036 0.0185 0.0156 -0.0031 305 -0.0207 -0.0058 -0.0085 0.0305 -0.0047 0.0063 0.0320 306 -0.0299 -0.0244 -0.0113 0.0465 -0.0110 0.0166 -0.0001 307 -0.0125 -0.0090 0.0043 0.0040 0.0119 0.0164 -0.0020 308 -0.0237 0.0133 -0.0113 0.0186 0.0196 -0.0058 -0.0020 309 -0.0312 -0.0008 0.0076 0.0229 0.0170 0.0083 -0.0012 310 0.0054 0.0018 -0.0200 -0.0119 0.0010 0.0367 0.0659 311 -0.0035 -0.0052 -0.0077 0.0059 -0.0031 0.0110 -0.0013 312 -0.0007 -0.0274 -0.0111 0.0321 -0.0347 -0.0017 0.0038 313 -0.0268 -0.0299 0.0166 0.0394 0.0456 -0.0053 0.0101 314 -0.0091 0.0126 0.0067 0.0019 0.0119 -0.0100 0.0003 315 -0.0035 0.0057 0.0144 0.0130 -0.0270 -0.0343 0.0029

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

Hat Diag Cov Obs Residual RStudent H Ratio DFFITS

316 -369.9919 -0.4367 0.0068 1.0186 -0.0362 317 33.8482 0.0399 0.0039 1.0183 0.0025 318 22.7376 0.0270 0.0170 1.0319 0.0035 319 -1188 -1.4092 0.0127 0.9987 -0.1598 320 531.3778 0.6307 0.0172 1.0263 0.0833 321 1518 1.8038 0.0137 0.9817 0.2123 322 598.2201 0.7063 0.0066 1.0139 0.0576 323 178.5485 0.2107 0.0062 1.0201 0.0167 324 -1411 -1.6738 0.0114 0.9858 -0.1794 325 2446 2.9263 0.0166 0.9133 0.3798 326 -189.6496 -0.2246 0.0134 1.0274 -0.0261 327 -228.2419 -0.2692 0.0051 1.0186 -0.0193 328 -298.9269 -0.3528 0.0063 1.0191 -0.0281 329 -409.0724 -0.4844 0.0130 1.0244 -0.0557 330 -259.4030 -0.3068 0.0111 1.0244 -0.0325 331 21.8481 0.0259 0.0171 1.0321 0.0034 332 70.2575 0.0833 0.0165 1.0313 0.0108 333 865.3859 1.0232 0.0083 1.0077 0.0935 334 114.7276 0.1355 0.0087 1.0231 0.0127 335 163.4286 0.1930 0.0080 1.0220 0.0173 336 1067 1.2624 0.0089 1.0005 0.1197 337 -197.0277 -0.2335 0.0147 1.0288 -0.0286 338 636.2186 0.7528 0.0109 1.0173 0.0790 339 -511.5163 -0.6045 0.0087 1.0180 -0.0568 340 -1212 -1.4476 0.0255 1.0103 -0.2344 341 -794.6823 -0.9440 0.0178 1.0197 -0.1270 342 -150.9132 -0.1801 0.0283 1.0435 -0.0307 343 -414.0687 -0.5120 0.0949 1.1165 -0.1658 344 -267.9780 -0.3188 0.0222 1.0359 -0.0480 345 503.7369 0.5969 0.0139 1.0235 0.0708 346 240.6730 0.2852 0.0148 1.0285 0.0350 347 595.4753 0.7029 0.0062 1.0135 0.0553 348 -1227 -1.4505 0.0055 0.9898 -0.1083 349 365.3848 0.4323 0.0112 1.0232 0.0460 350 -115.0429 -0.1360 0.0094 1.0238 -0.0133 351 26.0780 0.0308 0.0102 1.0248 0.0031 352 -387.9643 -0.4615 0.0218 1.0339 -0.0689 353 -163.2422 -0.1939 0.0197 1.0342 -0.0275 354 152.4876 0.1802 0.0088 1.0230 0.0170 355 -50.8850 -0.0602 0.0125 1.0273 -0.0068 356 362.5620 0.4285 0.0095 1.0214 0.0419 357 1688 2.0152 0.0214 0.9782 0.2980 358 -289.2570 -0.3411 0.0051 1.0180 -0.0245 359 -589.1093 -0.6967 0.0098 1.0174 -0.0693 360 407.1433 0.4818 0.0115 1.0228 0.0519

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

————————————-DFBETAS————————————- Obs Intercept income water80 educat retired peop81 cpeop

316 0.0045 0.0123 0.0185 -0.0152 0.0124 -0.0172 0.0018 317 -0.0001 -0.0005 0.0004 0.0011 -0.0012 -0.0006 0.0002 318 -0.0007 -0.0008 0.0008 0.0016 -0.0007 -0.0009 0.0028 319 -0.0246 0.0762 -0.1123 -0.0304 0.0640 0.0950 -0.0295 320 0.0227 0.0008 0.0430 -0.0240 -0.0183 -0.0223 -0.0511 321 0.0960 -0.0733 0.0888 -0.0627 0.0668 -0.0841 0.0369 322 0.0160 0.0161 -0.0072 -0.0279 -0.0072 0.0282 -0.0048 323 0.0133 -0.0052 -0.0010 -0.0082 -0.0096 -0.0013 0.0009 324 -0.0958 0.0778 -0.1151 0.0610 0.0727 0.0634 -0.0251 325 -0.1448 -0.0821 -0.0976 0.1023 0.0124 0.3306 -0.0427 326 -0.0161 0.0028 0.0042 0.0153 -0.0097 -0.0016 -0.0014 327 -0.0001 0.0009 0.0099 -0.0071 0.0085 -0.0017 0.0002 328 -0.0175 -0.0124 0.0122 0.0150 0.0108 0.0008 0.0010 329 -0.0103 0.0038 0.0196 0.0002 0.0186 -0.0094 0.0457 330 -0.0145 0.0096 0.0079 0.0059 -0.0103 0.0036 -0.0031 331 0.0004 -0.0006 -0.0011 -0.0002 0.0012 0.0008 -0.0023 332 0.0094 0.0034 -0.0021 -0.0073 -0.0047 -0.0050 0.0005 333 0.0666 -0.0421 -0.0168 -0.0196 -0.0608 -0.0236 0.0077 334 0.0042 0.0018 -0.0023 -0.0027 0.0066 -0.0032 0.0012 335 0.0098 0.0068 -0.0079 -0.0108 -0.0044 0.0051 -0.0015 336 0.0361 -0.0171 -0.0612 -0.0323 -0.0303 0.0823 -0.0123 337 0.0005 -0.0013 -0.0002 -0.0022 -0.0124 0.0047 0.0190 338 -0.0143 -0.0194 -0.0121 0.0368 0.0361 -0.0127 0.0086 339 -0.0010 0.0044 -0.0182 0.0095 -0.0420 -0.0052 -0.0051 340 -0.0630 -0.0056 -0.1554 0.0589 0.0337 0.1112 -0.1610 341 0.0147 0.0327 -0.0664 -0.0290 0.0164 0.0239 -0.0986 342 0.0012 -0.0074 0.0066 0.0079 -0.0022 -0.0204 0.0204 343 -0.0117 0.0423 -0.0510 -0.0086 0.0162 0.0275 -0.1584 344 -0.0354 0.0046 0.0076 0.0225 0.0228 0.0127 0.0270 345 0.0265 -0.0097 -0.0137 -0.0073 -0.0240 -0.0056 0.0566 346 0.0317 0.0098 0.0000 -0.0288 -0.0134 -0.0129 0.0015 347 0.0038 0.0351 0.0097 -0.0153 -0.0043 -0.0018 -0.0008 348 -0.0648 -0.0037 -0.0500 0.0522 0.0459 0.0435 -0.0115 349 0.0292 -0.0252 -0.0135 -0.0056 -0.0284 -0.0055 0.0028 350 -0.0060 -0.0009 0.0024 0.0043 -0.0061 0.0030 -0.0012 351 0.0014 -0.0010 -0.0000 -0.0006 0.0011 -0.0007 0.0004 352 0.0023 0.0280 0.0052 -0.0328 0.0282 0.0170 0.0370 353 0.0139 -0.0035 0.0072 -0.0180 -0.0130 0.0028 -0.0013 354 0.0011 -0.0029 -0.0029 0.0032 0.0082 -0.0034 0.0019 355 -0.0053 -0.0015 0.0007 0.0058 0.0018 -0.0009 0.0002 356 0.0146 -0.0090 -0.0122 -0.0095 0.0200 0.0059 0.0023 357 -0.0107 -0.0123 0.2069 -0.0694 0.1740 -0.0016 0.0281 358 -0.0175 0.0019 0.0092 0.0101 0.0138 -0.0005 -0.0001 359 -0.0116 -0.0338 0.0170 0.0213 -0.0473 0.0005 -0.0015 360 -0.0322 -0.0181 0.0048 0.0439 -0.0076 0.0077 0.0017

