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Statistical Methods and Data Analytics

Regression with Graphics by Lawrence Hamilton Chapter 4:  Regression Criticism | SPSS Textbook Examples

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

GET FILE 'd:concord1.sav'.

CORRELATIONS  
 /VARIABLES=income water80 educat retire peop81 cpeop water81
 /PRINT=TWOTAIL SIG.

Correlations

Correlations

Income in Thousands Summer 1980 Water Use Education in Years head of house retired? # of People Resident, 1981 Increase in # of People Summer 1981 Water Use
Income in Thousands Pearson Correlation 1 .337 .346 -.381 .311 .091 .418
Sig. (2-tailed) . .000 .000 .000 .000 .043 .000
N 496 496 496 496 496 496 496
Summer 1980 Water Use Pearson Correlation .337 1 .098 -.292 .525 -.031 .765
Sig. (2-tailed) .000 . .029 .000 .000 .489 .000
N 496 496 496 496 496 496 496
Education in Years Pearson Correlation .346 .098 1 -.174 .059 .005 .040
Sig. (2-tailed) .000 .029 . .000 .192 .903 .370
N 496 496 496 496 496 496 496
head of house retired? Pearson Correlation -.381 -.292 -.174 1 -.376 -.059 -.273
Sig. (2-tailed) .000 .000 .000 . .000 .193 .000
N 496 496 496 496 496 496 496
# of People Resident, 1981 Pearson Correlation .311 .525 .059 -.376 1 .144 .618
Sig. (2-tailed) .000 .000 .192 .000 . .001 .000
N 496 496 496 496 496 496 496
Increase in # of People Pearson Correlation .091 -.031 .005 -.059 .144 1 .066
Sig. (2-tailed) .043 .489 .903 .193 .001 . .142
N 496 496 496 496 496 496 496
Summer 1981 Water Use Pearson Correlation .418 .765 .040 -.273 .618 .066 1
Sig. (2-tailed) .000 .000 .370 .000 .000 .142 .
N 496 496 496 496 496 496 496

Page 115 Figure 4.1  Scatterplot matrix corresponding to Table 4.2 (household water use and predictors). 

GGRAPH 
  /GRAPHDATASET NAME="graphdataset" VARIABLES=water81 water80 income educat retire peop81 cpeop 
  /GRAPHSPEC SOURCE=INLINE. 
BEGIN GPL 
  SOURCE: s=userSource(id("graphdataset")) 
  DATA: water81=col(source(s), name("water81")) 
  DATA: water80=col(source(s), name("water80")) 
  DATA: income=col(source(s), name("income")) 
  DATA: educat=col(source(s), name("educat")) 
  DATA: retire=col(source(s), name("retire")) 
  DATA: peop81=col(source(s), name("peop81")) 
  DATA: cpeop=col(source(s), name("cpeop")) 
  GUIDE: text.title( label( "Figure 4.1" ) )
  GUIDE: axis(dim(1.1), ticks(null())) 
  GUIDE: axis(dim(2.1), ticks(null())) 
  GUIDE: axis(dim(1), gap(0px)) 
  GUIDE: axis(dim(2), gap(0px)) 
  TRANS: water81_label = eval("Summer 1981 Water Use") 
  TRANS: water80_label = eval("Summer 1980 Water Use") 
  TRANS: income_label = eval("Income in Thousands") 
  TRANS: educat_label = eval("Education in Years") 
  TRANS: retire_label = eval("head of house retired?") 
  TRANS: peop81_label = eval("# of People Resident, 1981") 
  TRANS: cpeop_label = eval("Increase in # of People") 
  ELEMENT: point(position((water81/water81_label+water80/water80_label+income/income_label+educat/educat_label+retire/retire_label+peop81/peop81_label+cpeop/cpeop_label)*
(water81/water81_label+water80/water80_label+income/income_label+educat/educat_label+retire/retire_label+peop81/peop81_label+cpeop/cpeop_label))) 
END GPL.

Image

Page 115 Figure 4.2  Scatterplot matrix for data from 122 countries. 

