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Statistical Methods and Data Analytics

Regression with Graphics by Lawrence Hamilton Chapter 3 :  Basics of multiple regression | SPSS Textbook Examples

Page 68 Table 3.1  Regression of postshortage (1981) water use on income and preshortage (1980) water use. 

GET FILE 'd:appsrwgdataconcord1.sav'.

REGRESSION
  /DEPENDENT water81
  /METHOD=ENTER income water80.

 

Variables Entered/Removed(b)
Model Variables Entered Variables Removed Method
1 Summer 1980 Water Use, Income in Thousands(a) . Enter
a All requested variables entered.
b Dependent Variable: Summer 1981 Water Use
Model Summary
Model R R Square Adjusted R Square Std. Error of the Estimate
1 .783(a) .614 .612 925.428
a Predictors: (Constant), Summer 1980 Water Use, Income in Thousands
ANOVA(b)
Model Sum of Squares df Mean Square F Sig.
1 Regression 671025350.237 2 335512675.119 391.763 .000(a)
Residual 422213359.440 493 856416.551

Total 1093238709.677 495


a Predictors: (Constant), Summer 1980 Water Use, Income in Thousands
b Dependent Variable: Summer 1981 Water Use
Coefficients(a)

Unstandardized Coefficients Standardized Coefficients t Sig.
Model B Std. Error Beta
1 (Constant) 203.822 94.361
2.160 .031
Income in Thousands 20.545 3.383 .181 6.072 .000
Summer 1980 Water Use .593 .025 .704 23.679 .000
a Dependent Variable: Summer 1981 Water Use

Page 70 Figure 3.1  Partial regression leverage plot: postshortage water use (Y) versus income (1), adjusting for preshortage water use (2).

REGRESSION
  /DEPENDENT water81
  /METHOD=ENTER water80
 /SAVE RESID.

 

Variables Entered/Removed(b)
Model Variables Entered Variables Removed Method
1 Summer 1980 Water Use(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 .765(a) .585 .584 958.440
a Predictors: (Constant), Summer 1980 Water Use
b Dependent Variable: Summer 1981 Water Use
ANOVA(b)
Model Sum of Squares df Mean Square F Sig.
1 Regression 639446986.677 1 639446986.677 696.105 .000(a)
Residual 453791723.000 494 918606.727

Total 1093238709.677 495


a Predictors: (Constant), 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) 537.871 79.401
6.774 .000
Summer 1980 Water Use .644 .024 .765 26.384 .000
a Dependent Variable: Summer 1981 Water Use
Casewise Diagnostics(a)
Case Number Std. Residual Summer 1981 Water Use
25 3.283 7100
79 3.318 8100
80 5.307 7300
85 5.548 6500
94 -5.135 3800
101 3.123 5400
118 4.992 7900
124 4.195 10100
125 4.802 9200
325 3.316 6100
362 -3.823 1900
a Dependent Variable: Summer 1981 Water Use
Residuals Statistics(a)

Minimum Maximum Mean Std. Deviation N
Predicted Value 666.75 8721.65 2298.39 1136.579 496
Residual -4921.65 5317.74 .00 957.471 496
Std. Predicted Value -1.436 5.651 .000 1.000 496
Std. Residual -5.135 5.548 .000 .999 496
a Dependent Variable: Summer 1981 Water Use 

REGRESSION
  /DEPENDENT income
  /METHOD=ENTER water80
  /SAVE RESID.

Variables Entered/Removed(b)
Model Variables Entered Variables Removed Method
1 Summer 1980 Water Use(a) . Enter
a All requested variables entered.
b Dependent Variable: Income in Thousands
Model Summary(b)
Model R R Square Adjusted R Square Std. Error of the Estimate
1 .337(a) .114 .112 12.306
a Predictors: (Constant), Summer 1980 Water Use
b Dependent Variable: Income in Thousands
ANOVA(b)
Model Sum of Squares df Mean Square F Sig.
1 Regression 9588.317 1 9588.317 63.313 .000(a)
Residual 74812.772 494 151.443

Total 84401.089 495


a Predictors: (Constant), Summer 1980 Water Use
b Dependent Variable: Income in Thousands
Coefficients(a)

Unstandardized Coefficients Standardized Coefficients t Sig.
Model B Std. Error Beta
1 (Constant) 16.259 1.019
15.948 .000
Summer 1980 Water Use 2.495E-03 .000 .337 7.957 .000
a Dependent Variable: Income in Thousands
Casewise Diagnostics(a)
Case Number Std. Residual Income in Thousands
65 3.921 72
118 5.181 90
125 5.527 100
281 3.170 68
a Dependent Variable: Income in Thousands
Residuals Statistics(a)