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

Hat Diag Cov Obs Residual RStudent H Ratio DFFITS

361 1308 1.5500 0.0099 0.9899 0.1547 362 -1871 -2.2723 0.0522 0.9943 -0.5334 363 1174 1.3918 0.0109 0.9976 0.1464 364 1437 1.7060 0.0129 0.9858 0.1952 365 -521.6255 -0.6182 0.0142 1.0235 -0.0743 366 146.5069 0.1735 0.0133 1.0277 0.0202 367 536.4550 0.6337 0.0079 1.0167 0.0566 368 501.9212 0.5916 0.0034 1.0128 0.0344 369 365.3881 0.4312 0.0062 1.0180 0.0341 370 -167.4129 -0.1976 0.0073 1.0213 -0.0170 371 175.0922 0.2082 0.0214 1.0359 0.0308 372 -270.5000 -0.3196 0.0089 1.0220 -0.0302 373 -159.8784 -0.1899 0.0197 1.0343 -0.0269 374 47.6570 0.0563 0.0079 1.0224 0.0050 375 -45.9015 -0.0543 0.0104 1.0250 -0.0056 376 -322.8677 -0.3823 0.0130 1.0256 -0.0439 377 1170 1.3820 0.0053 0.9923 0.1008 378 327.9275 0.3871 0.0071 1.0195 0.0328 379 -191.2605 -0.2264 0.0129 1.0269 -0.0259 380 -619.9539 -0.7354 0.0158 1.0227 -0.0930 381 1889 2.2459 0.0113 0.9547 0.2398 382 -336.7246 -0.3979 0.0087 1.0211 -0.0373 383 -487.5295 -0.5753 0.0059 1.0156 -0.0444 384 -141.0611 -0.1665 0.0073 1.0215 -0.0143 385 1114 1.3199 0.0104 0.9999 0.1356 386 -610.5992 -0.7272 0.0237 1.0312 -0.1134 387 366.6471 0.4331 0.0081 1.0200 0.0392 388 1128 1.3344 0.0076 0.9965 0.1168 389 593.1326 0.7008 0.0081 1.0155 0.0631 390 -79.4394 -0.0938 0.0075 1.0220 -0.0082 391 933.5237 1.1073 0.0142 1.0111 0.1330 392 448.4997 0.5303 0.0100 1.0205 0.0533 393 -612.5880 -0.7234 0.0070 1.0139 -0.0605 394 93.0171 0.1101 0.0128 1.0274 0.0125 395 11.3580 0.0134 0.0060 1.0206 0.0010 396 -250.5310 -0.2963 0.0105 1.0239 -0.0305 397 -351.1224 -0.4162 0.0149 1.0273 -0.0512 398 -790.1810 -0.9402 0.0210 1.0232 -0.1377 399 389.6380 0.4597 0.0056 1.0170 0.0345 400 -828.8270 -0.9802 0.0090 1.0096 -0.0933 401 1489 1.7780 0.0236 0.9931 0.2766 402 -51.1173 -0.0605 0.0128 1.0275 -0.0069 403 490.6402 0.5814 0.0142 1.0241 0.0698 404 176.8221 0.2097 0.0166 1.0309 0.0272 405 -144.7470 -0.1722 0.0229 1.0378 -0.0264

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

————————————-DFBETAS————————————- Obs Intercept income water80 educat retired peop81 cpeop

361 -0.0008 0.0214 0.0549 0.0077 0.0920 -0.0765 0.0246 362 -0.0067 0.2032 -0.4302 -0.0920 0.1194 0.2967 0.1223 363 0.0006 0.0363 0.1094 -0.0249 -0.0076 -0.0414 0.0120 364 -0.0156 -0.0359 -0.0028 0.0521 -0.0368 0.0125 0.1605 365 -0.0174 0.0061 -0.0067 0.0185 0.0100 -0.0153 -0.0563 366 0.0093 -0.0112 -0.0033 0.0028 -0.0125 -0.0075 0.0022 367 -0.0063 -0.0315 -0.0205 0.0261 -0.0209 0.0243 -0.0010 368 0.0048 0.0068 0.0054 -0.0053 -0.0100 0.0040 0.0002 369 0.0259 -0.0031 0.0057 -0.0137 -0.0203 -0.0188 0.0041 370 -0.0012 0.0002 0.0038 0.0002 -0.0114 -0.0011 -0.0011 371 -0.0167 -0.0148 -0.0051 0.0223 0.0132 0.0099 0.0011 372 -0.0106 0.0017 0.0091 0.0087 -0.0162 -0.0035 -0.0014 373 0.0089 -0.0081 -0.0069 -0.0045 -0.0156 0.0034 0.0157 374 0.0036 0.0013 -0.0023 -0.0022 -0.0025 -0.0013 0.0001 375 -0.0004 0.0019 0.0013 -0.0013 -0.0022 0.0006 -0.0006 376 0.0195 -0.0076 0.0207 -0.0292 0.0069 -0.0041 0.0016 377 0.0701 -0.0401 -0.0105 -0.0323 -0.0617 -0.0051 0.0057 378 0.0196 -0.0155 0.0013 -0.0133 -0.0148 0.0072 0.0009 379 -0.0158 -0.0013 0.0022 0.0168 -0.0111 0.0001 -0.0014 380 -0.0006 0.0072 0.0200 0.0204 -0.0003 -0.0781 0.0110 381 0.2214 0.0178 0.0228 -0.1771 -0.1136 -0.1017 0.0184 382 -0.0118 0.0215 0.0151 -0.0003 0.0166 -0.0165 0.0009 383 -0.0158 0.0209 0.0150 0.0033 0.0206 -0.0187 0.0010 384 -0.0108 0.0032 0.0044 0.0043 0.0091 0.0037 -0.0008 385 0.0862 -0.0281 -0.0424 -0.0142 -0.0845 -0.0593 0.0110 386 -0.0468 -0.0768 0.0076 0.0776 -0.0550 0.0133 -0.0005 387 -0.0027 -0.0009 -0.0099 -0.0001 0.0292 0.0146 0.0006 388 0.0528 0.0203 -0.0704 -0.0093 -0.0582 -0.0206 -0.0002 389 0.0125 -0.0201 0.0057 -0.0054 0.0356 -0.0018 0.0074 390 -0.0017 -0.0007 0.0016 0.0017 -0.0054 -0.0003 -0.0005 391 -0.0051 -0.0454 -0.0232 0.0413 -0.0449 0.0179 -0.0997 392 -0.0178 -0.0193 0.0048 0.0271 0.0309 -0.0007 0.0060 393 -0.0113 -0.0036 0.0447 0.0020 0.0190 -0.0308 0.0062 394 0.0000 -0.0001 -0.0045 0.0059 -0.0053 -0.0049 0.0007 395 0.0008 -0.0001 -0.0000 -0.0004 -0.0006 -0.0005 0.0001 396 -0.0138 0.0070 0.0071 0.0064 -0.0106 0.0041 -0.0030 397 -0.0337 -0.0133 0.0045 0.0345 -0.0188 0.0128 -0.0036 398 0.0355 -0.1045 0.0346 -0.0062 -0.0875 0.0054 0.0024 399 0.0127 -0.0054 -0.0210 0.0007 -0.0182 0.0055 -0.0008 400 -0.0850 0.0039 -0.0053 0.0594 0.0508 0.0399 -0.0081 401 -0.0213 -0.1339 0.1118 0.0291 -0.0225 0.0671 0.1744 402 0.0034 0.0014 0.0012 -0.0030 -0.0048 -0.0038 0.0000 403 -0.0221 -0.0228 -0.0139 0.0543 -0.0238 -0.0111 0.0040 404 0.0004 -0.0016 -0.0083 -0.0058 -0.0001 0.0235 -0.0035 405 -0.0015 -0.0209 -0.0023 0.0097 -0.0158 0.0056 -0.0006

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

Hat Diag Cov Obs Residual RStudent H Ratio DFFITS

406 -195.9041 -0.2315 0.0095 1.0234 -0.0227 407 -78.8265 -0.0932 0.0097 1.0242 -0.0092 408 -608.7011 -0.7262 0.0270 1.0348 -0.1210 409 377.8136 0.4461 0.0075 1.0192 0.0387 410 -202.6945 -0.2396 0.0098 1.0236 -0.0239 411 -202.0795 -0.2390 0.0110 1.0249 -0.0252 412 -959.2449 -1.1344 0.0083 1.0042 -0.1039 413 -429.0443 -0.5072 0.0096 1.0205 -0.0500 414 -341.3772 -0.4067 0.0251 1.0381 -0.0652 415 -247.2054 -0.2913 0.0036 1.0168 -0.0175 416 703.0921 0.8327 0.0123 1.0169 0.0929 417 -1703 -2.0314 0.0195 0.9754 -0.2865 418 -163.1994 -0.1925 0.0061 1.0201 -0.0150 419 -376.9749 -0.4445 0.0045 1.0161 -0.0298 420 423.5643 0.4997 0.0057 1.0166 0.0377 421 444.0551 0.5260 0.0136 1.0244 0.0618 422 -391.0959 -0.4621 0.0088 1.0203 -0.0436 423 51.7406 0.0613 0.0144 1.0292 0.0074 424 203.2925 0.2404 0.0105 1.0244 0.0248 425 14.9839 0.0177 0.0124 1.0272 0.0020 426 287.9200 0.3405 0.0105 1.0235 0.0350 427 596.4106 0.7064 0.0129 1.0203 0.0807 428 275.8699 0.3257 0.0074 1.0205 0.0282 429 595.9706 0.7033 0.0055 1.0129 0.0524 430 -162.1483 -0.1923 0.0162 1.0305 -0.0246 431 -797.9310 -0.9436 0.0089 1.0106 -0.0894 432 1207 1.4383 0.0212 1.0061 0.2114 433 87.5537 0.1037 0.0138 1.0285 0.0123 434 221.0290 0.2609 0.0070 1.0206 0.0219 435 2109 2.5030 0.0057 0.9331 0.1896 436 781.4270 0.9248 0.0106 1.0128 0.0956 437 -75.2078 -0.0893 0.0186 1.0335 -0.0123 438 -221.4429 -0.2615 0.0081 1.0218 -0.0237 439 -947.1840 -1.1292 0.0241 1.0207 -0.1776 440 348.6399 0.4116 0.0070 1.0191 0.0346 441 -123.5610 -0.1458 0.0067 1.0210 -0.0120 442 -207.3657 -0.2464 0.0202 1.0345 -0.0354 443 -193.4824 -0.2286 0.0086 1.0224 -0.0212 444 -119.2329 -0.1405 0.0042 1.0184 -0.0091 445 -723.8175 -0.8762 0.0544 1.0611 -0.2102 446 1094 1.3068 0.0271 1.0175 0.2181 447 -365.9584 -0.4329 0.0110 1.0230 -0.0457 448 561.5204 0.6741 0.0392 1.0489 0.1361 449 -468.1724 -0.5518 0.0035 1.0136 -0.0328 450 -687.0289 -0.8113 0.0066 1.0116 -0.0661

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

————————————-DFBETAS————————————- Obs Intercept income water80 educat retired peop81 cpeop

