SPSS Textbook Examples
Applied Regression Analysis by John Fox
Chapter 5: Linear least-squares regression

page 86 Figure 5.1 Scatterplot of Davis's data on the measured and reported weight of 101 women. The solid line give the least-squares fit; the broken line is Y = X. Both variables are discrete, since the weight is given to the nearest kilogram, but overplotting of points is not a serious problem here.

NOTE: There is an error in the data for subject number 12.

GET FILE='D:\davis.sav'.

if subject=12 measwt=57.
if subject=12 measht=166.
execute.

USE ALL.
COMPUTE filter_$=(female=1).
VARIABLE LABEL filter_$ 'female=1 (FILTER)'.
VALUE LABELS filter_$  0 'Not Selected' 1 'Selected'.
FORMAT filter_$ (f1.0).
FILTER BY filter_$.
EXECUTE.

GGRAPH
  /GRAPHDATASET NAME="graphdataset" VARIABLES=reptwt measwt 
  /GRAPHSPEC SOURCE=INLINE inlinetemplate="<addReferenceLine numberPoints='200' y='x'><style color='black' stroke-dasharray='5px,5px'/></addReferenceLine>".
BEGIN GPL
SOURCE: s=userSource(id("graphdataset"))
DATA: reptwt=col(source(s), name("reptwt"))
DATA: measwt=col(source(s), name("measwt"))
GUIDE: axis(dim(1), label("Reported Weight, Kg"))
GUIDE: axis(dim(2), label("Measured Weight, Kg"))
ELEMENT: point(position(reptwt*measwt))
ELEMENT: line(position(smooth.linear(reptwt*measwt)))
END GPL.

page 89 The regression equation in the middle of the page.

REGRESSION
  /DESCRIPTIVES=MEAN
  /STATISTICS COEFF OUTS R ANOVA
  /DEPENDENT measwt
  /METHOD=ENTER reptwt.

Descriptive Statistics

	Mean	N
Measured Weight	57.23	101
Reported Weight	56.74	101

Variables Entered/Removed(b)

Model	Variables Entered	Variables Removed	Method
1	Reported Weight(a)	.	Enter
a All requested variables entered.
b Dependent Variable: Measured Weight

Model Summary

Model	R	R Square	Adjusted R Square	Std. Error of the Estimate
1	.955(a)	.912	.911	2.057
a Predictors: (Constant), Reported Weight

ANOVA(b)

Model		Sum of Squares	df	Mean Square	F	Sig.
1	Regression	4334.889	1	4334.889	1024.544	.000(a)
	Residual	418.873	99	4.231
	Total	4753.762	100
a Predictors: (Constant), Reported Weight
b Dependent Variable: Measured Weight

Coefficients(a)

		Unstandardized Coefficients		Standardized Coefficients	t	Sig.
Model		B	Std. Error	Beta
1	(Constant)	1.778	1.744		1.019	.311
	Reported Weight	.977	.031	.955	32.009	.000
a Dependent Variable: Measured Weight

page 90 To get the standard error shown in the middle of the page,. take the square root of the mean square error, 4.231, listed in the. second row of the fourth column of the ANOVA table of the above . output.

page 97 Table 5.1 Data on the U.S. States and Washington, D.C. in 1970: State per-capita public school expenditures (E, in dollars); per-capita annual income (I, in dollars); proportion of residents under 18 (S, per 1000); and proportion residing in urban areas (U, per 1000).

GET FILE='D:\anscombe.sav'.

list state educspnd income prop18 propurb.


STATE  EDUCSPND    INCOME    PROP18   PROPURB

ME          189      2824    350.70       508
NH          169      3259    345.90       564
VT          230      3072    348.50       322
MA          168      3835    335.30       846
RI          180      3549    327.10       871
CT          193      4256    341.00       774
NY          261      4151    326.20       856
NJ          214      3954    333.50       889
PA          201      3419    326.20       715
OH          172      3509    354.50       753
IN          194      3412    359.30       649
IL          189      3981    348.90       830
MI          233      3675    369.20       738
WI          209      3363    360.70       659
MN          262      3341    365.40       664
IO          234      3265    343.80       572
MO          177      3257    336.10       701
ND          177      2730    369.10       443
SD          187      2876    368.70       446
NE          148      3239    349.90       615
KA          196      3303    339.90       661
DE          248      3795    375.90       722
MD          247      3742    364.10       766
DC          246      4425    352.10      1000
VA          180      3068    353.00       631
WV          149      2470    328.80       390
NC          155      2664    354.10       450
SC          149      2380    376.70       476
GA          156      2781    370.60       603
FL          191      3191    336.00       805
KY          140      2645    349.30       523
TN          137      2579    342.80       588
AL          112      2337    362.20       584
MS          130      2081    385.20       445
AR          134      2322    351.90       500
LA          162      2634    389.60       661
OK          135      2880    329.80       680
TX          155      3029    369.40       797
MT          238      2942    368.90       534
ID          170      2668    367.70       541
WY          238      3190    365.60       605
CO          192      3340    358.10       785
NM          227      2651    421.50       698
AZ          207      3027    387.50       796
UT          201      2790    412.40       804
NV          225      3957    385.10       809
WA          215      3688    341.30       726
OR          233      3317    332.70       671
CA          273      3968    348.40       909
AK          372      4146    439.70       484

