/* Education Expenditure data, table 7.3, p. 189 */
data p189;
length state $ 2 ;
input State Y X1 X2 X3 Region ;
label x1 = 'Income'
x2 = 'Residents under 18'
x3 = 'Residents in Urban Areas'
y = 'Expenditure';
cards;
ME 235 3944 325 508 1
NH 231 4578 323 564 1
VT 270 4011 328 322 1
MA 261 5233 305 846 1
RI 300 4780 303 871 1
CT 317 5889 307 774 1
NY 387 5663 301 856 1
NJ 285 5759 310 889 1
PA 300 4894 300 715 1
OH 221 5012 324 753 2
IN 264 4908 329 649 2
IL 308 5753 320 830 2
MI 379 5439 337 738 2
WI 342 4634 328 659 2
MN 378 4921 330 664 2
IA 232 4869 318 572 2
MO 231 4672 309 701 2
ND 246 4782 333 443 2
SD 230 4296 330 446 2
NB 268 4827 318 615 2
KS 337 5057 304 661 2
DE 344 5540 328 722 3
MD 330 5331 323 766 3
VA 261 4715 317 631 3
WV 214 3828 310 390 3
NC 245 4120 321 450 3
SC 233 3817 342 476 3
GA 250 4243 339 603 3
FL 243 4647 287 805 3
KY 216 3967 325 523 3
TN 212 3946 315 588 3
AL 208 3724 332 584 3
MS 215 3448 358 445 3
AR 221 3680 320 500 3
LA 244 3825 355 661 3
OK 234 4189 306 680 3
TX 269 4336 335 797 3
MT 302 4418 335 534 4
ID 268 4323 344 541 4
WY 323 4813 331 605 4
CO 304 5046 324 785 4
NM 317 3764 366 698 4
AZ 332 4504 340 796 4
UT 315 4005 378 804 4
NV 291 5560 330 809 4
WA 312 4989 313 726 4
OR 316 4697 305 671 4
CA 332 5438 307 909 4
AK 546 5613 386 484 4
HI 311 5309 333 831 4
;
run;
/* Table 7.4, fig. 7.3-7.7, p. 191-192 */
goptions reset = all;
symbol v=dot h=.8 c=blue;
proc reg data = p189;
var region;
model y = x1 x2 x3;
plot student.*p. student.*region student.*x1 student.*x2 student.*x3;
run;
quit;
The REG Procedure
Model: MODEL1
Dependent Variable: Y Expenditure
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 3 109020 36340 22.19 <.0001
Error 46 75348 1637.99091
Corrected Total 49 184368
Root MSE 40.47210 R-Square 0.5913
Dependent Mean 284.60000 Adj R-Sq 0.5647
Coeff Var 14.22070
Parameter Estimates
Parameter Standard
Variable Label DF Estimate Error t Value Pr > |t|
Intercept Intercept 1 -556.56804 123.19525 -4.52 <.0001
X1 Income 1 0.07239 0.01160 6.24 <.0001
X2 Residents under 18 1 1.55205 0.31467 4.93 <.0001
X3 Residents in Urban Areas 1 -0.00427
0.05139 -0.08 0.9342
/* Table 7.5 and fig. 7.8-7.9, p. 193-194. The where statement
omits Alaska from the analysis. */
symbol v=dot h=.8 c=blue;
proc reg data = p189;
where State ~= 'AK';
var region;
model y = x1 x2 x3;
output out=outr r=resid ;
plot student.*p. student.*region;
run;
quit;
The REG Procedure
Model: MODEL1
Dependent Variable: Y Expenditure
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 3 56944 18981 14.80 <.0001
Error 45 57700 1282.21687
Corrected Total 48 114644
Root MSE 35.80806 R-Square 0.4967
Dependent Mean 279.26531 Adj R-Sq 0.4631
Coeff Var 12.82224
Parameter Estimates
Parameter Standard
Variable Label DF Estimate Error t Value Pr > |t|
Intercept Intercept 1 -277.57731 132.42286 -2.10 0.0417
X1 Income 1 0.04829 0.01215 3.98 0.0003
X2 Residents under 18 1 0.88693 0.33114 2.68 0.0103
X3 Residents in Urban Areas 1 0.06679 0.04934 1.35 0.1826
/* By looking at the plot of standardized residuals against region we can observe that the variance for each region is different (the points for each category of region have a different range). In order to fix this problem we create by the appropriate weights and run the regression model again the resulting residuals should have the same variance. */ /* Generating the weights to be used in the WLS, p. 190. */ proc sql; create table outresid as select *, sum(resid*resid)/(count(region) - 1) as ratio from outr group by region; quit; proc sql; create table outresid1 as select *, 1/sqrt(ratio/mean(resid*resid)) as c from outresid; quit; proc sql; create table weighted as select *, y*c as ty, x1*c as tx1, c*x2 as tx2, c*x3 as tx3 from outresid1; quit; /* Table 7.6, p. 195 */ proc sql; select distinct region, count(region) as n, ratio as sigma2, 1/c as cj from weighted group by region; quit;Region n sigma2 cj ------------------------------------ 1 9 1632.502 1.177438 2 12 2658.521 1.502557 3 16 266.0621 0.475338 4 12 1036.825 0.938348/* The WLS part of table 7.7, p. 195 and fig. 7.8-7.9, p. 196 */ symbol v=dot h=.8 c=blue; proc reg data = weighted; var region; model ty = c tx1 tx2 tx3/ noint; plot student.*p. student.*region; run; quit;The REG Procedure Model: MODEL1 Dependent Variable: ty Number of Observations Read 49 Number of Observations Used 49 NOTE: No intercept in model. R-Square is redefined. Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 4 6668300 1667075 1595.08 <.0001 Error 45 47031 1045.13869 Uncorrected Total 49 6715332 Root MSE 32.32860 R-Square 0.9930 Dependent Mean 341.57976 Adj R-Sq 0.9924 Coeff Var 9.46444 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| c 1 -316.02374 77.41893 -4.08 0.0002 tx1 1 0.06246 0.00780 8.00 <.0001 tx2 1 0.87399 0.19840 4.41 <.0001 tx3 1 0.02892 0.03399 0.85 0.3994