406 -0.0154 0.0109 0.0063 0.0039 0.0144 0.0039 -0.0015 407 -0.0031 0.0023 0.0020 0.0007 -0.0035 0.0014 -0.0010 408 -0.0150 0.0034 -0.1116 0.0195 0.0135 0.0631 -0.0174 409 0.0081 -0.0066 -0.0016 -0.0051 0.0238 0.0003 0.0037 410 -0.0108 0.0058 0.0014 0.0087 -0.0110 -0.0008 -0.0020 411 -0.0132 0.0055 -0.0045 0.0092 -0.0092 0.0083 -0.0037 412 -0.0376 0.0523 -0.0587 0.0241 0.0366 0.0042 -0.0102 413 -0.0217 0.0112 -0.0336 0.0082 0.0218 0.0339 -0.0088 414 0.0333 0.0215 0.0087 -0.0400 0.0054 -0.0289 0.0397 415 -0.0068 0.0027 0.0003 0.0046 0.0075 -0.0045 -0.0000 416 0.0272 -0.0049 -0.0207 -0.0134 -0.0322 0.0095 -0.0770 417 -0.0715 -0.0516 -0.1175 0.0353 0.0816 0.1759 0.1542 418 -0.0091 0.0030 -0.0038 0.0083 0.0058 -0.0012 -0.0006 419 -0.0152 -0.0003 -0.0057 0.0151 0.0107 -0.0030 -0.0006 420 -0.0089 0.0222 -0.0039 0.0047 -0.0026 0.0046 -0.0018 421 -0.0261 -0.0228 -0.0175 0.0502 -0.0171 0.0063 0.0011 422 0.0168 0.0080 0.0213 -0.0276 0.0098 -0.0182 0.0023 423 0.0020 0.0004 -0.0022 -0.0021 -0.0017 0.0025 -0.0061 424 0.0021 -0.0081 -0.0067 0.0058 0.0096 -0.0024 0.0025 425 -0.0002 0.0005 -0.0000 0.0003 -0.0004 -0.0001 -0.0016 426 0.0046 -0.0057 -0.0074 -0.0089 -0.0039 0.0268 -0.0034 427 0.0187 0.0087 0.0070 -0.0065 -0.0189 -0.0215 0.0689 428 0.0208 -0.0113 -0.0028 -0.0071 -0.0185 -0.0091 0.0027 429 0.0343 0.0092 -0.0108 -0.0159 -0.0298 -0.0234 0.0034 430 -0.0072 0.0042 -0.0022 0.0048 -0.0077 0.0040 0.0152 431 -0.0392 -0.0150 0.0643 0.0322 0.0272 -0.0411 0.0095 432 -0.0449 -0.1138 0.0164 0.0691 -0.0375 0.0855 -0.1321 433 -0.0006 -0.0046 -0.0006 0.0039 -0.0041 0.0009 -0.0091 434 0.0158 -0.0074 0.0053 -0.0066 -0.0136 -0.0113 0.0030 435 0.0799 0.0002 0.0926 -0.0880 -0.0539 -0.0123 0.0113 436 0.0042 -0.0568 -0.0409 0.0420 -0.0443 0.0188 0.0013 437 0.0068 0.0015 0.0033 -0.0054 -0.0010 -0.0101 0.0014 438 -0.0019 -0.0005 0.0091 0.0003 -0.0148 -0.0033 -0.0009 439 0.0113 0.0192 0.0475 0.0277 -0.0084 -0.1595 0.0231 440 0.0218 -0.0172 -0.0096 -0.0075 -0.0205 0.0026 0.0012 441 -0.0037 0.0030 0.0016 0.0037 0.0032 -0.0070 0.0007 442 -0.0164 -0.0238 -0.0054 0.0163 0.0072 0.0230 -0.0022 443 -0.0011 0.0043 0.0001 -0.0040 -0.0107 0.0059 -0.0030 444 -0.0036 0.0003 0.0045 0.0003 0.0050 -0.0005 0.0001 445 0.0211 0.0183 -0.0473 0.0244 -0.0773 -0.0659 0.1631 446 -0.0220 -0.0275 0.1972 -0.0089 0.0004 -0.0394 0.0218 447 -0.0132 0.0218 -0.0345 0.0033 0.0167 0.0183 -0.0073 448 0.0322 0.0153 0.0095 -0.0288 -0.0275 -0.0190 -0.1219 449 -0.0128 0.0029 0.0010 0.0094 0.0137 -0.0083 0.0001 450 -0.0474 -0.0093 -0.0152 0.0309 0.0337 0.0404 -0.0075

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

Hat Diag Cov Obs Residual RStudent H Ratio DFFITS

451 1364 1.6446 0.0437 1.0205 0.3516 452 431.4733 0.5100 0.0092 1.0200 0.0490 453 -205.1153 -0.2429 0.0136 1.0276 -0.0285 454 -39.2160 -0.0462 0.0053 1.0198 -0.0034 455 -330.7656 -0.3921 0.0154 1.0280 -0.0491 456 -821.1114 -0.9744 0.0158 1.0168 -0.1235 457 476.5952 0.5618 0.0038 1.0137 0.0345 458 325.0201 0.3842 0.0098 1.0223 0.0382 459 -894.3886 -1.0614 0.0155 1.0139 -0.1330 460 -483.8646 -0.5748 0.0190 1.0292 -0.0801 461 -244.9013 -0.2891 0.0073 1.0207 -0.0248 462 426.5026 0.5040 0.0089 1.0198 0.0478 463 -288.2592 -0.3427 0.0208 1.0342 -0.0499 464 -46.5100 -0.0549 0.0060 1.0205 -0.0043 465 -630.5377 -0.7470 0.0132 1.0199 -0.0865 466 -1503 -1.7868 0.0148 0.9837 -0.2191 467 708.9811 0.8366 0.0049 1.0093 0.0590 468 -17.4669 -0.0206 0.0091 1.0238 -0.0020 469 -41.9393 -0.0495 0.0063 1.0208 -0.0039 470 -915.8035 -1.0817 0.0061 1.0037 -0.0846 471 -498.3548 -0.5884 0.0069 1.0164 -0.0491 472 -446.4687 -0.5315 0.0234 1.0346 -0.0823 473 1456 1.7238 0.0076 0.9797 0.1512 474 647.6613 0.7682 0.0155 1.0217 0.0962 475 -1804 -2.1451 0.0122 0.9616 -0.2381 476 -220.6899 -0.2608 0.0094 1.0230 -0.0254 477 -743.5057 -0.8911 0.0354 1.0398 -0.1708 478 -1154 -1.3646 0.0061 0.9938 -0.1069 479 238.2221 0.2823 0.0147 1.0284 0.0345 480 1089 1.2895 0.0107 1.0013 0.1340 481 -228.4774 -0.2698 0.0077 1.0212 -0.0237 482 -1143 -1.3641 0.0248 1.0129 -0.2175 483 -1198 -1.4185 0.0088 0.9944 -0.1334 484 839.0254 0.9948 0.0140 1.0143 0.1183 485 105.7633 0.1256 0.0198 1.0347 0.0178 486 -1833 -2.1831 0.0155 0.9626 -0.2739 487 67.5403 0.0798 0.0086 1.0232 0.0074 488 236.1348 0.2795 0.0126 1.0263 0.0316 489 -584.5019 -0.6973 0.0271 1.0355 -0.1165 490 -638.2786 -0.7570 0.0153 1.0217 -0.0942 491 -209.1926 -0.2481 0.0165 1.0305 -0.0321 492 147.3582 0.1743 0.0107 1.0250 0.0182 493 614.1531 0.7243 0.0044 1.0113 0.0484 494 -2224 -2.6545 0.0146 0.9312 -0.3232 495 1272 1.5042 0.0055 0.9876 0.1121

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

————————————-DFBETAS————————————- Obs Intercept income water80 educat retired peop81 cpeop

451 -0.0523 -0.0900 0.3144 0.0030 0.0104 -0.0279 0.0326 452 -0.0238 -0.0085 0.0285 0.0273 -0.0051 -0.0054 0.0042 453 -0.0087 -0.0035 -0.0151 0.0129 -0.0155 0.0090 -0.0037 454 -0.0006 0.0021 0.0001 -0.0005 0.0015 -0.0010 -0.0001 455 0.0289 0.0115 -0.0282 -0.0334 0.0027 0.0062 -0.0044 456 -0.0636 0.0252 -0.0520 0.0662 -0.0461 0.0249 -0.0158 457 -0.0021 0.0056 -0.0019 0.0113 -0.0137 -0.0070 0.0016 458 0.0040 0.0049 -0.0036 -0.0139 -0.0009 0.0258 -0.0038 459 0.0145 0.0117 -0.1158 -0.0216 0.0190 0.0675 -0.0198 460 -0.0566 0.0052 0.0152 0.0558 -0.0221 -0.0059 -0.0027 461 0.0028 -0.0041 -0.0004 -0.0020 -0.0191 0.0020 -0.0022 462 0.0168 -0.0106 0.0191 -0.0214 -0.0095 0.0122 0.0009 463 0.0250 0.0176 -0.0052 -0.0384 -0.0186 0.0094 -0.0059 464 -0.0028 -0.0009 0.0022 0.0020 0.0020 -0.0002 0.0001 465 -0.0094 -0.0004 -0.0743 0.0083 0.0154 0.0457 -0.0124 466 -0.0742 0.0877 -0.1762 0.0417 0.0690 0.0928 -0.0341 467 0.0196 -0.0358 0.0119 0.0066 -0.0345 -0.0098 0.0066 468 -0.0009 0.0001 -0.0001 0.0006 -0.0009 0.0007 -0.0003 469 -0.0022 -0.0002 -0.0015 0.0011 0.0020 0.0027 -0.0006 470 -0.0688 0.0160 0.0166 0.0449 0.0477 0.0028 -0.0025 471 0.0228 0.0054 0.0157 -0.0329 0.0099 -0.0167 0.0017 472 0.0033 0.0236 -0.0682 -0.0023 -0.0333 0.0310 -0.0145 473 0.0519 -0.0080 0.0915 -0.0118 -0.0645 -0.1094 0.0254 474 0.0416 0.0697 0.0146 -0.0490 -0.0158 -0.0496 0.0039 475 -0.0347 0.0378 -0.1687 0.0683 0.0242 -0.0086 -0.0151 476 -0.0107 -0.0036 -0.0021 0.0093 -0.0129 0.0094 -0.0032 477 -0.0416 0.0335 -0.1556 0.0286 0.0341 0.1047 -0.0288 478 0.0421 0.0098 -0.0339 -0.0332 0.0067 -0.0390 0.0004 479 -0.0105 -0.0106 -0.0094 0.0264 -0.0117 -0.0042 0.0016 480 -0.0256 -0.0355 -0.0087 0.0631 0.0625 -0.0272 0.0164 481 -0.0024 0.0113 -0.0092 0.0020 0.0054 -0.0081 -0.0007 482 -0.0312 0.0329 -0.1977 0.0465 0.0225 0.0723 -0.0272 483 0.0322 0.0141 -0.1014 -0.0316 0.0158 0.0277 -0.0139 484 -0.0471 -0.0010 0.0470 0.0766 -0.0229 -0.0605 0.0141 485 -0.0041 -0.0061 0.0072 0.0115 -0.0057 -0.0105 0.0028 486 0.0044 -0.0751 -0.2147 0.0474 0.0025 0.0891 -0.0235 487 0.0004 0.0042 0.0011 0.0004 -0.0017 -0.0043 0.0005 488 -0.0058 -0.0030 -0.0010 0.0074 -0.0056 0.0079 -0.0261 489 0.0494 0.0021 -0.0666 -0.0524 0.0058 0.0329 0.0539 490 -0.0217 0.0378 -0.0186 -0.0075 0.0316 0.0200 -0.0780 491 0.0014 0.0144 0.0039 -0.0108 0.0082 -0.0052 -0.0234 492 0.0008 -0.0065 0.0121 0.0054 -0.0069 -0.0114 0.0033 493 0.0253 -0.0050 0.0082 -0.0227 -0.0190 0.0064 0.0011 494 0.0010 -0.1690 -0.1587 0.0026 0.0369 0.2100 -0.0319 495 0.0159 -0.0031 -0.0184 0.0365 -0.0588 -0.0479 0.0093

