SPSS Textbook Examples: Regression with Graphics, Chapter 3



Stat Computing > SPSS > Textbook Examples > Regression with Graphics, by Hamilton

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

A three-variable example

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

GET FILE 'd:\apps\rwgdata\concord1.sav'.

REGRESSION
  /DEPENDENT water81
  /METHOD=ENTER income water80.

Regression

**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	t	Sig.
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

Partial effects

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.

Regression

**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	t	Sig.
1	(Constant)	537.871	79.401		6.774	.000
1	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.

Regression

**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	t	Sig.
1	(Constant)	16.259	1.019		15.948	.000
1	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


IGRAPH
 /X1 = VAR(res_2)
 /Y = VAR(res_1)
 /FITLINE METHOD = REGRESSION LINEAR  LINE = TOTAL
 /SCATTER COINCIDENT = NONE.

Interactive Graph

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.

Regression

**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	t	Sig.
1	(Constant)	1201.124	123.325		9.740	.000
1	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.

Regression

**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	t	Sig.
1	(Constant)	1681.433	151.674		11.086	.000
1	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

IGRAPH
 /X1 = VAR(res_4)
 /Y = VAR(res_3)
 /FITLINE METHOD = REGRESSION LINEAR  LINE = TOTAL
 /SCATTER COINCIDENT = NONE.

Interactive Graph

A seven-variable example

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.

Regression

**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	t	Sig.
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

F-tests for sets of coefficients

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

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

Regression

**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	t	Sig.
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

Intercept dummy variables

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

GET FILE 'd:\apps\rwgdata\wells.sav'.

COMPUTE lnchlor = LG10(chlor).
EXECUTE.

REGRESSION
  /DEPENDENT lnchlor
  /METHOD=ENTER deep.

Regression

**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	t	Sig.
1	(Constant)	1.640	.186		8.801	.000
1	bedrock or shallow well?	-.307	.207	-.205	-1.479	.145
a Dependent Variable: LNCHLOR


IGRAPH
 /X1 = VAR(deep)
 /Y = VAR(lnchlor)
 /FITLINE METHOD = REGRESSION LINEAR  LINE = TOTAL
 /SCATTER COINCIDENT = NONE.

Interactive Graph

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  /METHOD=ENTER lnroad
  /SAVE RESID.

Regression

**Variables Entered/Removed(b)**
Model	Variables Entered	Variables Removed	Method
1	LNROAD(a)	.	Enter
a All requested variables entered.
b Dependent Variable: LNCHLOR

**Model Summary(b)**
Model	R	R Square	Adjusted R Square	Std. Error of the Estimate
1	.078(a)	.006	-.014	.60002
a Predictors: (Constant), LNROAD
b Dependent Variable: LNCHLOR

**ANOVA(b)**
Model		Sum of Squares	df	Mean Square	F	Sig.
1	Regression	.110	1	.110	.305	.583(a)
	Residual	18.001	50	.360
	Total	18.111	51
a Predictors: (Constant), LNROAD
b Dependent Variable: LNCHLOR

**Coefficients(a)**
		Unstandardized Coefficients		Standardized Coefficients	t	Sig.
Model		B	Std. Error	Beta	t	Sig.
1	(Constant)	1.603	.392		4.094	.000
1	LNROAD	-.100	.182	-.078	-.552	.583
a Dependent Variable: LNCHLOR

**Residuals Statistics(a)**
	Minimum	Maximum	Mean	Std. Deviation	N
Predicted Value	1.2602	1.4728	1.3919	.04638	52
Residual	-.9558	1.5960	.0000	.59411	52
Std. Predicted Value	-2.840	1.743	.000	1.000	52
Std. Residual	-1.593	2.660	.000	.990	52
a Dependent Variable: LNCHLOR


if deep=0 yhat0=res_1.
if deep=1 yhat1=res_1.
execute.

GRAPH
 /SCATTERPLOT(BIVAR)=lnroad WITH lnchlor.