GET FILE 'd:nations.sav'.

GGRAPH 
  /GRAPHDATASET NAME="graphdataset" VARIABLES=encon85 popgro85 fert84 birthr85 
  /GRAPHSPEC SOURCE=INLINE. 
BEGIN GPL 
  SOURCE: s=userSource(id("graphdataset")) 
  DATA: encon85=col(source(s), name("encon85")) 
  DATA: popgro85=col(source(s), name("popgro85")) 
  DATA: fert84=col(source(s), name("fert84")) 
  DATA: birthr85=col(source(s), name("birthr85")) 
  GUIDE: text.title( label( "Figure 4.2" ) )
  GUIDE: axis(dim(1.1), ticks(null())) 
  GUIDE: axis(dim(2.1), ticks(null())) 
  GUIDE: axis(dim(1), gap(0px)) 
  GUIDE: axis(dim(2), gap(0px)) 
  TRANS: encon85_label = eval("Energy Consumption Per Person") 
  TRANS: popgro85_label = eval("Mean Annual Population Growth") 
  TRANS: fert84_label = eval("Fertilizer Use per Hectare") 
  TRANS: birthr85_label = eval("Crude Birth Rate") 
  ELEMENT: point(position((encon85/encon85_label+popgro85/popgro85_label+fert84/fert84_label+birthr85/birthr85_label)*
(encon85/encon85_label+popgro85/popgro85_label+fert84/fert84_label+birthr85/birthr85_label))) 
END GPL.

Image

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

GET FILE 'd:concord1.sav'.

REGRESSION
  /DEPENDENT water81
  /METHOD=ENTER income water80 educat retire peop81 cpeop peop80
  /SAVE PRED RESID.
Variables Entered/Removed(b)
Model Variables Entered Variables Removed Method
1 # people living in 1980, Education in Years, Increase in # of People, head of house retired?, Income in Thousands, Summer 1980 Water Use(a) . Enter
a Tolerance = .000 limits reached.
b Dependent Variable: Summer 1981 Water Use
Model Summary(b)
Model R R Square Adjusted R Square Std. Error of the Estimate
1 .823(a) .677 .673 849.349
a Predictors: (Constant), # people living in 1980, Education in Years, Increase in # of People, head of house retired?, Income in Thousands, Summer 1980 Water Use
b Dependent Variable: Summer 1981 Water Use
ANOVA(b)
Model Sum of Squares df Mean Square F Sig.
1 Regression 740477522.059 6 123412920.343 171.076 .000(a)
Residual 352761187.618 489 721393.022

Total 1093238709.677 495


a Predictors: (Constant), # people living in 1980, Education in Years, Increase in # of People, head of house retired?, Income in Thousands, Summer 1980 Water Use
b Dependent Variable: Summer 1981 Water Use

Coefficients(a)

Unstandardized Coefficients Standardized Coefficients t Sig.
Model B Std. Error Beta
1 (Constant) 242.220 206.864
1.171 .242
Income in Thousands 20.967 3.464 .184 6.053 .000
Summer 1980 Water Use .492 .026 .584 18.671 .000
Education in Years -41.866 13.220 -.087 -3.167 .002
head of house retired? 189.184 95.021 .058 1.991 .047
Increase in # of People 344.651 80.806 .112 4.265 .000
# people living in 1980 248.197 28.725 .277 8.641 .000
a Dependent Variable: Summer 1981 Water Use
Excluded Variables(b)

Beta In t Sig. Partial Correlation Collinearity Statistics
Model Tolerance
1 # of People Resident, 1981 .(a) . . . .000
a Predictors in the Model: (Constant), # people living in 1980, Education in Years, Increase in # of People, head of house retired?, Income in Thousands, Summer 1980 Water Use
b Dependent Variable: Summer 1981 Water Use
Casewise Diagnostics(a)
Case Number Std. Residual Summer 1981 Water Use
79 3.020 8100
80 5.313 7300
85 5.932 6500
94 -4.753 3800
118 3.904 7900
124 4.842 10100
125 4.341 9200
a Dependent Variable: Summer 1981 Water Use
Residuals Statistics(a)