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

Hat Diag Cov Obs Residual RStudent H Ratio DFFITS

496 -1475 -1.7535 0.0143 0.9849 -0.2115

Output Statistics

————————————-DFBETAS————————————- Obs Intercept income water80 educat retired peop81 cpeop

496 -0.0050 -0.1796 -0.0178 0.0673 -0.0130 0.0179 0.0078

Sum of Residuals 0 Sum of Squared Residuals 352761188 Predicted Residual SS (PRESS) 371381058

The MEANS Procedure

Variable Label N Mean Std Dev Minimum Maximum ———————————————————————————————– DFB_income income DFBETAS 496 0.000440410 0.0907714 -0.2481540 1.3403712 DFB_water80 water80 DFBETAS 496 -0.000207389 0.0895012 -1.3878896 0.6845321 DFB_educat educat DFBETAS 496 -0.000197280 0.0434508 -0.3601133 0.1023189 DFB_retired retired DFBETAS 496 0.000068168 0.0445025 -0.2167040 0.2785343 DFB_peop81 peop81 DFBETAS 496 0.000074661 0.0612796 -0.4263415 0.4554408 DFB_cpeop cpeop DFBETAS 496 -0.000053492 0.0406626 -0.2337100 0.3507265 ———————————————————————————————–

page 127 Figure 4.10 Leverage plot of 1981 household water use versus income, adjusting for other predictors.

proc reg data=concy;
  model water81 = water80 educat retired peop81 cpeop peop80;
  output out=out11 (keep=case yres) residual=yres;
run;
quit;

The REG Procedure Model: MODEL1 Dependent Variable: water81

Analysis of Variance

Sum of Mean Source DF Squares Square F Value Pr > F

Model 5 714043771 142808754 184.54 <.0001 Error 490 379194939 773867 Corrected Total 495 1093238710

Root MSE 879.69723 R-Square 0.6531 Dependent Mean 2298.38710 Adj R-Sq 0.6496 Coeff Var 38.27455

peop80 = peop81 – cpeop

Parameter Estimates

Parameter Standard Variable DF Estimate Error t Value Pr > |t|

Intercept 1 291.34579 214.09047 1.36 0.1742 water80 1 0.52188 0.02680 19.47 <.0001 educat 1 -17.03541 13.01692 -1.31 0.1912 retired 1 47.74677 95.39495 0.50 0.6169 peop81 B 263.92288 29.62926 8.91 <.0001 cpeop B 134.89999 83.13626 1.62 0.1053 peop80 0 0 . . .

proc reg data=concy;
  model income = water80 educat retired peop81 cpeop peop80;
  output out=out12(keep=case xres) residual=xres;
run;
quit;

The REG Procedure Model: MODEL1 Dependent Variable: income

Analysis of Variance

Sum of Mean Source DF Squares Square F Value Pr > F

Model 5 24272 4854.34630 39.56 <.0001 Error 490 60129 122.71297 Corrected Total 495 84401

Root MSE 11.07759 R-Square 0.2876 Dependent Mean 23.07661 Adj R-Sq 0.2803 Coeff Var 48.00353

peop80 = peop81 – cpeop

Parameter Estimates

Parameter Standard Variable DF Estimate Error t Value Pr > |t|

Intercept 1 2.34299 2.69593 0.87 0.3852 water80 1 0.00143 0.00033753 4.23 <.0001 educat 1 1.18425 0.16392 7.22 <.0001 retired 1 -6.74572 1.20126 -5.62 <.0001 peop81 B 0.75003 0.37311 2.01 0.0450 cpeop B 1.83366 1.04689 1.75 0.0805 peop80 0 0 . . .

data both;
  merge out11 out12;
  by case;
run;
proc reg data=both;
  model yres=xres;
  output out=out13 h=lev;
run;
quit;

The REG Procedure Model: MODEL1 Dependent Variable: yres Residual

Analysis of Variance

Sum of Mean Source DF Squares Square F Value Pr > F

Model 1 26433751 26433751 37.02 <.0001 Error 494 352761188 714091 Corrected Total 495 379194939

Root MSE 845.03933 R-Square 0.0697 Dependent Mean 1.1002E-14 Adj R-Sq 0.0678 Coeff Var 7.680813E18

Parameter Estimates

Parameter Standard Variable Label DF Estimate Error t Value Pr > |t|

Intercept Intercept 1 6.92721E-14 37.94339 0.00 1.0000 xres Residual 1 20.96699 3.44615 6.08 <.0001

The interpol=r option is used to draw in the regression line.

symbol1 color=black interpol=r value=circle height=0.5;
axis1 order=(-30 to 70 by 10);
proc gplot data=out13;
  plot yres*xres=1 / haxis=axis1;
run; 
quit;

Figure 4.10

page 128 Figure 4.11 Proportional leverage plot (symbols proportional to DFBETAS) of 1981 household water use versus income, adjusting for five other predictors.

proc reg data=concy;
  model water81 = income water80 educat retired peop81 cpeop peop80 / influence;
  ods output OutputStatistics=out14;
run;
quit;

The REG Procedure Model: MODEL1 Dependent Variable: water81

Analysis of Variance

Sum of Mean Source DF Squares Square F Value Pr > F

Model 6 740477522 123412920 171.08 <.0001 Error 489 352761188 721393 Corrected Total 495 1093238710

Root MSE 849.34859 R-Square 0.6773 Dependent Mean 2298.38710 Adj R-Sq 0.6734 Coeff Var 36.95411

peop80 = peop81 – cpeop

Parameter Estimates

Parameter Standard Variable DF Estimate Error t Value Pr > |t|

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

Hat Diag Cov Obs Residual RStudent H Ratio DFFITS

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

————————————-DFBETAS————————————- Obs Intercept income water80 educat retired peop81 cpeop

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

Hat Diag Cov Obs Residual RStudent H Ratio DFFITS

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

————————————-DFBETAS————————————- Obs Intercept income water80 educat retired peop81 cpeop

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

Hat Diag Cov Obs Residual RStudent H Ratio DFFITS

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

————————————-DFBETAS————————————- Obs Intercept income water80 educat retired peop81 cpeop

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

Hat Diag Cov Obs Residual RStudent H Ratio DFFITS

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

————————————-DFBETAS————————————- Obs Intercept income water80 educat retired peop81 cpeop

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

Hat Diag Cov Obs Residual RStudent H Ratio DFFITS

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

————————————-DFBETAS————————————- Obs Intercept income water80 educat retired peop81 cpeop

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

Hat Diag Cov Obs Residual RStudent H Ratio DFFITS

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

————————————-DFBETAS————————————- Obs Intercept income water80 educat retired peop81 cpeop

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

Hat Diag Cov Obs Residual RStudent H Ratio DFFITS

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

————————————-DFBETAS————————————- Obs Intercept income water80 educat retired peop81 cpeop

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

Hat Diag Cov Obs Residual RStudent H Ratio DFFITS

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

————————————-DFBETAS————————————- Obs Intercept income water80 educat retired peop81 cpeop

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

Hat Diag Cov Obs Residual RStudent H Ratio DFFITS

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

————————————-DFBETAS————————————- Obs Intercept income water80 educat retired peop81 cpeop

