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.
IGRAPH
/X1 = VAR(reptwt)
/Y = VAR(measwt)
/FITLINE METHOD = REGRESSION LINEAR LINE = TOTAL MEFFECT
/SCATTER COINCIDENT = NONE.
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.
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