Minimum Maximum Mean Std. Deviation N
Predicted Value 262.78 7837.05 2298.39 1223.076 496
Residual -4037.05 5037.99 .00 844.185 496
Std. Predicted Value -1.664 4.528 .000 1.000 496
Std. Residual -4.753 5.932 .000 .994 496
a Dependent Variable: Summer 1981 Water Use 
formats pred_1 (f4.0) resid_1 (f5.0).
GGRAPH 
  /GRAPHDATASET NAME="graphdataset" VARIABLES=pred_1 resid_1
  /GRAPHSPEC SOURCE=INLINE. 
BEGIN GPL 
SOURCE: s=userSource(id("graphdataset")) 
DATA: pred_1=col(source(s), name("pred_1")) 
DATA: resid_1=col(source(s), name("resid_1")) 
GRAPH: begin(origin(15.0%, 10.0%), scale(70.0%, 70.0%))
GUIDE: axis( dim( 1 ), label( "Y-hat" ))
GUIDE: axis( dim( 2 ), label( "e" ) )
GUIDE: form.line(position(*, 0))
SCALE: linear( dim( 1 ), min(0), max(8000) )
SCALE: linear( dim( 2 ), min(-4000), max(4000) )
ELEMENT: point(position(pred_1*resid_1)) 
GRAPH: end()
GRAPH: begin(origin(15.0%, 80.0%), scale(70.0%, 10.0%))
COORD: transpose()
GUIDE: axis(dim(1), ticks(null()))
GUIDE: axis(dim(2), null())
ELEMENT: schema(position(bin.quantile.letter(1*pred_1)))
GRAPH: end()
GRAPH: begin(origin(85.0%, 10.0%), scale(10.0%, 70.0%))
GUIDE: axis(dim(1), ticks(null()))
GUIDE: axis(dim(2), null())
ELEMENT: schema(position(bin.quantile.letter(1*resid_1)))
GRAPH: end()
END GPL.

Image

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

compute abse=abs(res_1).
execute.

NOTE:  We do not know how to do band regression in SPSS, so the lines are not included on this graph. 

compute abse=abs(resid_1).
execute.
GGRAPH 
  /GRAPHDATASET NAME="graphdataset" VARIABLES=pred_1 abse 
  /GRAPHSPEC SOURCE=INLINE. 
BEGIN GPL 
SOURCE: s=userSource(id("graphdataset")) 
DATA: pred_1=col(source(s), name("pred_1")) 
DATA: abse=col(source(s), name("abse")) 
GUIDE: text.title( label( "Figure 4.4" ) )
GUIDE: axis(dim(1), label("Y-hat")) 
GUIDE: axis(dim(2), label("abse")) 
ELEMENT: point(position(pred_1*abse)) 
END GPL.

Image

Page 119 Figure 4.5  Time plot of average daily water use by the city of Concord, 1970-1981. 

GET FILE 'd:concord2.sav'.

TSPLOT VARIABLES= h2ouse
  /ID= month
  /NOLOG
  /FORMAT NOFILL NOREFERENCE.

MODEL:  MOD_4.


Image

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

REGRESSION
  /DEPENDENT h2ouse
  /METHOD=ENTER temp rain educ
  /SAVE RESID.

Variables Entered/Removed(b)
Model Variables Entered Variables Removed Method
1 conservation campaign dummy, average monthly temperature, precipitation in inches(a) . Enter
a All requested variables entered.
b Dependent Variable: average daily water use
Model Summary(b)
Model R R Square Adjusted R Square Std. Error of the Estimate
1 .572(a) .327 .312 .36045
a Predictors: (Constant), conservation campaign dummy, average monthly temperature, precipitation in inches
b Dependent Variable: average daily water use
ANOVA(b)
Model Sum of Squares df Mean Square F Sig.
1 Regression 8.409 3 2.803 21.574 .000(a)
Residual 17.280 133 .130