STATE  EDUCSPND    INCOME    PROP18   PROPURB

HI          212      3513    382.90       831

Number of cases read:  51    Number of cases listed:  51

page 100 The regression coefficients listed at the top of the page.

GET  FILE='D:\duncan.sav'.

REGRESSION
  /STATISTICS COEFF OUTS R ANOVA
  /DEPENDENT prestige
  /METHOD=ENTER educ income.
 

Variables Entered/Removed(b)

Model	Variables Entered	Variables Removed	Method
1	Percent of males in occupation earning $3500 or more in 1950, Percent of males in occupation in 1950 who were high-school graduates(a)	.	Enter
a All requested variables entered.
b Dependent Variable: Percent of raters in NORC study rating occupation as excellent or good in presti

Model Summary

Model	R	R Square	Adjusted R Square	Std. Error of the Estimate
1	.910(a)	.828	.820	13.369
a Predictors: (Constant), Percent of males in occupation earning $3500 or more in 1950, Percent of males in occupation in 1950 who were high-school graduates

ANOVA(b)

Model		Sum of Squares	df	Mean Square	F	Sig.
1	Regression	36180.946	2	18090.473	101.216	.000(a)
	Residual	7506.699	42	178.731
	Total	43687.644	44
a Predictors: (Constant), Percent of males in occupation earning $3500 or more in 1950, Percent of males in occupation in 1950 who were high-school graduates
b Dependent Variable: Percent of raters in NORC study rating occupation as excellent or good in presti

Coefficients(a)

		Unstandardized Coefficients		Standardized Coefficients	t	Sig.
Model		B	Std. Error	Beta
1	(Constant)	-6.065	4.272		-1.420	.163
	Percent of males in occupation in 1950 who were high-school graduates	.546	.098	.516	5.555	.000
	Percent of males in occupation earning $3500 or more in 1950	.599	.120	.464	5.003	.000
a Dependent Variable: Percent of raters in NORC study rating occupation as excellent or good in presti

page 102 The regression coefficients in the middle of the page.

GET  FILE='D:\prestige.sav'.

REGRESSION
  /STATISTICS COEFF OUTS R ANOVA
  /DEPENDENT prestige
  /METHOD=ENTER educat income percwomn.
 

Variables Entered/Removed(b)

Model	Variables Entered	Variables Removed	Method
1	% of incumbents who were women, Average education, years, Average income, dollars(a)	.	Enter
a All requested variables entered.
b Dependent Variable: Pineo-Porter prestige score occ.

Model Summary

Model	R	R Square	Adjusted R Square	Std. Error of the Estimate
1	.893(a)	.798	.792	7.84647
a Predictors: (Constant), % of incumbents who were women, Average education, years, Average income, dollars

ANOVA(b)

Model		Sum of Squares	df	Mean Square	F	Sig.
1	Regression	23861.856	3	7953.952	129.192	.000(a)
	Residual	6033.570	98	61.567
	Total	29895.426	101
a Predictors: (Constant), % of incumbents who were women, Average education, years, Average income, dollars
b Dependent Variable: Pineo-Porter prestige score occ.

Coefficients(a)

		Unstandardized Coefficients		Standardized Coefficients	t	Sig.
Model		B	Std. Error	Beta
1	(Constant)	-6.794	3.239		-2.098	.039
	Average education, years	4.187	.389	.664	10.771	.000
	Average income, dollars	1.314E-03	.000	.324	4.729	.000
	% of incumbents who were women	-8.905E-03	.030	-.016	-.293	.770
a Dependent Variable: Pineo-Porter prestige score occ.

page 103 Table 5.2 Sums of squares (diagonal), sums of products (off diagonal), and sums (last row) for the Canadian occupational prestige data.

NOTE: This is a covariance matrix that was not divided by the degrees of freedom. Because this is not a standard table, we did not reproduce it.

page 108 These regression coefficients were obtained in the regression done on page 102.