Minimum Maximum Mean Std. Deviation N
Predicted Value 16.76 47.95 23.08 4.401 496
Residual -25.72 68.02 .00 12.294 496
Std. Predicted Value -1.436 5.651 .000 1.000 496
Std. Residual -2.090 5.527 .000 .999 496
a Dependent Variable: Income in Thousands 

formats res_1 res_2 (f4.0) .
GGRAPH
  /GRAPHDATASET NAME="GraphDataset" VARIABLES= res_1 res_2 
  /GRAPHSPEC SOURCE=INLINE .
BEGIN GPL
SOURCE: s=userSource( id( "GraphDataset" ) )
DATA: res_1=col( source(s), name( "res_1" ) )
DATA: res_2=col( source(s), name( "res_2" ) )
COORD: rect( dim( 1, 2 ) )
GUIDE: axis( dim( 1 ), label( "res_2" ) )
GUIDE: axis( dim( 2 ), label( "res_1" ) )
SCALE: linear( dim( 1 ), min(-20), max(60))
SCALE: linear( dim( 2 ), min(-4000), max(4000) )
ELEMENT: point( position(res_2 * res_1 ) )
ELEMENT: line(position( smooth.linear(res_2 * res_1 ) ) )
END GPL.

Image

Page 71 Figure 3.2  Partial regression leverage plot:  postshortage water use (Y) versus preshortage water use (2), adjusting for income (1).

REGRESSION
  /DEPENDENT water81
  /METHOD=ENTER income
  /SAVE RESID.
Variables Entered/Removed(b)
Model Variables Entered Variables Removed Method
1 Income in Thousands(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 .418(a) .175 .173 1351.576
a Predictors: (Constant), Income in Thousands
b Dependent Variable: Summer 1981 Water Use
ANOVA(b)
Model Sum of Squares df Mean Square F Sig.
1 Regression 190820566.279 1 190820566.279 104.459 .000(a)
Residual 902418143.398 494 1826757.375

Total 1093238709.677 495


a Predictors: (Constant), Income in Thousands
b Dependent Variable: Summer 1981 Water Use
Coefficients(a)

Unstandardized Coefficients Standardized Coefficients t Sig.
Model B Std. Error Beta
1 (Constant) 1201.124 123.325
9.740 .000
Income in Thousands 47.549 4.652 .418 10.221 .000
a Dependent Variable: Summer 1981 Water Use
Casewise Diagnostics(a)
Case Number Std. Residual Summer 1981 Water Use
25 3.661 7100
62 5.187 9400
68 3.429 7500
79 3.979 8100
108 3.661 7100
124 5.001 10100
194 3.277 7200
446 3.161 6900
451 4.225 8100
a Dependent Variable: Summer 1981 Water Use
Residuals Statistics(a)

Minimum Maximum Mean Std. Deviation N
Predicted Value 1296.22 5955.99 2298.39 620.883 496
Residual -2765.33 7010.16 .00 1350.210 496
Std. Predicted Value -1.614 5.891 .000 1.000 496
Std. Residual -2.046 5.187 .000 .999 496
a Dependent Variable: Summer 1981 Water Use 

REGRESSION
  /DEPENDENT water80
  /METHOD=ENTER income
  /SAVE RESID.

 

Variables Entered/Removed(b)
Model Variables Entered Variables Removed Method
1 Income in Thousands(a) . Enter
a All requested variables entered.
b Dependent Variable: Summer 1980 Water Use
Model Summary(b)
Model R R Square Adjusted R Square Std. Error of the Estimate
1 .337(a) .114 .112 1662.273
a Predictors: (Constant), Income in Thousands
b Dependent Variable: Summer 1980 Water Use
ANOVA(b)
Model Sum of Squares df Mean Square F Sig.
1 Regression 174943659.340 1 174943659.340 63.313 .000(a)
Residual 1364996643.080 494 2763151.099

Total 1539940302.419 495


a Predictors: (Constant), Income in Thousands
b Dependent Variable: Summer 1980 Water Use
Coefficients(a)

Unstandardized Coefficients Standardized Coefficients t Sig.
Model B Std. Error Beta
1 (Constant) 1681.433 151.674
11.086 .000
Income in Thousands 45.528 5.722 .337 7.957 .000
a Dependent Variable: Summer 1980 Water Use
Casewise Diagnostics(a)
Case Number Std. Residual Summer 1980 Water Use
62 3.899 9300
94 5.396 12700
155 3.029 7400
194 3.318 8700
362 3.407 7800
446 3.401 8700
451 4.500 10300
477 3.073 7700
482 3.056 7900
a Dependent Variable: Summer 1980 Water Use
Residuals Statistics(a)

Minimum Maximum Mean Std. Deviation N
Predicted Value 1772.49 6234.20 2732.06 594.493 496
Residual -3157.81 8969.82 .00 1660.593 496
Std. Predicted Value -1.614 5.891 .000 1.000 496
Std. Residual -1.900 5.396 .000 .999 496
a Dependent Variable: Summer 1980 Water Use 
formats res_3 res_4 (f4.0) .
GGRAPH
  /GRAPHDATASET NAME="GraphDataset" VARIABLES= res_3 res_4 
  /GRAPHSPEC SOURCE=INLINE .
BEGIN GPL
SOURCE: s=userSource( id( "GraphDataset" ) )
DATA: res_3=col( source(s), name( "res_3" ) )
DATA: res_4=col( source(s), name( "res_4" ) )
GUIDE: axis( dim( 1 ), label( "res_4" ) )
GUIDE: axis( dim( 2 ), label( "res_3" ))
SCALE: linear( dim( 1 ), min(-2000), max(8000))
SCALE: linear( dim( 2 ), min(-2000), max(6000) )
ELEMENT: point( position( res_4 * res_3 ) )
ELEMENT: line(position( smooth.linear(res_4 * res_3 ) ) )
END GPL.