Total 25.689 136


a Predictors: (Constant), conservation campaign dummy, average monthly temperature, precipitation in inches
b Dependent Variable: average daily water use
Coefficients(a)

Unstandardized Coefficients Standardized Coefficients t Sig.
Model B Std. Error Beta
1 (Constant) 3.828 .101
38.035 .000
average monthly temperature 1.286E-02 .002 .540 7.574 .000
precipitation in inches -4.743E-02 .021 -.160 -2.234 .027
conservation campaign dummy -.247 .113 -.155 -2.176 .031
a Dependent Variable: average daily water use
Residuals Statistics(a)

Minimum Maximum Mean Std. Deviation N
Predicted Value 3.6085 4.6821 4.2350 .24866 137
Residual -.7493 .8434 .0000 .35646 137
Std. Predicted Value -2.519 1.798 .000 1.000 137
Std. Residual -2.079 2.340 .000 .989 137
a Dependent Variable: average daily water use 

ACF  VARIABLES= res_1
  /MXAUTO 25.


MODEL:  MOD_5.

Autocorrelations:   RES_1   Unstandardized Residual

     Auto- Stand.
Lag  Corr.   Err. -1  -.75  -.5 -.25   0   .25  .5   .75   1   Box-Ljung  Prob.
                                                            
  1   .730   .085                   .   **.************           74.665   .000
  2   .474   .084                   .   **.******                106.294   .000
  3   .345   .084                   .   **.****                  123.220   .000
  4   .460   .084                   .   **.******                153.457   .000
  5   .559   .083                   .   **.********              198.592   .000
  6   .590   .083                   .   **.*********             249.138   .000
  7   .462   .083                   .   **.******                280.362   .000
  8   .281   .082                   .   **.***                   292.008   .000
  9   .154   .082                   .   ***                      295.533   .000
 10   .240   .082                   .   **.**                    304.149   .000
 11   .424   .081                   .   **.*****                 331.345   .000
 12   .485   .081                   .   **.*******               367.238   .000
 13   .341   .081                   .   **.****                  385.068   .000
 14   .153   .080                   .   ***                      388.689   .000
 15   .130   .080                   .   ***                      391.315   .000
 16   .216   .080                   .   **.*                     398.639   .000
 17   .340   .079                   .   **.****                  416.933   .000
 18   .369   .079                   .   **.****                  438.779   .000
 19   .272   .079                   .   **.**                    450.690   .000
 20   .086   .078                   .   **.                      451.881   .000
 21  -.019   .078                   .  *  .                      451.940   .000
 22   .029   .078                   .   * .                      452.082   .000
 23   .198   .077                   .   **.*                     458.645   .000
 24   .261   .077                   .   **.**                    470.114   .000
 25   .162   .077                   .   ***                      474.561   .000

Plot Symbols:      Autocorrelations *     Two Standard Error Limits .

Total cases:  137     Computable first lags:  136


Image


Page 122 Figure 4.7  Time plot of concord water-use residuals. 

TSPLOT VARIABLES= res_1
  /ID= month.


MODEL:  MOD_6.

 Image

Page 122 Figure 4.8  Time plots of Concord water-use residuals, showing effects of repeated smoothing by running means of span 3.

NOTE:  We do not know how smooth by running means.

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

GET FILE 'd:concord1.sav'.

REGRESSION
  /DEPENDENT water81
  /METHOD=ENTER income water80 educat retire peop81 cpeop
  /SAVE RESID.