Graph

Scatter of lnchlor lnroad

Slope dummy variables

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 RESID.

Regression

**Variables Entered/Removed(b)**
Model	Variables Entered	Variables Removed	Method
1	DEEPROAD, LNROAD(a)	.	Enter
a All requested variables entered.
b Dependent Variable: LNCHLOR

**Model Summary(b)**
Model	R	R Square	Adjusted R Square	Std. Error of the Estimate
1	.140(a)	.019	-.021	.60200
a Predictors: (Constant), DEEPROAD, LNROAD
b Dependent Variable: LNCHLOR

**ANOVA(b)**
Model		Sum of Squares	df	Mean Square	F	Sig.
1	Regression	.353	2	.176	.487	.618(a)
	Residual	17.758	49	.362
	Total	18.111	51
a Predictors: (Constant), DEEPROAD, LNROAD
b Dependent Variable: LNCHLOR

**Coefficients(a)**
		Unstandardized Coefficients		Standardized Coefficients	t	Sig.
Model		B	Std. Error	Beta	t	Sig.
1	(Constant)	1.592	.393		4.050	.000
	LNROAD	-2.897E-02	.202	-.022	-.144	.886
	DEEPROAD	-8.147E-02	.099	-.128	-.819	.417
a Dependent Variable: LNCHLOR

**Residuals Statistics(a)**
	Minimum	Maximum	Mean	Std. Deviation	N
Predicted Value	1.2143	1.5475	1.3919	.08318	52
Residual	-.9274	1.6394	.0000	.59008	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

If deep=0 yhat20=res_2.
If deep=1 yhat10=res_2.
Execute.

GRAPH
  /SCATTERPLOT(BIVAR)=lnroad WITH lnchlor.

Graph

Scatter of lnchlor lnroad

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.

Regression

**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	t	Sig.
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.

NOTE: SPSS will not allow you to include two regression lines and the data points as shown in this figure. However, you can graph one regression line and the data points, as shown below.

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

USE ALL.
COMPUTE filter_$=(deep=0).
VARIABLE LABEL filter_$ 'deep=0 (FILTER)'.
VALUE LABELS filter_$  0 'Not Selected' 1 'Selected'.
FILTER BY filter_$.
EXECUTE.

IGRAPH
 /X1 = VAR(lnroad)
 /Y = VAR (lnchlor)
 /FITLINE METHOD = REGRESSION  LINEAR LINE = TOTAL
 /SCATTER COINCIDENT = NONE.

Interactive Graph



USE ALL.
COMPUTE filter_$=(deep=1).
VARIABLE LABEL filter_$ 'deep=1 (FILTER)'.
VALUE LABELS filter_$  0 'Not Selected' 1 'Selected'.
FILTER BY filter_$.
EXECUTE.

USE ALL.
IGRAPH
 /X1 = VAR(lnroad)
 /Y = VAR (lnchlor)
 /FITLINE METHOD = REGRESSION  LINEAR LINE = TOTAL
 /SCATTER COINCIDENT = NONE.

Interactive Graph

Oneway analysis of variance

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

GET FILE 'd:\apps\rwgdata\radon.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.

List

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).

Regression

**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	t	Sig.
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.

Oneway

**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

Twoway analysis of variance

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

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

Regression

**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
	Subset Tests	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	t	Sig.
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.

Univariate analysis of variance

**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).

Regression

**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
	Subset Tests	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	t	Sig.
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.

Univariate analysis of variance

**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.

List

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.

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

A three-variable example

Regression

Partial effects

Regression

Regression

Interactive Graph

Regression

Regression

Interactive Graph

A seven-variable example

Regression

F-tests for sets of coefficients

Regression

Intercept dummy variables

Regression

Interactive Graph

Regression

Graph

Slope dummy variables

Regression

Graph

Regression

Interactive Graph

Interactive Graph

Oneway analysis of variance

List

Regression

Oneway

Twoway analysis of variance

Regression

Univariate analysis of variance

Regression

Univariate analysis of variance

List

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