< 361 -0.0008 0.0214 0.0549 0.0077 0.0920 -0.0765 0.0246 362 -0.0067 0.2032 -0.4302 -0.0920 0.1194 0.2967 0.1223 363 0.0006 0.0363 0.1094 -0.0249 -0.0076 -0.0414 0.0120 364 -0.0156 -0.0359 -0.0028 0.0521 -0.0368 0.0125 0.1605 365 -0.0174 0.0061 -0.0067 0.0185 0.0100 -0.0153 -0.0563 366 0.0093 -0.0112 -0.0033 0.0028 -0.0125 -0.0075 0.0022 367 -0.0063 -0.0315 -0.0205 0.0261 -0.0209 0.0243 -0.0010 368 0.0048 0.0068 0.0054 -0.0053 -0.0100 0.0040 0.0002 369 0.0259 -0.0031 0.0057 -0.0137 -0.0203 -0.0188 0.0041 370 -0.0012 0.0002 0.0038 0.0002 -0.0114 -0.0011 -0.0011 371 -0.0167 -0.0148 -0.0051 0.0223 0.0132 0.0099 0.0011 372 -0.0106 0.0017 0.0091 0.0087 -0.0162 -0.0035 -0.0014 373 0.0089 -0.0081 -0.0069 -0.0045 -0.0156 0.0034 0.0157 374 0.0036 0.0013 -0.0023 -0.0022 -0.0025 -0.0013 0.0001 375 -0.0004 0.0019 0.0013 -0.0013 -0.0022 0.0006 -0.0006 376 0.0195 -0.0076 0.0207 -0.0292 0.0069 -0.0041 0.0016 377 0.0701 -0.0401 -0.0105 -0.0323 -0.0617 -0.0051 0.0057 378 0.0196 -0.0155 0.0013 -0.0133 -0.0148 0.0072 0.0009 379 -0.0158 -0.0013 0.0022 0.0168 -0.0111 0.0001 -0.0014 380 -0.0006 0.0072 0.0200 0.0204 -0.0003 -0.0781 0.0110 381 0.2214 0.0178 0.0228 -0.1771 -0.1136 -0.1017 0.0184 382 -0.0118 0.0215 0.0151 -0.0003 0.0166 -0.0165 0.0009 383 -0.0158 0.0209 0.0150 0.0033 0.0206 -0.0187 0.0010 384 -0.0108 0.0032 0.0044 0.0043 0.0091 0.0037 -0.0008 385 0.0862 -0.0281 -0.0424 -0.0142 -0.0845 -0.0593 0.0110 386 -0.0468 -0.0768 0.0076 0.0776 -0.0550 0.0133 -0.0005 387 -0.0027 -0.0009 -0.0099 -0.0001 0.0292 0.0146 0.0006 388 0.0528 0.0203 -0.0704 -0.0093 -0.0582 -0.0206 -0.0002 389 0.0125 -0.0201 0.0057 -0.0054 0.0356 -0.0018 0.0074 390 -0.0017 -0.0007 0.0016 0.0017 -0.0054 -0.0003 -0.0005 391 -0.0051 -0.0454 -0.0232 0.0413 -0.0449 0.0179 -0.0997 392 -0.0178 -0.0193 0.0048 0.0271 0.0309 -0.0007 0.0060 393 -0.0113 -0.0036 0.0447 0.0020 0.0190 -0.0308 0.0062 394 0.0000 -0.0001 -0.0045 0.0059 -0.0053 -0.0049 0.0007 395 0.0008 -0.0001 -0.0000 -0.0004 -0.0006 -0.0005 0.0001 396 -0.0138 0.0070 0.0071 0.0064 -0.0106 0.0041 -0.0030 397 -0.0337 -0.0133 0.0045 0.0345 -0.0188 0.0128 -0.0036 398 0.0355 -0.1045 0.0346 -0.0062 -0.0875 0.0054 0.0024 399 0.0127 -0.0054 -0.0210 0.0007 -0.0182 0.0055 -0.0008 400 -0.0850 0.0039 -0.0053 0.0594 0.0508 0.0399 -0.0081 401 -0.0213 -0.1339 0.1118 0.0291 -0.0225 0.0671 0.1744 402 0.0034 0.0014 0.0012 -0.0030 -0.0048 -0.0038 0.0000 403 -0.0221 -0.0228 -0.0139 0.0543 -0.0238 -0.0111 0.0040 404 0.0004 -0.0016 -0.0083 -0.0058 -0.0001 0.0235 -0.0035 405 -0.0015 -0.0209 -0.0023 0.0097 -0.0158 0.0056 -0.0006 The REG Procedure Model: MODEL1 Dependent Variable: water81 Output Statistics Hat Diag Cov Obs Residual RStudent H Ratio DFFITS 406 -195.9041 -0.2315 0.0095 1.0234 -0.0227 407 -78.8265 -0.0932 0.0097 1.0242 -0.0092 408 -608.7011 -0.7262 0.0270 1.0348 -0.1210 409 377.8136 0.4461 0.0075 1.0192 0.0387 410 -202.6945 -0.2396 0.0098 1.0236 -0.0239 411 -202.0795 -0.2390 0.0110 1.0249 -0.0252 412 -959.2449 -1.1344 0.0083 1.0042 -0.1039 413 -429.0443 -0.5072 0.0096 1.0205 -0.0500 414 -341.3772 -0.4067 0.0251 1.0381 -0.0652 415 -247.2054 -0.2913 0.0036 1.0168 -0.0175 416 703.0921 0.8327 0.0123 1.0169 0.0929 417 -1703 -2.0314 0.0195 0.9754 -0.2865 418 -163.1994 -0.1925 0.0061 1.0201 -0.0150 419 -376.9749 -0.4445 0.0045 1.0161 -0.0298 420 423.5643 0.4997 0.0057 1.0166 0.0377 421 444.0551 0.5260 0.0136 1.0244 0.0618 422 -391.0959 -0.4621 0.0088 1.0203 -0.0436 423 51.7406 0.0613 0.0144 1.0292 0.0074 424 203.2925 0.2404 0.0105 1.0244 0.0248 425 14.9839 0.0177 0.0124 1.0272 0.0020 426 287.9200 0.3405 0.0105 1.0235 0.0350 427 596.4106 0.7064 0.0129 1.0203 0.0807 428 275.8699 0.3257 0.0074 1.0205 0.0282 429 595.9706 0.7033 0.0055 1.0129 0.0524 430 -162.1483 -0.1923 0.0162 1.0305 -0.0246 431 -797.9310 -0.9436 0.0089 1.0106 -0.0894 432 1207 1.4383 0.0212 1.0061 0.2114 433 87.5537 0.1037 0.0138 1.0285 0.0123 434 221.0290 0.2609 0.0070 1.0206 0.0219 435 2109 2.5030 0.0057 0.9331 0.1896 436 781.4270 0.9248 0.0106 1.0128 0.0956 437 -75.2078 -0.0893 0.0186 1.0335 -0.0123 438 -221.4429 -0.2615 0.0081 1.0218 -0.0237 439 -947.1840 -1.1292 0.0241 1.0207 -0.1776 440 348.6399 0.4116 0.0070 1.0191 0.0346 441 -123.5610 -0.1458 0.0067 1.0210 -0.0120 442 -207.3657 -0.2464 0.0202 1.0345 -0.0354 443 -193.4824 -0.2286 0.0086 1.0224 -0.0212 444 -119.2329 -0.1405 0.0042 1.0184 -0.0091 445 -723.8175 -0.8762 0.0544 1.0611 -0.2102 446 1094 1.3068 0.0271 1.0175 0.2181 447 -365.9584 -0.4329 0.0110 1.0230 -0.0457 448 561.5204 0.6741 0.0392 1.0489 0.1361 449 -468.1724 -0.5518 0.0035 1.0136 -0.0328 450 -687.0289 -0.8113 0.0066 1.0116 -0.0661 The REG Procedure Model: MODEL1 Dependent Variable: water81 Output Statistics -------------------------------------DFBETAS------------------------------------- Obs Intercept income water80 educat retired peop81 cpeop 406 -0.0154 0.0109 0.0063 0.0039 0.0144 0.0039 -0.0015 407 -0.0031 0.0023 0.0020 0.0007 -0.0035 0.0014 -0.0010 408 -0.0150 0.0034 -0.1116 0.0195 0.0135 0.0631 -0.0174 409 0.0081 -0.0066 -0.0016 -0.0051 0.0238 0.0003 0.0037 410 -0.0108 0.0058 0.0014 0.0087 -0.0110 -0.0008 -0.0020 411 -0.0132 0.0055 -0.0045 0.0092 -0.0092 0.0083 -0.0037 412 -0.0376 0.0523 -0.0587 0.0241 0.0366 0.0042 -0.0102 413 -0.0217 0.0112 -0.0336 0.0082 0.0218 0.0339 -0.0088 414 0.0333 0.0215 0.0087 -0.0400 0.0054 -0.0289 0.0397 415 -0.0068 0.0027 0.0003 0.0046 0.0075 -0.0045 -0.0000 416 0.0272 -0.0049 -0.0207 -0.0134 -0.0322 0.0095 -0.0770 417 -0.0715 -0.0516 -0.1175 0.0353 0.0816 0.1759 0.1542 418 -0.0091 0.0030 -0.0038 0.0083 0.0058 -0.0012 -0.0006 419 -0.0152 -0.0003 -0.0057 0.0151 0.0107 -0.0030 -0.0006 420 -0.0089 0.0222 -0.0039 0.0047 -0.0026 0.0046 -0.0018 421 -0.0261 -0.0228 -0.0175 0.0502 -0.0171 0.0063 0.0011 422 0.0168 0.0080 0.0213 -0.0276 0.0098 -0.0182 0.0023 423 0.0020 0.0004 -0.0022 -0.0021 -0.0017 0.0025 -0.0061 424 0.0021 -0.0081 -0.0067 0.0058 0.0096 -0.0024 0.0025 425 -0.0002 0.0005 -0.0000 0.0003 -0.0004 -0.0001 -0.0016 426 0.0046 -0.0057 -0.0074 -0.0089 -0.0039 0.0268 -0.0034 427 0.0187 0.0087 0.0070 -0.0065 -0.0189 -0.0215 0.0689 428 0.0208 -0.0113 -0.0028 -0.0071 -0.0185 -0.0091 0.0027 429 0.0343 0.0092 -0.0108 -0.0159 -0.0298 -0.0234 0.0034 430 -0.0072 0.0042 -0.0022 0.0048 -0.0077 0.0040 0.0152 431 -0.0392 -0.0150 0.0643 0.0322 0.0272 -0.0411 0.0095 432 -0.0449 -0.1138 0.0164 