Image

Page 74 Table 3.2  Regression of postshortage water use on income, preshortage  water use, education, retirement, number of people in resident, and increase in people in resident. 

REGRESSION
  /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
Model Summary
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
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

Page 80 Table 3.3  Regression of postshortage water use omitting income and education . 

REGRESSION
  /DEPENDENT water81
  /METHOD=ENTER water80 retire peop81 cpeop.

 

Variables Entered/Removed(b)
Model Variables Entered Variables Removed Method
1 Increase in # of People, Summer 1980 Water Use, head of house retired?, # of People Resident, 1981(a) . Enter
a All requested variables entered.
b Dependent Variable: Summer 1981 Water Use
Model Summary
Model R R Square Adjusted R Square Std. Error of the Estimate
1 .807(a) .652 .649 880.335
a Predictors: (Constant), Increase in # of People, Summer 1980 Water Use, head of house retired?, # of People Resident, 1981
ANOVA(b)
Model Sum of Squares df Mean Square F Sig.
1 Regression 712718346.262 4 178179586.565 229.912 .000(a)
Residual 380520363.415 491 774990.557

Total 1093238709.677 495


a Predictors: (Constant), Increase in # of People, Summer 1980 Water Use, head of house retired?, # 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) 48.649 107.055
.454 .650
Summer 1980 Water Use .520 .027 .617 19.412 .000
head of house retired? 67.280 94.288 .021 .714 .476
# of People Resident, 1981 265.289 29.632 .296 8.953 .000
Increase in # of People 134.463 83.196 .044 1.616 .107
a Dependent Variable: Summer 1981 Water Use

Page 87 Figure 3.3  Regression of log chloride concentration on a dummy variable for well type. 

GET FILE 'd:appsrwgdatawells.sav'.

COMPUTE lnchlor = LG10(chlor).
EXECUTE.

REGRESSION
  /DEPENDENT lnchlor
  /METHOD=ENTER deep.

 

Variables Entered/Removed(b)
Model Variables Entered Variables Removed Method
1 bedrock or shallow well?(a) . Enter
a All requested variables entered.
b Dependent Variable: LNCHLOR
Model Summary
Model R R Square Adjusted R Square Std. Error of the Estimate
1 .205(a) .042 .023 .58910
a Predictors: (Constant), bedrock or shallow well?
ANOVA(b)
Model Sum of Squares df Mean Square F Sig.
1 Regression .759 1 .759 2.187 .145(a)
Residual 17.352 50 .347

Total 18.111 51


a Predictors: (Constant), bedrock or shallow well?
b Dependent Variable: LNCHLOR
Coefficients(a)

Unstandardized Coefficients Standardized Coefficients t Sig.
Model B Std. Error Beta
1 (Constant) 1.640 .186
8.801 .000
bedrock or shallow well? -.307 .207 -.205 -1.479 .145
a Dependent Variable: LNCHLOR 
formats deep lnchlor (f1.0).
GGRAPH
  /GRAPHDATASET NAME="GraphDataset" VARIABLES= lnchlor deep 
  /GRAPHSPEC SOURCE=INLINE.
BEGIN GPL
SOURCE: s=userSource( id( "GraphDataset" ) )
DATA: lnchlor=col( source(s), name( "lnchlor" ) )
DATA: deep=col( source(s), name( "deep" ) )
GUIDE: axis( dim( 1 ), label( "Well Type" ), delta(1) )
GUIDE: axis( dim( 2 ), label( "Natural Log of Cholride Consentration" ) )
SCALE: linear( dim( 1 ), min(0), max(1) )
SCALE: linear( dim( 2 ), min(1), max(6) )
ELEMENT: point( position( deep * lnchlor ) )
ELEMENT: line(position( smooth.linear(deep * lnchlor ) ) )
END GPL.

Image

Page 88 Figure 3.4  Regression of log chloride concentration on log distance from road and an intercept dummy variable for well type.

COMPUTE LNROAD=LG10(DROAD).
EXECUTE.

REGRESSION
  /DEPENDENT lnchlor deep
  /METHOD=ENTER lnroad
  /SAVE pred (pred1).

Variables Entered/Removedb

Model

Variables Entered

Variables Removed

Method

1

deep bedrock or shallow well?, LNROADa

.