Variables Entered/Removed(b)
Model Variables Entered Variables Removed Method
1 Increase in # of People, Education in Years, Summer 1980 Water Use, head of house retired?, Income in Thousands, # of People Resident, 1981(a) . Enter
a All requested variables entered.
b Dependent Variable: Summer 1981 Water Use
Model Summary(b)
Model R R Square Adjusted R Square Std. Error of the Estimate
1 .823(a) .677 .673 849.349
a Predictors: (Constant), Increase in # of People, Education in Years, Summer 1980 Water Use, head of house retired?, Income in Thousands, # of People Resident, 1981
b Dependent Variable: Summer 1981 Water Use
ANOVA(b)
Model Sum of Squares df Mean Square F Sig.
1 Regression 740477522.059 6 123412920.343 171.076 .000(a)
Residual 352761187.618 489 721393.022

Total 1093238709.677 495


a Predictors: (Constant), Increase in # of People, Education in Years, Summer 1980 Water Use, head of house retired?, Income in Thousands, # of People Resident, 1981
b Dependent Variable: Summer 1981 Water Use
Coefficients(a)

Unstandardized Coefficients Standardized Coefficients t Sig.
Model B Std. Error Beta
1 (Constant) 242.220 206.864
1.171 .242
Income in Thousands 20.967 3.464 .184 6.053 .000
Summer 1980 Water Use .492 .026 .584 18.671 .000
Education in Years -41.866 13.220 -.087 -3.167 .002
head of house retired? 189.184 95.021 .058 1.991 .047
# of People Resident, 1981 248.197 28.725 .277 8.641 .000
Increase in # of People 96.454 80.519 .031 1.198 .232
a Dependent Variable: Summer 1981 Water Use
Casewise Diagnostics(a)
Case Number Std. Residual Summer 1981 Water Use
79 3.020 8100
80 5.313 7300
85 5.932 6500
94 -4.753 3800
118 3.904 7900
124 4.842 10100
125 4.341 9200
a Dependent Variable: Summer 1981 Water Use
Residuals Statistics(a)

Minimum Maximum Mean Std. Deviation N
Predicted Value 262.78 7837.05 2298.39 1223.076 496
Residual -4037.05 5037.99 .00 844.185 496
Std. Predicted Value -1.664 4.528 .000 1.000 496
Std. Residual -4.753 5.932 .000 .994 496
a Dependent Variable: Summer 1981 Water Use

Upper left panel of Figure 4.9

formats resid_1 pred_1 (f5.0).
GGRAPH
  /GRAPHDATASET NAME="GraphDataset" VARIABLES= resid_1 
  /GRAPHSPEC SOURCE=INLINE .
BEGIN GPL
SOURCE: s=userSource( id( "GraphDataset" ) )
DATA: Y_Var=col( source(s), name( "$count" ) )
DATA: resid_1=col( source(s), name( "resid_1" ) )
GUIDE: text.title( label( "Figure 4.9, upper left" ) )
GUIDE: axis( dim( 1 ), label( "Residual" ), delta(2000) )
GUIDE: axis( dim( 2 ), label( "Count" ) )
SCALE: linear( dim( 1 ), min(-4000), max(4000) )
ELEMENT: interval( position( summary.count( bin.rect( resid_1, binStart( 0 ), binCount( 13 ) ) ) ) )
ELEMENT: line( position( density.normal( resid_1 ) ) )
END GPL.

Image

Upper right panel of Figure 4.9

GGRAPH 
  /GRAPHDATASET NAME="graphdataset" VARIABLES=resid_1 
  /GRAPHSPEC SOURCE=INLINE. 
BEGIN GPL 
SOURCE: s=userSource(id("graphdataset")) 
DATA: resid_1=col(source(s), name("resid_1")) 
GUIDE: text.title( label( "Figure 4.9, upper right" ))
COORD: rect(dim(1), transpose()) 
GUIDE: axis(dim(1), label("Residual"), delta(2000)) 
SCALE: linear( dim( 2 ), min(-4000), max(4000) )
ELEMENT: schema(position(bin.quantile.letter(resid_1))) 
END GPL.

Image

Lower left panel of Figure 4.9

NOTE:  We do not know how to make a symmetry plot in SPSS.

Lower right panel of Figure 4.9

pplot
/variable = resid_1
/type q-q.

Image

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

REGRESSION
  /DEPENDENT water81
  /METHOD=ENTER income water80 educat retire peop81 cpeop
  /SAVE DFBETA.