0.0691 -0.0375 0.0855 -0.1321 433 -0.0006 -0.0046 -0.0006 0.0039 -0.0041 0.0009 -0.0091 434 0.0158 -0.0074 0.0053 -0.0066 -0.0136 -0.0113 0.0030 435 0.0799 0.0002 0.0926 -0.0880 -0.0539 -0.0123 0.0113 436 0.0042 -0.0568 -0.0409 0.0420 -0.0443 0.0188 0.0013 437 0.0068 0.0015 0.0033 -0.0054 -0.0010 -0.0101 0.0014 438 -0.0019 -0.0005 0.0091 0.0003 -0.0148 -0.0033 -0.0009 439 0.0113 0.0192 0.0475 0.0277 -0.0084 -0.1595 0.0231 440 0.0218 -0.0172 -0.0096 -0.0075 -0.0205 0.0026 0.0012 441 -0.0037 0.0030 0.0016 0.0037 0.0032 -0.0070 0.0007 442 -0.0164 -0.0238 -0.0054 0.0163 0.0072 0.0230 -0.0022 443 -0.0011 0.0043 0.0001 -0.0040 -0.0107 0.0059 -0.0030 444 -0.0036 0.0003 0.0045 0.0003 0.0050 -0.0005 0.0001 445 0.0211 0.0183 -0.0473 0.0244 -0.0773 -0.0659 0.1631 446 -0.0220 -0.0275 0.1972 -0.0089 0.0004 -0.0394 0.0218 447 -0.0132 0.0218 -0.0345 0.0033 0.0167 0.0183 -0.0073 448 0.0322 0.0153 0.0095 -0.0288 -0.0275 -0.0190 -0.1219 449 -0.0128 0.0029 0.0010 0.0094 0.0137 -0.0083 0.0001 450 -0.0474 -0.0093 -0.0152 0.0309 0.0337 0.0404 -0.0075 The REG Procedure Model: MODEL1 Dependent Variable: water81 Output Statistics Hat Diag Cov Obs Residual RStudent H Ratio DFFITS 451 1364 1.6446 0.0437 1.0205 0.3516 452 431.4733 0.5100 0.0092 1.0200 0.0490 453 -205.1153 -0.2429 0.0136 1.0276 -0.0285 454 -39.2160 -0.0462 0.0053 1.0198 -0.0034 455 -330.7656 -0.3921 0.0154 1.0280 -0.0491 456 -821.1114 -0.9744 0.0158 1.0168 -0.1235 457 476.5952 0.5618 0.0038 1.0137 0.0345 458 325.0201 0.3842 0.0098 1.0223 0.0382 459 -894.3886 -1.0614 0.0155 1.0139 -0.1330 460 -483.8646 -0.5748 0.0190 1.0292 -0.0801 461 -244.9013 -0.2891 0.0073 1.0207 -0.0248 462 426.5026 0.5040 0.0089 1.0198 0.0478 463 -288.2592 -0.3427 0.0208 1.0342 -0.0499 464 -46.5100 -0.0549 0.0060 1.0205 -0.0043 465 -630.5377 -0.7470 0.0132 1.0199 -0.0865 466 -1503 -1.7868 0.0148 0.9837 -0.2191 467 708.9811 0.8366 0.0049 1.0093 0.0590 468 -17.4669 -0.0206 0.0091 1.0238 -0.0020 469 -41.9393 -0.0495 0.0063 1.0208 -0.0039 470 -915.8035 -1.0817 0.0061 1.0037 -0.0846 471 -498.3548 -0.5884 0.0069 1.0164 -0.0491 472 -446.4687 -0.5315 0.0234 1.0346 -0.0823 473 1456 1.7238 0.0076 0.9797 0.1512 474 647.6613 0.7682 0.0155 1.0217 0.0962 475 -1804 -2.1451 0.0122 0.9616 -0.2381 476 -220.6899 -0.2608 0.0094 1.0230 -0.0254 477 -743.5057 -0.8911 0.0354 1.0398 -0.1708 478 -1154 -1.3646 0.0061 0.9938 -0.1069 479 238.2221 0.2823 0.0147 1.0284 0.0345 480 1089 1.2895 0.0107 1.0013 0.1340 481 -228.4774 -0.2698 0.0077 1.0212 -0.0237 482 -1143 -1.3641 0.0248 1.0129 -0.2175 483 -1198 -1.4185 0.0088 0.9944 -0.1334 484 839.0254 0.9948 0.0140 1.0143 0.1183 485 105.7633 0.1256 0.0198 1.0347 0.0178 486 -1833 -2.1831 0.0155 0.9626 -0.2739 487 67.5403 0.0798 0.0086 1.0232 0.0074 488 236.1348 0.2795 0.0126 1.0263 0.0316 489 -584.5019 -0.6973 0.0271 1.0355 -0.1165 490 -638.2786 -0.7570 0.0153 1.0217 -0.0942 491 -209.1926 -0.2481 0.0165 1.0305 -0.0321 492 147.3582 0.1743 0.0107 1.0250 0.0182 493 614.1531 0.7243 0.0044 1.0113 0.0484 494 -2224 -2.6545 0.0146 0.9312 -0.3232 495 1272 1.5042 0.0055 0.9876 0.1121 The REG Procedure Model: MODEL1 Dependent Variable: water81 Output Statistics -------------------------------------DFBETAS------------------------------------- Obs Intercept income water80 educat retired peop81 cpeop 451 -0.0523 -0.0900 0.3144 0.0030 0.0104 -0.0279 0.0326 452 -0.0238 -0.0085 0.0285 0.0273 -0.0051 -0.0054 0.0042 453 -0.0087 -0.0035 -0.0151 0.0129 -0.0155 0.0090 -0.0037 454 -0.0006 0.0021 0.0001 -0.0005 0.0015 -0.0010 -0.0001 455 0.0289 0.0115 -0.0282 -0.0334 0.0027 0.0062 -0.0044 456 -0.0636 0.0252 -0.0520 0.0662 -0.0461 0.0249 -0.0158 457 -0.0021 0.0056 -0.0019 0.0113 -0.0137 -0.0070 0.0016 458 0.0040 0.0049 -0.0036 -0.0139 -0.0009 0.0258 -0.0038 459 0.0145 0.0117 -0.1158 -0.0216 0.0190 0.0675 -0.0198 460 -0.0566 0.0052 0.0152 0.0558 -0.0221 -0.0059 -0.0027 461 0.0028 -0.0041 -0.0004 -0.0020 -0.0191 0.0020 -0.0022 462 0.0168 -0.0106 0.0191 -0.0214 -0.0095 0.0122 0.0009 463 0.0250 0.0176 -0.0052 -0.0384 -0.0186 0.0094 -0.0059 464 -0.0028 -0.0009 0.0022 0.0020 0.0020 -0.0002 0.0001 465 -0.0094 -0.0004 -0.0743 0.0083 0.0154 0.0457 -0.0124 466 -0.0742 0.0877 -0.1762 0.0417 0.0690 0.0928 -0.0341 467 0.0196 -0.0358 0.0119 0.0066 -0.0345 -0.0098 0.0066 468 -0.0009 0.0001 -0.0001 0.0006 -0.0009 0.0007 -0.0003 469 -0.0022 -0.0002 -0.0015 0.0011 0.0020 0.0027 -0.0006 470 -0.0688 0.0160 0.0166 0.0449 0.0477 0.0028 -0.0025 471 0.0228 0.0054 0.0157 -0.0329 0.0099 -0.0167 0.0017 472 0.0033 0.0236 -0.0682 -0.0023 -0.0333 0.0310 -0.0145 473 0.0519 -0.0080 0.0915 -0.0118 -0.0645 -0.1094 0.0254 474 0.0416 0.0697 0.0146 -0.0490 -0.0158 -0.0496 0.0039 475 -0.0347 0.0378 -0.1687 0.0683 0.0242 -0.0086 -0.0151 476 -0.0107 -0.0036 -0.0021 0.0093 -0.0129 0.0094 -0.0032 477 -0.0416 0.0335 -0.1556 0.0286 0.0341 0.1047 -0.0288 478 0.0421 0.0098 -0.0339 -0.0332 0.0067 -0.0390 0.0004 479 -0.0105 -0.0106 -0.0094 0.0264 -0.0117 -0.0042 0.0016 480 -0.0256 -0.0355 -0.0087 0.0631 0.0625 -0.0272 0.0164 481 -0.0024 0.0113 -0.0092 0.0020 0.0054 -0.0081 -0.0007 482 -0.0312 0.0329 -0.1977 0.0465 0.0225 0.0723 -0.0272 483 0.0322 0.0141 -0.1014 -0.0316 0.0158 0.0277 -0.0139 484 -0.0471 -0.0010 0.0470 0.0766 -0.0229 -0.0605 0.0141 485 -0.0041 -0.0061 0.0072 0.0115 -0.0057 -0.0105 0.0028 486 0.0044 -0.0751 -0.2147 0.0474 0.0025 0.0891 -0.0235 487 0.0004 0.0042 0.0011 0.0004 -0.0017 -0.0043 0.0005 488 -0.0058 -0.0030 -0.0010 0.0074 -0.0056 0.0079 -0.0261 489 0.0494 0.0021 -0.0666 -0.0524 0.0058 0.0329 0.0539 490 -0.0217 0.0378 -0.0186 -0.0075 0.0316 0.0200 -0.0780 491 0.0014 0.0144 0.0039 -0.0108 0.0082 -0.0052 -0.0234 492 0.0008 -0.0065 0.0121 0.0054 -0.0069 -0.0114 0.0033 493 0.0253 -0.0050 0.0082 -0.0227 -0.0190 0.0064 0.0011 494 0.0010 -0.1690 -0.1587 0.0026 0.0369 0.2100 -0.0319 495 0.0159 -0.0031 -0.0184 0.0365 -0.0588 -0.0479 0.0093 The REG Procedure Model: MODEL1 Dependent Variable: water81 Output Statistics Hat Diag Cov Obs Residual RStudent H Ratio DFFITS 496 -1475 -1.7535 0.0143 0.9849 -0.2115 Output Statistics -------------------------------------DFBETAS------------------------------------- Obs Intercept income water80 educat retired peop81 cpeop 496 -0.0050 -0.1796 -0.0178 0.0673 -0.0130 0.0179 0.0078 Sum of Residuals 0 Sum of Squared Residuals 352761188 Predicted Residual SS (PRESS) 371381058