Enter

a. All requested variables entered.

b. Dependent Variable: lnchlor

Model Summaryb

Model

R

R Square

Adjusted R Square

Std. Error of the Estimate

1

.217a

.047

.008

1.36666

a. Predictors: (Constant), deep bedrock or shallow well?, LNROAD

b. Dependent Variable: lnchlor

ANOVAb

Model

Sum of Squares

df

Mean Square

F

Sig.

1

Regression

4.502

2

2.251

1.205

.308a

Residual

91.520

49

1.868

    

Total

96.022

51

      

a. Predictors: (Constant), deep bedrock or shallow well?, LNROAD

b. Dependent Variable: lnchlor

Coefficientsa

Model

Unstandardized Coefficients

Standardized Coefficients

t

Sig.

B

Std. Error

Beta

1

(Constant)

4.210

.961

  

4.381

.000

LNROAD

-.091

.180

-.071

-.506

.615

deep bedrock or shallow well?

-.697

.481

-.202

-1.449

.154

a. Dependent Variable: lnchlor

Residuals Statisticsa
 

Minimum

Maximum

Mean

Std. Deviation

N

Predicted Value

2.7957

3.8861

3.2050

.29711

52

Residual

-2.05794

3.78616

.00000

1.33960

52

Std. Predicted Value

-1.378

2.292

.000

1.000

52

Std. Residual

-1.506

2.770

.000

.980

52

a. Dependent Variable: lnchlor

 
formats lnroad lnchlor pred1 (f1.0).
GGRAPH 
  /GRAPHDATASET NAME="graphdataset" VARIABLES=lnroad lnchlor deep pred1
  /GRAPHSPEC SOURCE=INLINE. 
BEGIN GPL 
SOURCE: s=userSource(id("graphdataset")) 
DATA: lnroad=col(source(s), name("lnroad")) 
DATA: pred1=col(source(s), name("pred1")) 
DATA: deep=col(source(s), name("deep"), unit.category() ) 
DATA: lnchlor=col(source(s), name("lnchlor")) 
GUIDE: axis( dim( 1 ), label( "natural log distance from road" ), delta(2) )
GUIDE: axis( dim( 2 ), label( "natural log of cholride consentration" ), delta(1) )
SCALE: linear( dim( 1 ), min(0), max(8) )
SCALE: linear( dim( 2 ), min(0), max(7) )
ELEMENT: point(position(lnroad*lnchlor)) 
ELEMENT: line(position( smooth.linear(lnroad * pred1 ) ), shape(deep) )
END GPL.

Image

Page 89 Figure 3.5  Regression of log chloride concentration on log distance from road and a slope dummy variable for well type.

Compute deeproad=deep*lnroad.
Execute.

REGRESSION
 /DEPENDENT lnchlor
 /METHOD=ENTER lnroad deeproad
 /SAVE pred (pred2).

Variables Entered/Removedb

Model

Variables Entered

Variables Removed

Method

1

deeproad, LNROADa

.

Enter

a. All requested variables entered.

b. Dependent Variable: lnchlor

Model Summaryb

Model

R

R Square

Adjusted R Square

Std. Error of the Estimate

1

.140a

.019

-.021

1.386

a. Predictors: (Constant), deeproad, LNROAD

b. Dependent Variable: lnchlor

ANOVAb

Model

Sum of Squares

df

Mean Square

F

Sig.

1

Regression

1.871

2

.935

.487

.618a

Residual

94.151

49

1.921

    

Total

96.022

51

      

a. Predictors: (Constant), deeproad, LNROAD

b. Dependent Variable: lnchlor

Coefficientsa

Model

Unstandardized Coefficients

Standardized Coefficients

t

Sig.

B

Std. Error

Beta

1

(Constant)

3.666

.905

  

4.050

.000

LNROAD

-.029

.202

-.022

-.144

.886

deeproad

-.081

.099

-.128

-.819

.417

a. Dependent Variable: lnchlor

Residuals Statisticsa
 

Minimum

Maximum

Mean

Std. Deviation

N

Predicted Value

2.80

3.56

3.21

.192

52

Residual

-2.135

3.775

.000

1.359

52

Std. Predicted Value

-2.135

1.870

.000

1.000

52

Std. Residual

-1.541

2.723

.000

.980

52

a. Dependent Variable: lnchlor

 
formats lnroad lnchlor pred2 (f1.0).
GGRAPH 
  /GRAPHDATASET NAME="graphdataset" VARIABLES=lnroad lnchlor deep pred2
  /GRAPHSPEC SOURCE=INLINE. 
BEGIN GPL 
SOURCE: s=userSource(id("graphdataset")) 
DATA: lnroad=col(source(s), name("lnroad")) 
DATA: pred2=col(source(s), name("pred2")) 
DATA: deep=col(source(s), name("deep"), unit.category() ) 
DATA: lnchlor=col(source(s), name("lnchlor")) 
GUIDE: axis( dim( 1 ), label( "natural log distance from road" ), delta(2) )
GUIDE: axis( dim( 2 ), label( "natural log of cholride consentration" ), delta(1) )
SCALE: linear( dim( 1 ), min(0), max(8) )
SCALE: linear( dim( 2 ), min(0), max(7) )
ELEMENT: point(position(lnroad*lnchlor)) 
ELEMENT: line(position( smooth.linear(lnroad * pred2 ) ), shape(deep) )
END GPL.