Variables Entered/Removed(b)
Model Variables Entered Variables Removed Method
1 Increase in # of People, Education in Years, Summer 1980 Water Use, head of house retired?, Income in Thousands, # of People Resident, 1981(a) . Enter
a All requested variables entered.
b Dependent Variable: Summer 1981 Water Use
Model Summary(b)
Model R R Square Adjusted R Square Std. Error of the Estimate
1 .823(a) .677 .673 849.349
a Predictors: (Constant), Increase in # of People, Education in Years, Summer 1980 Water Use, head of house retired?, Income in Thousands, # of People Resident, 1981
b Dependent Variable: Summer 1981 Water Use
ANOVA(b)
Model Sum of Squares df Mean Square F Sig.
1 Regression 740477522.059 6 123412920.343 171.076 .000(a)
Residual 352761187.618 489 721393.022

Total 1093238709.677 495


a Predictors: (Constant), Increase in # of People, Education in Years, Summer 1980 Water Use, head of house retired?, Income in Thousands, # of People Resident, 1981
b Dependent Variable: Summer 1981 Water Use
Coefficients(a)

Unstandardized Coefficients Standardized Coefficients t Sig.
Model B Std. Error Beta
1 (Constant) 242.220 206.864
1.171 .242
Income in Thousands 20.967 3.464 .184 6.053 .000
Summer 1980 Water Use .492 .026 .584 18.671 .000
Education in Years -41.866 13.220 -.087 -3.167 .002
head of house retired? 189.184 95.021 .058 1.991 .047
# of People Resident, 1981 248.197 28.725 .277 8.641 .000
Increase in # of People 96.454 80.519 .031 1.198 .232
a Dependent Variable: Summer 1981 Water Use
Casewise Diagnostics(a)
Case Number Std. Residual Summer 1981 Water Use
79 3.020 8100
80 5.313 7300
85 5.932 6500
94 -4.753 3800
118 3.904 7900
124 4.842 10100
125 4.341 9200
a Dependent Variable: Summer 1981 Water Use
Residuals Statistics(a)

Minimum Maximum Mean Std. Deviation N
Predicted Value 262.78 7837.05 2298.39 1223.076 496
Std. Predicted Value -1.664 4.528 .000 1.000 496
Standard Error of Predicted Value 48.840 273.580 95.681 32.066 496
Adjusted Predicted Value 256.12 8196.38 2297.98 1222.737 496
Residual -4037.05 5037.99 .00 844.185 496
Std. Residual -4.753 5.932 .000 .994 496
Stud. Residual -4.960 5.966 .000 1.007 496
Deleted Residual -4396.38 5095.83 .41 866.178 496
Stud. Deleted Residual -5.085 6.189 .002 1.016 496
Mahal. Distance .639 50.359 5.988 5.710 496
Cook’s Distance .000 .313 .004 .021 496
Centered Leverage Value .001 .102 .012 .012 496
a Dependent Variable: Summer 1981 Water Use 

DESCRIPTIVES VARIABLES=dfb1_1 dfb2_1 dfb3_1 dfb4_1 dfb5_1 dfb6_1
  /STATISTICS=MEAN STDDEV MIN MAX.

Descriptive Statistics

N Minimum Maximum Mean Std. Deviation
DFBETA INCOME 496 -.85919 4.54791 .0010205 .30944938
DFBETA WATER80 496 -.03567 .01760 -.0000037 .00231794
DFBETA EDUCAT 496 -4.64425 1.34235 -.0017557 .56819471
DFBETA RETIRE 496 -19.84839 26.33657 .0058540 4.20308173
DFBETA PEOP81 496 -11.99661 12.76215 .0016764 1.74564279
DFBETA CPEOP 496 -18.80571 28.17114 -.0031481 3.26555664
Valid N (listwise) 496




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

REGRESSION
  /DEPENDENT water81
  /METHOD=ENTER income water80 educat retire peop81 cpeop
  /PARTIALPLOT ALL.