proc reg data=concy;
  model water81 = water80 educat retired peop81 cpeop peop80;
  output out=out11 residual=yres;
run;
quit;

The REG Procedure Model: MODEL1 Dependent Variable: water81

Analysis of Variance

Sum of Mean Source DF Squares Square F Value Pr > F

Model 5 714043771 142808754 184.54 <.0001 Error 490 379194939 773867 Corrected Total 495 1093238710

Root MSE 879.69723 R-Square 0.6531 Dependent Mean 2298.38710 Adj R-Sq 0.6496 Coeff Var 38.27455

peop80 = peop81 – cpeop

Parameter Estimates

Parameter Standard Variable DF Estimate Error t Value Pr > |t|

proc reg data=concy;
  model income = water80 educat retired peop81 cpeop peop80;
  output out=out12 residual=xres;
run;
quit;

The REG Procedure Model: MODEL1 Dependent Variable: income

Analysis of Variance

Sum of Mean Source DF Squares Square F Value Pr > F

Model 5 24272 4854.34630 39.56 <.0001 Error 490 60129 122.71297 Corrected Total 495 84401

Root MSE 11.07759 R-Square 0.2876 Dependent Mean 23.07661 Adj R-Sq 0.2803 Coeff Var 48.00353

peop80 = peop81 – cpeop

Parameter Estimates

Parameter Standard Variable DF Estimate Error t Value Pr > |t|

data out12_1;
set out12;
Observation=_n_;
run;
data out11_1;
set out11;
Observation=_n_;
run;
data both;
  merge out11_1 out12_1 out14;
  by Observation;
  keep xres yres DFB_income case;
run;
proc reg data=both;
  model yres=xres;
  output out=both_1 p=ypred;
run;
quit;

The REG Procedure Model: MODEL1 Dependent Variable: yres Residual

Analysis of Variance

Sum of Mean Source DF Squares Square F Value Pr > F

Model 1 26433751 26433751 37.02 <.0001 Error 494 352761188 714091 Corrected Total 495 379194939

Root MSE 845.03933 R-Square 0.0697 Dependent Mean 1.1002E-14 Adj R-Sq 0.0678 Coeff Var 7.680813E18

Parameter Estimates

Parameter Standard Variable Label DF Estimate Error t Value Pr > |t|

Intercept Intercept 1 6.92721E-14 37.94339 0.00 1.0000 xres Residual 1 20.96699 3.44615 6.08 <.0001

We again need to use an annotated data set to make this graph. The bsize=10 option tells SAS to set the bubble size to 10. The default is much smaller, and without this option, it the smaller points look like dots instead of circles.

proc sort data=both_1;
by xres;
run;
 
data anno_both;
set both_1 nobs=total;
length function color $8;
retain xsys ysys '2' size 1 color 'red';
 if _n_=1 then do;
 function='move'; x=xres; y=ypred; output; end;
 if _n_=total then do;
 function='draw'; x=xres; y=ypred; output; end;
run;
axis1 order=(-30 to 70 by 10);
proc gplot data=both;
  bubble yres*xres=DFB_income / anno=anno_both bsize=10 haxis=axis1;
run;
quit;

Figure 4.11

page 129 Figure 4.12 Proportional leverage plot of 1981 household water use versus 1980 water use, adjusting for five other predictors.

proc reg data=concy;
  model water81 = income water80 educat retired peop81 cpeop peop80 / influence;
  ods output OutputStatistics=out20;
run;
quit;

The REG Procedure Model: MODEL1 Dependent Variable: water81

Analysis of Variance

Sum of Mean Source DF Squares Square F Value Pr > F

Model 6 740477522 123412920 171.08 <.0001 Error 489 352761188 721393 Corrected Total 495 1093238710

Root MSE 849.34859 R-Square 0.6773 Dependent Mean 2298.38710 Adj R-Sq 0.6734 Coeff Var 36.95411

peop80 = peop81 – cpeop

Parameter Estimates

Parameter Standard Variable DF Estimate Error t Value Pr > |t|

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

Hat Diag Cov Obs Residual RStudent H Ratio DFFITS

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

————————————-DFBETAS————————————- Obs Intercept income water80 educat retired peop81 cpeop

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

Hat Diag Cov Obs Residual RStudent H Ratio DFFITS

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

————————————-DFBETAS————————————- Obs Intercept income water80 educat retired peop81 cpeop

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

Hat Diag Cov Obs Residual RStudent H Ratio DFFITS

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

————————————-DFBETAS————————————- Obs Intercept income water80 educat retired peop81 cpeop

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

Hat Diag Cov Obs Residual RStudent H Ratio DFFITS

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

————————————-DFBETAS————————————- Obs Intercept income water80 educat retired peop81 cpeop

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

Hat Diag Cov Obs Residual RStudent H Ratio DFFITS

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

————————————-DFBETAS————————————- Obs Intercept income water80 educat retired peop81 cpeop

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

Hat Diag Cov Obs Residual RStudent H Ratio DFFITS

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

————————————-DFBETAS————————————- Obs Intercept income water80 educat retired peop81 cpeop

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

Hat Diag Cov Obs Residual RStudent H Ratio DFFITS

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

————————————-DFBETAS————————————- Obs Intercept income water80 educat retired peop81 cpeop

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

Hat Diag Cov Obs Residual RStudent H Ratio DFFITS

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

————————————-DFBETAS————————————- Obs Intercept income water80 educat retired peop81 cpeop

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

Hat Diag Cov Obs Residual RStudent H Ratio DFFITS

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

————————————-DFBETAS————————————- Obs Intercept income water80 educat retired peop81 cpeop

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

Hat Diag Cov Obs Residual RStudent H Ratio DFFITS

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

————————————-DFBETAS————————————- Obs Intercept income water80 educat retired peop81 cpeop

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

Hat Diag Cov Obs Residual RStudent H Ratio DFFITS

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

————————————-DFBETAS————————————- Obs Intercept income water80 educat retired peop81 cpeop

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

Hat Diag Cov Obs Residual RStudent H Ratio DFFITS

496 -1475 -1.7535 0.0143 0.9849 -0.2115

Output Statistics

————————————-DFBETAS————————————- Obs Intercept income water80 educat retired peop81 cpeop

496 -0.0050 -0.1796 -0.0178 0.0673 -0.0130 0.0179 0.0078

Sum of Residuals 0 Sum of Squared Residuals 352761188 Predicted Residual SS (PRESS) 371381058

proc reg data=concy;
  model water81 = income educat retired peop81 cpeop peop80;
  output out=out21 residual=yres;
run;
quit;

The REG Procedure Model: MODEL1 Dependent Variable: water81

Analysis of Variance

Sum of Mean Source DF Squares Square F Value Pr > F

Model 5 488996056 97799211 79.31 <.0001 Error 490 604242653 1233148 Corrected Total 495 1093238710

Root MSE 1110.47209 R-Square 0.4473 Dependent Mean 2298.38710 Adj R-Sq 0.4417 Coeff Var 48.31528

peop80 = peop81 – cpeop

Parameter Estimates

Parameter Standard Variable DF Estimate Error t Value Pr > |t|

Intercept 1 586.03373 269.38829 2.18 0.0301 income 1 33.10548 4.44812 7.44 <.0001 educat 1 -42.21332 17.28474 -2.44 0.0149 retired 1 84.66143 124.01899 0.68 0.4952 peop81 B 491.51608 33.46848 14.69 <.0001 cpeop B -114.97998 104.22744 -1.10 0.2705 peop80 0 0 . . .

proc reg data=concy;
  model water80 = income educat retired peop81 cpeop peop80;
  output out=out22 residual=xres;
run;
quit;

The REG Procedure Model: MODEL1 Dependent Variable: water80

Analysis of Variance

Sum of Mean Source DF Squares Square F Value Pr > F

Model 5 500781798 100156360 47.23 <.0001 Error 490 1039158505 2120732 Corrected Total 495 1539940302

Root MSE 1456.27320 R-Square 0.3252 Dependent Mean 2732.05645 Adj R-Sq 0.3183 Coeff Var 53.30319

peop80 = peop81 – cpeop

Parameter Estimates

Parameter Standard Variable DF Estimate Error t Value Pr > |t|

Intercept 1 698.89282 353.27582 1.98 0.0485 income 1 24.67473 5.83326 4.23 <.0001 educat 1 -0.70700 22.66721 -0.03 0.9751 retired 1 -212.47084 162.63851 -1.31 0.1920 peop81 B 494.61130 43.89057 11.27 <.0001 cpeop B -429.79551 136.68387 -3.14 0.0018 peop80 0 0 . . .

data out22_1;
set out22;
Observation=_n_;
run;
data out21_1;
set out21;
Observation=_n_;
run;
data both20;
  merge out21_1 out22_1 out20;
  by Observation;
  keep xres yres DFB_water80 case;
run;
proc reg data=both20;
  model yres=xres;
  output out=both20_1 p=ypred;
run;
quit;

The REG Procedure Model: MODEL1 Dependent Variable: yres Residual

Analysis of Variance

Sum of Mean Source DF Squares Square F Value Pr > F

Model 1 251481466 251481466 352.17 <.0001 Error 494 352761188 714091 Corrected Total 495 604242653

Root MSE 845.03933 R-Square 0.4162 Dependent Mean 1.63196E-13 Adj R-Sq 0.4150 Coeff Var 5.178076E17

Parameter Estimates

Parameter Standard Variable Label DF Estimate Error t Value Pr > |t|

Intercept Intercept 1 9.5711E-14 37.94339 0.00 1.0000 xres Residual 1 0.49194 0.02621 18.77 <.0001

proc sort data=both20_1;
by xres;
run;
data anno_both20;
set both20_1 nobs=total;
length function color $8;
retain xsys ysys '2' size 1 color 'red';
 if _n_=1 then do;
 function='move'; x=xres; y=ypred; output; end;
 if _n_=total then do;
 function='draw'; x=xres; y=ypred; output; end;
run;
axis1 order=(-4000 to 10000 by 2000);
proc gplot data=both20;
 bubble yres*xres=DFB_water80 / anno=anno_both20 bsize=10 haxis=axis1;
run;
quit;

Figure 4.12

page 129 Figure 4.13 Proportional leverage plots of 1981 household water use versus X, each adjusting for five other predictors. This is done just as the above two were done, substituting the correct variables.