Image

Page 90 Table 3.4  Regression of log chloride concentration on log distance from road, with intercept and slope dummy variables for well type. 

REGRESSION
/DEPENDENT lnchlor
/METHOD=ENTER deep lnroad deeproad.
Variables Entered/Removed(b)
Model Variables Entered Variables Removed Method
1 DEEPROAD, LNROAD, bedrock or shallow well?(a) . Enter
a All requested variables entered.
b Dependent Variable: LNCHLOR
Model Summary
Model R R Square Adjusted R Square Std. Error of the Estimate
1 .439(a) .192 .142 .55198
a Predictors: (Constant), DEEPROAD, LNROAD, bedrock or shallow well?
ANOVA(b)
Model Sum of Squares df Mean Square F Sig.
1 Regression 3.486 3 1.162 3.814 .016(a)
Residual 14.625 48 .305

Total 18.111 51


a Predictors: (Constant), DEEPROAD, LNROAD, bedrock or shallow well?
b Dependent Variable: LNCHLOR
Coefficients(a)

Unstandardized Coefficients Standardized Coefficients t Sig.
Model B Std. Error Beta
1 (Constant) 3.941 .816
4.828 .000
bedrock or shallow well? -2.917 .910 -1.948 -3.207 .002
LNROAD -1.109 .384 -.862 -2.886 .006
DEEPROAD 1.256 .427 1.979 2.942 .005
a Dependent Variable: LNCHLOR


Page 91 Figure 3.6  Regression of log chloride concentration on log distance from road, with slope and intercept dummy variables for well type. 

GGRAPH 
  /GRAPHDATASET NAME="graphdataset" VARIABLES=lnroad lnchlor deep
  /GRAPHSPEC SOURCE=INLINE. 
BEGIN GPL 
SOURCE: s=userSource(id("graphdataset")) 
DATA: lnroad=col(source(s), name("lnroad")) 
DATA: deep=col(source(s), name("deep"), unit.category() ) 
DATA: lnchlor=col(source(s), name("lnchlor")) 
GUIDE: axis( dim( 1 ), label( "natural log distance from road" ), delta(2) )
GUIDE: axis( dim( 2 ), label( "natural log of cholride consentration" ), delta(1) )
SCALE: linear( dim( 1 ), min(0), max(8) )
SCALE: linear( dim( 2 ), min(0), max(9) )
ELEMENT: point(position(lnroad*lnchlor)) 
ELEMENT: line(position( smooth.linear(lnroad * lnchlor ) ), shape(deep) )
END GPL.

Image

Page 91 Figure 3.7  Separate regression for shallow (left) and deep (right) wells; same line as in Figure 3.6. 

sort cases by deep.
split file by deep.
GGRAPH 
  /GRAPHDATASET NAME="graphdataset" VARIABLES=lnroad lnchlor
  /GRAPHSPEC SOURCE=INLINE. 
BEGIN GPL 
SOURCE: s=userSource(id("graphdataset")) 
DATA: lnroad=col(source(s), name("lnroad")) 
DATA: lnchlor=col(source(s), name("lnchlor")) 
GUIDE: axis( dim( 1 ), label( "natural log distance from road" ), delta(2) )
GUIDE: axis( dim( 2 ), label( "natural log of cholride consentration" ), delta(1) )
SCALE: linear( dim( 1 ), min(0), max(8) )
SCALE: linear( dim( 2 ), min(0), max(9) )
ELEMENT: point(position(lnroad*lnchlor)) 
ELEMENT: line(position( smooth.linear(lnroad * lnchlor ) ) )
END GPL.
split file off.

Image Image

Page 93 Table 3.5  Cancer, bedrock and radon in 26 counties. 

GET FILE 'd:appsrwgdataradon.sav'.

USE ALL.
SELECT IF(number > 0).
EXECUTE.

if reading=1 area=1.
if fringe=1 area=2.
if control=1 area=3.

recode radon (0 thru 1.5=1) into mnradon.
recode radon (1.6 thru 2.45=2) into mnradon.
recode radon (2.5 thru 10.0=3) into mnradon.

compute lowradon=0.
if mnradon=1 lowradon=1.
compute midradon=0.
if mnradon=2 midradon=1.
execute.

list county cancer locale reading fringe mnradon lowradon midradon.