Variables Entered/Removed(b)
Model Variables Entered Variables Removed Method
1 Increase in # of People, Education in Years, Summer 1980 Water Use, head of house retired?, Income in Thousands, # of People Resident, 1981(a) . Enter
a All requested variables entered.
b Dependent Variable: Summer 1981 Water Use
Model Summary(b)
Model R R Square Adjusted R Square Std. Error of the Estimate
1 .823(a) .677 .673 849.349
a Predictors: (Constant), Increase in # of People, Education in Years, Summer 1980 Water Use, head of house retired?, Income in Thousands, # of People Resident, 1981
b Dependent Variable: Summer 1981 Water Use
ANOVA(b)
Model Sum of Squares df Mean Square F Sig.
1 Regression 740477522.059 6 123412920.343 171.076 .000(a)
Residual 352761187.618 489 721393.022

Total 1093238709.677 495


a Predictors: (Constant), Increase in # of People, Education in Years, Summer 1980 Water Use, head of house retired?, Income in Thousands, # of People Resident, 1981
b Dependent Variable: Summer 1981 Water Use
Coefficients(a)

Unstandardized Coefficients Standardized Coefficients t Sig.
Model B Std. Error Beta
1 (Constant) 242.220 206.864
1.171 .242
Income in Thousands 20.967 3.464 .184 6.053 .000
Summer 1980 Water Use .492 .026 .584 18.671 .000
Education in Years -41.866 13.220 -.087 -3.167 .002
head of house retired? 189.184 95.021 .058 1.991 .047
# of People Resident, 1981 248.197 28.725 .277 8.641 .000
Increase in # of People 96.454 80.519 .031 1.198 .232
a Dependent Variable: Summer 1981 Water Use
Casewise Diagnostics(a)
Case Number Std. Residual Summer 1981 Water Use
79 3.020 8100
80 5.313 7300
85 5.932 6500
94 -4.753 3800
118 3.904 7900
124 4.842 10100
125 4.341 9200
a Dependent Variable: Summer 1981 Water Use
Residuals Statistics(a)

Minimum Maximum Mean Std. Deviation N
Predicted Value 262.78 7837.05 2298.39 1223.076 496
Residual -4037.05 5037.99 .00 844.185 496
Std. Predicted Value -1.664 4.528 .000 1.000 496
Std. Residual -4.753 5.932 .000 .994 496
a Dependent Variable: Summer 1981 Water Use

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

NOTE:  This syntax for this graph is the same as above.  The only difference between
the two graphs is the use of the symbols proportional to DFBETAS, and SPSS does not 
allow you to make the symbols proportional on this type of graph. 

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

NOTE:  The syntax for this graph is the same as for Figure 4.10, as SPSS gives you all 
of the possible leverage plots.

Page 129 Figure 4.13  Proportional leverage plots of 1981 household water use versus X, 
each adjusting for five other predictors.

NOTE:  The syntax for this graph is the same as for Figure 4.10, as SPSS gives you all 
of the possible leverage plots.

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

REGRESSION
 /DEPENDENT water81
 /METHOD=ENTER income water80 educat retire peop81 cpeop
 /SAVE COOK LEVER RESID ZRESID SRESID DFBETA.

 

Variables Entered/Removed(b)
Model Variables Entered Variables Removed Method
1 Increase in # of People, Education in Years, Summer 1980 Water Use, head of house retired?, Income in Thousands, # of People Resident, 1981(a) . Enter
a All requested variables entered.
b Dependent Variable: Summer 1981 Water Use
Model Summary(b)
Model R R Square Adjusted R Square Std. Error of the Estimate
1 .823(a) .677 .673 849.349
a Predictors: (Constant), Increase in # of People, Education in Years, Summer 1980 Water Use, head of house retired?, Income in Thousands, # of People Resident, 1981
b Dependent Variable: Summer 1981 Water Use
ANOVA(b)
Model Sum of Squares df Mean Square F Sig.
1 Regression 740477522.059 6 123412920.343 171.076 .000(a)
Residual 352761187.618 489 721393.022