More Case Statistics

page 133 Table 4.4 Case statistics for three influential households (see Figures 4.11 and 4.12).

proc reg data=concy;
 model water81 = income water80 educat retired peop81 cpeop ;
 output out=concy1 cookd=cookd r=res;
run;
quit;

The REG Procedure Model: MODEL1 Dependent Variable: water81

Analysis of Variance

Sum of Mean Source DF Squares Square F Value Pr > F

Model 6 740477522 123412920 171.08 <.0001 Error 489 352761188 721393 Corrected Total 495 1093238710

Root MSE 849.34859 R-Square 0.6773 Dependent Mean 2298.38710 Adj R-Sq 0.6734 Coeff Var 36.95411

Parameter Estimates

Parameter Standard Variable DF Estimate Error t Value Pr > |t|

Intercept 1 242.22043 206.86382 1.17 0.2422 income 1 20.96699 3.46372 6.05 <.0001 water80 1 0.49194 0.02635 18.67 <.0001 educat 1 -41.86552 13.22031 -3.17 0.0016 retired 1 189.18433 95.02142 1.99 0.0470 peop81 1 248.19702 28.72480 8.64 <.0001 cpeop 1 96.45360 80.51903 1.20 0.2315

proc reg data = concy1;
 model water81 = income water80 educat retired peop81 cpeop / influence;
 ods output OutputStatistics=outb1;
run;
quit;

The REG Procedure Model: MODEL1 Dependent Variable: water81

Analysis of Variance

Sum of Mean Source DF Squares Square F Value Pr > F

Model 6 740477522 123412920 171.08 <.0001 Error 489 352761188 721393 Corrected Total 495 1093238710

Root MSE 849.34859 R-Square 0.6773 Dependent Mean 2298.38710 Adj R-Sq 0.6734 Coeff Var 36.95411

Parameter Estimates

Parameter Standard Variable DF Estimate Error t Value Pr > |t|

Intercept 1 242.22043 206.86382 1.17 0.2422 income 1 20.96699 3.46372 6.05 <.0001 water80 1 0.49194 0.02635 18.67 <.0001 educat 1 -41.86552 13.22031 -3.17 0.0016 retired 1 189.18433 95.02142 1.99 0.0470 peop81 1 248.19702 28.72480 8.64 <.0001 cpeop 1 96.45360 80.51903 1.20 0.2315

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

Hat Diag Cov Obs Residual RStudent H Ratio DFFITS

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

————————————-DFBETAS————————————- Obs Intercept income water80 educat retired peop81 cpeop

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

Hat Diag Cov Obs Residual RStudent H Ratio DFFITS

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

————————————-DFBETAS————————————- Obs Intercept income water80 educat retired peop81 cpeop

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

Hat Diag Cov Obs Residual RStudent H Ratio DFFITS

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

————————————-DFBETAS————————————- Obs Intercept income water80 educat retired peop81 cpeop

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

Hat Diag Cov Obs Residual RStudent H Ratio DFFITS

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

————————————-DFBETAS————————————- Obs Intercept income water80 educat retired peop81 cpeop

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

Hat Diag Cov Obs Residual RStudent H Ratio DFFITS

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

————————————-DFBETAS————————————- Obs Intercept income water80 educat retired peop81 cpeop

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

Hat Diag Cov Obs Residual RStudent H Ratio DFFITS

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

————————————-DFBETAS————————————- Obs Intercept income water80 educat retired peop81 cpeop

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

Hat Diag Cov Obs Residual RStudent H Ratio DFFITS

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

————————————-DFBETAS————————————- Obs Intercept income water80 educat retired peop81 cpeop

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

Hat Diag Cov Obs Residual RStudent H Ratio DFFITS

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

————————————-DFBETAS————————————- Obs Intercept income water80 educat retired peop81 cpeop

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

Hat Diag Cov Obs Residual RStudent H Ratio DFFITS

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

————————————-DFBETAS————————————- Obs Intercept income water80 educat retired peop81 cpeop

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

Hat Diag Cov Obs Residual RStudent H Ratio DFFITS

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

————————————-DFBETAS————————————- Obs Intercept income water80 educat retired peop81 cpeop

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

Hat Diag Cov Obs Residual RStudent H Ratio DFFITS

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

————————————-DFBETAS————————————- Obs Intercept income water80 educat retired peop81 cpeop

The REG Procedure Model: MODEL1 Dependent Variable: water81

Output Statistics

Hat Diag Cov Obs Residual RStudent H Ratio DFFITS

496 -1475 -1.7535 0.0143 0.9849 -0.2115

Output Statistics

————————————-DFBETAS————————————- Obs Intercept income water80 educat retired peop81 cpeop

496 -0.0050 -0.1796 -0.0178 0.0673 -0.0130 0.0179 0.0078

Sum of Residuals 0 Sum of Squared Residuals 352761188 Predicted Residual SS (PRESS) 371381058

proc means std mean data=concy1;
 var res;
run;
data concy2;
set concy1;
Observation=_n_;
stdres=(res+2.24623E-14)/ 844.1853256;
keep Observation stdres cookd case;
run;
data outb2;
merge  outb1 concy2;
by Observation;
keep case Residual HatDiagonal stdres Rstudent cookd DFB_income DFB_water80;
run;
proc print data=outb2 noobs;
var case Residual HatDiagonal stdres Rstudent cookd DFB_income DFB_water80; 
where cookd>= .15;
run;

The MEANS Procedure

Analysis Variable : res Residual

Std Dev Mean —————————- 844.1853256 -2.24623E-14 —————————- Hat DFB_ DFB_ case Residual Diagonal stdres RStudent cookd income water80

101 -4037 0.0817 -4.78218 -5.0846 0.31284 0.0630 -1.3879 127 3316 0.0616 3.92756 4.0942 0.15232 0.9804 -0.1809 134 3687 0.0904 4.36766 4.6465 0.29407 1.3404 0.2510

Symptoms of Multicollinearity

page 134 Table 4.5 Checking for multicollinearity: tolerances of X variables in water-use regression.

proc reg data=concy;
 model income=water80 educat retired peop80 cpeop;
 model water80=income educat retired peop80 cpeop;
 model educat=income water80 retired peop80 cpeop;
 model retired=income water80 educat peop80 cpeop;
 model peop80=income water80 educat retired cpeop;
 model cpeop=income water80 educat retired peop80;
run;
quit;

The REG Procedure Model: MODEL1 Dependent Variable: income

Analysis of Variance

Sum of Mean Source DF Squares Square F Value Pr > F

Model 5 24272 4854.34630 39.56 <.0001 Error 490 60129 122.71297 Corrected Total 495 84401

Root MSE 11.07759 R-Square 0.2876 Dependent Mean 23.07661 Adj R-Sq 0.2803 Coeff Var 48.00353

Parameter Estimates

Parameter Standard Variable DF Estimate Error t Value Pr > |t|

Intercept 1 2.34299 2.69593 0.87 0.3852 water80 1 0.00143 0.00033753 4.23 <.0001 educat 1 1.18425 0.16392 7.22 <.0001 retired 1 -6.74572 1.20126 -5.62 <.0001 peop80 1 0.75003 0.37311 2.01 0.0450 cpeop 1 2.58369 1.04743 2.47 0.0140

The REG Procedure Model: MODEL2 Dependent Variable: water80

Analysis of Variance

Sum of Mean Source DF Squares Square F Value Pr > F

Model 5 500781798 100156360 47.23 <.0001 Error 490 1039158505 2120732 Corrected Total 495 1539940302

Root MSE 1456.27320 R-Square 0.3252 Dependent Mean 2732.05645 Adj R-Sq 0.3183 Coeff Var 53.30319

Parameter Estimates

Parameter Standard Variable DF Estimate Error t Value Pr > |t|

Intercept 1 698.89282 353.27582 1.98 0.0485 income 1 24.67473 5.83326 4.23 <.0001 educat 1 -0.70700 22.66721 -0.03 0.9751 retired 1 -212.47084 162.63851 -1.31 0.1920 peop80 1 494.61130 43.89057 11.27 <.0001 cpeop 1 64.81579 138.51756 0.47 0.6400

The REG Procedure Model: MODEL3 Dependent Variable: educat

Analysis of Variance

Sum of Mean Source DF Squares Square F Value Pr > F

Model 5 600.47544 120.09509 14.26 <.0001 Error 490 4127.51649 8.42350 Corrected Total 495 4727.99194

Root MSE 2.90233 R-Square 0.1270 Dependent Mean 14.00403 Adj R-Sq 0.1181 Coeff Var 20.72494

Parameter Estimates

Parameter Standard Variable DF Estimate Error t Value Pr > |t|

Intercept 1 12.68463 0.41390 30.65 <.0001 income 1 0.08129 0.01125 7.22 <.0001 water80 1 -0.00000281 0.00009003 -0.03 0.9751 retired 1 -0.48787 0.32395 -1.51 0.1327 peop80 1 -0.13346 0.09797 -1.36 0.1737 cpeop 1 -0.25932 0.27588 -0.94 0.3477

The REG Procedure Model: MODEL4 Dependent Variable: retired

Analysis of Variance

Sum of Mean Source DF Squares Square F Value Pr > F

Model 5 23.12748 4.62550 28.37 <.0001 Error 490 79.89671 0.16305 Corrected Total 495 103.02419

Root MSE 0.40380 R-Square 0.2245 Dependent Mean 0.29435 Adj R-Sq 0.2166 Coeff Var 137.18140

Parameter Estimates

Parameter Standard Variable DF Estimate Error t Value Pr > |t|

Intercept 1 0.89718 0.08961 10.01 <.0001 income 1 -0.00896 0.00160 -5.62 <.0001 water80 1 -0.00001634 0.00001250 -1.31 0.1920 educat 1 -0.00944 0.00627 -1.51 0.1327 peop80 1 -0.07130 0.01327 -5.37 <.0001 cpeop 1 -0.07074 0.03828 -1.85 0.0652

The REG Procedure Model: MODEL5 Dependent Variable: peop80

Analysis of Variance

Sum of Mean Source DF Squares Square F Value Pr > F

Model 5 486.60634 97.32127 54.54 <.0001 Error 490 874.29487 1.78428 Corrected Total 495 1360.90121

Root MSE 1.33577 R-Square 0.3576 Dependent Mean 3.11089 Adj R-Sq 0.3510 Coeff Var 42.93848

Parameter Estimates

Parameter Standard Variable DF Estimate Error t Value Pr > |t|

Intercept 1 2.32764 0.30787 7.56 <.0001 income 1 0.01091 0.00543 2.01 0.0450 water80 1 0.00041614 0.00003693 11.27 <.0001 educat 1 -0.02827 0.02075 -1.36 0.1737 retired 1 -0.78024 0.14522 -5.37 <.0001 cpeop 1 -0.52808 0.12482 -4.23 <.0001

The REG Procedure Model: MODEL6 Dependent Variable: cpeop

Analysis of Variance

Sum of Mean Source DF Squares Square F Value Pr > F

Model 5 5.79259 1.15852 5.14 0.0001 Error 490 110.47959 0.22547 Corrected Total 495 116.27218

Root MSE 0.47484 R-Square 0.0498 Dependent Mean -0.03831 Adj R-Sq 0.0401 Coeff Var -1239.57000

Parameter Estimates

Parameter Standard Variable DF Estimate Error t Value Pr > |t|

Intercept 1 0.16690 0.11540 1.45 0.1487 income 1 0.00475 0.00192 2.47 0.0140 water80 1 0.00000689 0.00001473 0.47 0.6400 educat 1 -0.00694 0.00738 -0.94 0.3477 retired 1 -0.09781 0.05294 -1.85 0.0652 peop80 1 -0.06673 0.01577 -4.23 <.0001