COUNTY         CANCER   LOCALE  READING   FRINGE  MNRADON LOWRADON MIDRADON

Orange           6.00        1        1        0     1.00     1.00      .00
Putnam          10.50        1        1        0     2.00      .00     1.00
Sussex           6.70        1        1        0     2.00      .00     1.00
Warren           6.00        1        1        0     3.00      .00      .00
Morris           6.10        1        1        0     1.00     1.00      .00
Hunterdon        6.70        1        1        0     3.00      .00      .00
Berks            5.20        2        0        1     3.00      .00      .00
Lehigh           5.60        2        0        1     3.00      .00      .00
Northampton      5.80        2        0        1     3.00      .00      .00
Pike             4.50        2        0        1     1.00     1.00      .00
Dutchess         5.50        2        0        1     2.00      .00     1.00
Sullivan         5.40        2        0        1     1.00     1.00      .00
Ulster           6.30        2        0        1     1.00     1.00      .00
Columbia         6.30        3        0        0     2.00      .00     1.00
Delaware         4.30        3        0        0     2.00      .00     1.00
Greene           4.00        3        0        0     2.00      .00     1.00
Otsego           5.90        3        0        0     2.00      .00     1.00
Tioga            4.70        3        0        0     2.00      .00     1.00
Carbon           4.80        3        0        0     2.00      .00     1.00
Lebanon          5.80        3        0        0     3.00      .00      .00
Lackawanna       5.40        3        0        0     1.00     1.00      .00
Luzerne          5.20        3        0        0     1.00     1.00      .00
Schuylkill       3.60        3        0        0     3.00      .00      .00
Susquehanna      4.30        3        0        0     1.00     1.00      .00
Wayne            3.50        3        0        0     1.00     1.00      .00
Wyoming          6.90        3        0        0     2.00      .00     1.00

Number of cases read:  26    Number of cases listed:  26


Page 94 Table 3.6  Relation between cancer rate and bedrock area. 

REGRESSION
  /VAR=cancer reading fringe
  /DEPENDENT cancer
  /METHOD=TEST(reading fringe).

Variables Entered/Removed(a)
Model Variables Entered Variables Removed Method
1 Fringe area dummy, Reading Prong dummy . Test
a Dependent Variable: Wt.Female Lung Cancer (x10^-5/y
Model Summary
Model R R Square Adjusted R Square Std. Error of the Estimate
1 .598(a) .358 .302 1.14848
a Predictors: (Constant), Fringe area dummy, Reading Prong dummy
ANOVA(c)
Model Sum of Squares df Mean Square F Sig. R Square Change
1 Subset Tests Reading Prong dummy, Fringe area dummy 16.909 2 8.454 6.410 .006(a) .358
Regression 16.909 2 8.454 6.410 .006(b)
Residual 30.337 23 1.319


Total 47.246 25



a Tested against the full model.
b Predictors in the Full Model: (Constant), Fringe area dummy, Reading Prong dummy.
c Dependent Variable: Wt.Female Lung Cancer (x10^-5/y
Coefficients(a)

Unstandardized Coefficients Standardized Coefficients t Sig.
Model B Std. Error Beta
1 (Constant) 4.977 .319
15.625 .000
Reading Prong dummy 2.023 .567 .632 3.569 .002
Fringe area dummy .495 .538 .163 .918 .368
a Dependent Variable: Wt.Female Lung Cancer (x10^-5/y 

ONEWAY
  cancer BY area.

ANOVA
Wt.Female Lung Cancer (x10^-5/y

Sum of Squares df Mean Square F Sig.
Between Groups 16.909 2 8.454 6.410 .006
Within Groups 30.337 23 1.319

Total 47.246 25


Page 96 Table 3.7  Relation among cancer rate, bedrock area, and radon. 

REGRESSION
  /VAR=cancer reading fringe lowradon midradon
  /DEPENDENT cancer
  /METHOD=TEST(reading fringe) (lowradon midradon).

 

Variables Entered/Removed(a)
Model Variables Entered Variables Removed Method
1 MIDRADON, Reading Prong dummy, Fringe area dummy, LOWRADON . Test
a Dependent Variable: Wt.Female Lung Cancer (x10^-5/y
Model Summary
Model R R Square Adjusted R Square Std. Error of the Estimate
1 .684(a) .468 .367 1.09376
a Predictors: (Constant), MIDRADON, Reading Prong dummy, Fringe area dummy, LOWRADON
ANOVA(c)
Model Sum of Squares df Mean Square F Sig. R Square Change
1 Subset Tests Reading Prong dummy, Fringe area dummy 19.285 2 9.642 8.060 .003(a) .408
LOWRADON, MIDRADON 5.215 2 2.607 2.180 .138(a) .110
Regression 22.124 4 5.531 4.623 .008(b)
Residual 25.123 21 1.196


Total 47.246 25



a Tested against the full model.
b Predictors in the Full Model: (Constant), MIDRADON, Reading Prong dummy, Fringe area dummy, LOWRADON.
c Dependent Variable: Wt.Female Lung Cancer (x10^-5/y
Coefficients(a)