Total 1093238709.677 495


a Predictors: (Constant), Increase in # of People, Education in Years, Summer 1980 Water Use, head of house retired?, Income in Thousands, # of People Resident, 1981
b Dependent Variable: Summer 1981 Water Use
Coefficients(a)

Unstandardized Coefficients Standardized Coefficients t Sig.
Model B Std. Error Beta
1 (Constant) 242.220 206.864
1.171 .242
Income in Thousands 20.967 3.464 .184 6.053 .000
Summer 1980 Water Use .492 .026 .584 18.671 .000
Education in Years -41.866 13.220 -.087 -3.167 .002
head of house retired? 189.184 95.021 .058 1.991 .047
# of People Resident, 1981 248.197 28.725 .277 8.641 .000
Increase in # of People 96.454 80.519 .031 1.198 .232
a Dependent Variable: Summer 1981 Water Use
Casewise Diagnostics(a)
Case Number Std. Residual Summer 1981 Water Use
79 3.020 8100
80 5.313 7300
85 5.932 6500
94 -4.753 3800
118 3.904 7900
124 4.842 10100
125 4.341 9200
a Dependent Variable: Summer 1981 Water Use
Residuals Statistics(a)

Minimum Maximum Mean Std. Deviation N
Predicted Value 262.78 7837.05 2298.39 1223.076 496
Std. Predicted Value -1.664 4.528 .000 1.000 496
Standard Error of Predicted Value 48.840 273.580 95.681 32.066 496
Adjusted Predicted Value 256.12 8196.38 2297.98 1222.737 496
Residual -4037.05 5037.99 .00 844.185 496
Std. Residual -4.753 5.932 .000 .994 496
Stud. Residual -4.960 5.966 .000 1.007 496
Deleted Residual -4396.38 5095.83 .41 866.178 496
Stud. Deleted Residual -5.085 6.189 .002 1.016 496
Mahal. Distance .639 50.359 5.988 5.710 496
Cook’s Distance .000 .313 .004 .021 496
Centered Leverage Value .001 .102 .012 .012 496
a Dependent Variable: Summer 1981 Water Use 

USE ALL.
COMPUTE filter_$=(case = 101 | case=127 | case=134).
VARIABLE LABEL filter_$ 'case = 101 | case=127 | case=134 (FILTER)'.
VALUE LABELS filter_$  0 'Not Selected' 1 'Selected'.
FILTER BY filter_$.
EXECUTE.

list case res_1 lev_1 zre_1 sre_1 coo_1 dfb1_1 dfb2_1.
The variables are listed in the following order:

LINE   1: CASE RES_1 LEV_1 ZRE_1 SRE_1 COO_1

LINE   2: DFB1_1 DFB2_1


    CASE: 101 -4037.04714   .07972   -4.75311   -4.96013   .31284    .21282    -.03567

    CASE: 127  3315.58478   .05959   3.90368     4.02979   .15232   3.34230    -.00469

    CASE: 134  3687.11597   .08836   4.34111     4.55167   .29407   4.54791     .00648


Number of cases read:  3    Number of cases listed:  3

Page 134 Table 4.5  Checking for multicollinearlity:  tolerances of X variables in water-use regression [4.3]. 

FILTER OFF.
REGRESSION
  /statistics=tol
  /DEPENDENT water81
  /METHOD=ENTER income water80 educat retire peop81 cpeop.

 

Variables Entered/Removed(b)
Model Variables Entered Variables Removed Method
1 Increase in # of People, Education in Years, Summer 1980 Water Use, head of house retired?, Income in Thousands, # of People Resident, 1981(a) . Enter
a All requested variables entered.
b Dependent Variable: Summer 1981 Water Use
Coefficients(a)

Collinearity Statistics
Model Tolerance VIF
1 Income in Thousands .712 1.404
Summer 1980 Water Use .675 1.482
Education in Years .873 1.145
head of house retired? .776 1.289
# of People Resident, 1981 .643 1.555
Increase in # of People .957 1.045
a Dependent Variable: Summer 1981 Water Use

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