Unstandardized Coefficients Standardized Coefficients t Sig.
Model B Std. Error Beta
1 (Constant) 4.525 .528
8.569 .000
Reading Prong dummy 2.212 .551 .691 4.014 .001
Fringe area dummy .867 .549 .285 1.579 .129
LOWRADON -.117 .556 -.041 -.210 .836
MIDRADON .906 .576 .327 1.573 .131
a Dependent Variable: Wt.Female Lung Cancer (x10^-5/y 

UNIANOVA
  cancer  BY area mnradon
  /DESIGN = area mnradon.
Between-Subjects Factors

N
AREA 1.00 6
2.00 7
3.00 13
MNRADON 1.00 9
2.00 10
3.00 7
Tests of Between-Subjects Effects
Dependent Variable: Wt.Female Lung Cancer (x10^-5/y
Source Type III Sum of Squares df Mean Square F Sig.
Corrected Model 22.124(a) 4 5.531 4.623 .008
Intercept 784.039 1 784.039 655.380 .000
AREA 19.285 2 9.642 8.060 .003
MNRADON 5.215 2 2.607 2.180 .138
Error 25.123 21 1.196

Total 855.900 26


Corrected Total 47.246 25


a R Squared = .468 (Adjusted R Squared = .367)

Page 98 Table 3.8  Relation among cancer rate, bedrock area, and radon, with interaction. 

compute x1x3=reading*lowradon.
compute x1x4=reading*midradon.
compute x2x3=fringe*lowradon.
compute x2x4=fringe*midradon.
execute.

REGRESSION
  /VAR cancer reading fringe lowradon midradon x1x3 x1x4 x2x3 x2x4
  /DEPENDENT cancer
  /METHOD=TEST(reading fringe lowradon midradon) (x1x3 x1x4 x2x3 x2x4).
Variables Entered/Removed(a)
Model Variables Entered Variables Removed Method
1 X2X4, X1X4, X1X3, X2X3, MIDRADON, LOWRADON, Fringe area dummy, Reading Prong dummy . Test
a Dependent Variable: Wt.Female Lung Cancer (x10^-5/y
Model Summary
Model R R Square Adjusted R Square Std. Error of the Estimate
1 .742(a) .551 .340 1.11701
a Predictors: (Constant), X2X4, X1X4, X1X3, X2X3, MIDRADON, LOWRADON, Fringe area dummy, Reading Prong dummy
ANOVA(c)
Model Sum of Squares df Mean Square F Sig. R Square Change
1 Subset Tests Reading Prong dummy, Fringe area dummy, LOWRADON, MIDRADON 4.945 4 1.236 .991 .439(a) .105
X1X3, X1X4, X2X3, X2X4 3.912 4 .978 .784 .551(a) .083
Regression 26.035 8 3.254 2.608 .046(b)
Residual 21.211 17 1.248


Total 47.246 25



a Tested against the full model.
b Predictors in the Full Model: (Constant), X2X4, X1X4, X1X3, X2X3, MIDRADON, LOWRADON, Fringe area dummy, Reading Prong dummy.
c Dependent Variable: Wt.Female Lung Cancer (x10^-5/y
Coefficients(a)

Unstandardized Coefficients Standardized Coefficients t Sig.
Model B Std. Error Beta
1 (Constant) 4.700 .790
5.951 .000
Reading Prong dummy 1.650 1.117 .516 1.477 .158
Fringe area dummy .833 1.020 .274 .817 .425
LOWRADON -.100 .967 -.035 -.103 .919
MIDRADON .571 .896 .206 .638 .532
X1X3 -.200 1.478 -.040 -.135 .894
X1X4 1.679 1.432 .332 1.172 .257
X2X3 -3.333E-02 1.330 -.008 -.025 .980
X2X4 -.605 1.570 -.086 -.385 .705
a Dependent Variable: Wt.Female Lung Cancer (x10^-5/y 

UNIANOVA  cancer  BY area mnradon
  /DESIGN = area mnradon area*mnradon.

Between-Subjects Factors

N
AREA 1.00 6
2.00 7
3.00 13
MNRADON 1.00 9
2.00 10
3.00 7
Tests of Between-Subjects Effects
Dependent Variable: Wt.Female Lung Cancer (x10^-5/y
Source Type III Sum of Squares df Mean Square F Sig.
Corrected Model 26.035(a) 8 3.254 2.608 .046
Intercept 666.210 1 666.210 533.949 .000
AREA 17.400 2 8.700 6.973 .006
MNRADON 4.358 2 2.179 1.746 .204
AREA * MNRADON 3.912 4 .978 .784 .551
Error 21.211 17 1.248

Total 855.900 26


Corrected Total 47.246 25


a R Squared = .551 (Adjusted R Squared = .340)

Page 99 Table 3.9  Effect coding of bedrock area from Table 3.5. 

if area=1 rev1=1.
if area=2 rev1=0.
if area=3 rev1=-1.
if area=1 fev2=0.
if area=2 fev2=1.
if area=3 fev2=-1.
execute.

list county area reading ereading fringe efringe.


COUNTY          AREA  READING EREADING   FRINGE  EFRINGE

Orange          1.00        1        1        0        0
Putnam          1.00        1        1        0        0
Sussex          1.00        1        1        0        0
Warren          1.00        1        1        0        0
Morris          1.00        1        1        0        0
Hunterdon       1.00        1        1        0        0
Berks           2.00        0        0        1        1
Lehigh          2.00        0        0        1        1
Northampton     2.00        0        0        1        1
Pike            2.00        0        0        1        1
Dutchess        2.00        0        0        1        1
Sullivan        2.00        0        0        1        1
Ulster          2.00        0        0        1        1
Columbia        3.00        0       -1        0       -1
Delaware        3.00        0       -1        0       -1
Greene          3.00        0       -1        0       -1
Otsego          3.00        0       -1        0       -1
Tioga           3.00        0       -1        0       -1
Carbon          3.00        0       -1        0       -1
Lebanon         3.00        0       -1        0       -1
Lackawanna      3.00        0       -1        0       -1
Luzerne         3.00        0       -1        0       -1
Schuylkill      3.00        0       -1        0       -1
Susquehanna     3.00        0       -1        0       -1
Wayne           3.00        0       -1        0       -1
Wyoming         3.00        0       -1        0       -1

Number of cases read:  26    Number of cases listed:  26

Page 100 Table 3.10  Relation among cancer rate, bedrock area, and radon. 

compute v3=lowradon.
if mnradon=3 v3=-1.
compute v4=midradon.
if mnradon=3 v4=-1.
compute v1v3=ereading*v3.
compute v1v4=ereading*v4.
compute v2v3=efringe*v3.
compute v2v4=efringe*v4.
execute.

REGRESSION
 /VAR cancer ereading efringe v3 v4 v1v3 v1v4 v2v3 v2v4
 /DEPENDENT cancer
 /METHOD=TEST (ereading efringe v3 v4) (v1v3 v1v4 v2v3 v2v4).
Variables Entered/Removed(a)
Model Variables Entered Variables Removed Method
1 V2V4, effects-coded fringe, V3, V1V3, V2V3, effects-coded Reading, V4, V1V4 . Test
a Dependent Variable: Wt.Female Lung Cancer (x10^-5/y
Model Summary
Model R R Square Adjusted R Square Std. Error of the Estimate
1 .742(a) .551 .340 1.11701
a Predictors: (Constant), V2V4, effects-coded fringe, V3, V1V3, V2V3, effects-coded Reading, V4, V1V4
ANOVA(c)
Model Sum of Squares df Mean Square F Sig. R Square Change
1 Subset Tests effects-coded Reading, effects-coded fringe, V3, V4 21.612 4 5.403 4.330 .013(a) .457
V1V3, V1V4, V2V3, V2V4 3.912 4 .978 .784 .551(a) .083
Regression 26.035 8 3.254 2.608 .046(b)
Residual 21.211 17 1.248


Total 47.246 25



a Tested against the full model.
b Predictors in the Full Model: (Constant), V2V4, effects-coded fringe, V3, V1V3, V2V3, effects-coded Reading, V4, V1V4.
c Dependent Variable: Wt.Female Lung Cancer (x10^-5/y
Coefficients(a)

Unstandardized Coefficients Standardized Coefficients t Sig.
Model B Std. Error Beta
1 (Constant) 5.778 .250
23.107 .000
effects-coded Reading 1.222 .363 .735 3.365 .004
effects-coded fringe -.301 .374 -.189 -.804 .432
V3 -.428 .336 -.248 -1.276 .219
V4 .679 .372 .403 1.824 .086
V1V3 -.522 .501 -.238 -1.041 .313
V1V4 .921 .526 .465 1.750 .098
V2V3 .351 .486 .176 .722 .480
V2V4 -.657 .595 -.318 -1.103 .285
a Dependent Variable: Wt.Female Lung Cancer (x10^-5/y 
UNIANOVA  cancer  BY area mnradon
  /DESIGN = area mnradon area*mnradon.

Between-Subjects Factors

N
AREA 1.00 6
2.00 7
3.00 13
MNRADON 1.00 9
2.00 10
3.00 7
Tests of Between-Subjects Effects
Dependent Variable: Wt.Female Lung Cancer (x10^-5/y
Source Type III Sum of Squares df Mean Square F Sig.
Corrected Model 26.035(a) 8 3.254 2.608 .046
Intercept 666.210 1 666.210 533.949 .000
AREA 17.400 2 8.700 6.973 .006
MNRADON 4.358 2 2.179 1.746 .204
AREA * MNRADON 3.912 4 .978 .784 .551
Error 21.211 17 1.248

Total 855.900 26


Corrected Total 47.246 25


a R Squared = .551 (Adjusted R Squared = .340)

 

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