SPSS Textbook Examples
Applied Regression Analysis by John Fox
Chapter 13: Collinearity and its purported
remedies
page 343 Table 13.1 Regression of estimated 1980 U.S. census undercount
of area characteristics, for 66 central cities, state remainders, and states.
GET FILE='D:\ericksen.sav'.
regression
/statistics=defaults tol
/dep=undcount
/method=enter perc_min crimrate poverty diffeng hsgrad housing city countprc.
Variables Entered/Removed(b)
| Model |
Variables Entered |
Variables Removed |
Method |
|---|
| 1 |
Percentage of households counted by conventional personal enumeration, Percentage of housing in small, multiunit buildings, Percentage having difficulty speaking or writing English, Percentage poor, Rate of serious crimes per 1000 population, City 1=yes, 0=no, Percentage age 25 or older who had not finished high school, Percentage black or Hispanic(a) |
. |
Enter |
|---|
| a All requested variables entered. |
| b Dependent Variable: Preliminary estimate of percentage undercount
|
Model Summary
| Model |
R |
R Square |
Adjusted R Square |
Std. Error of the Estimate |
|---|
| 1 |
.841(a) |
.708 |
.667 |
1.42647 |
|---|
| a Predictors: (Constant), Percentage of households counted by conventional personal enumeration, Percentage of housing in small, multiunit buildings, Percentage having difficulty speaking or writing English, Percentage poor, Rate of serious crimes per 1000 population, City 1=yes, 0=no, Percentage age 25 or older who had not finished highschool, Percentage black or Hispanic
|
ANOVA(b)
| Model |
Sum of Squares |
df |
Mean Square |
F |
Sig. |
|---|
| 1 |
Regression |
280.795 |
8 |
35.099 |
17.249 |
.000(a) |
|---|
| Residual |
115.985 |
57 |
2.035 |
|
|
|---|
| Total |
396.780 |
65 |
|
|
|
|---|
| a Predictors: (Constant), Percentage of households counted by conventional personal enumeration, Percentage of housing in small, multiunit buildings, Percentage having difficulty speaking or writing English, Percentage poor, Rate of serious crimes per 1000 population, City 1=yes, 0=no, Percentage age 25 or older who had not finished highschool, Percentage black or Hispanic |
| b Dependent Variable: Preliminary estimate of percentage undercount
|
Coefficients(a)
|
Unstandardized Coefficients |
Standardized Coefficients |
t |
Sig. |
Collinearity Statistics |
|---|
| Model |
B |
Std. Error |
Beta |
Tolerance |
VIF |
|---|
| 1 |
(Constant) |
-1.771 |
1.382 |
|
-1.282 |
.205 |
|
|
|---|
| Percentage black or Hispanic |
7.983E-02 |
.023 |
.566 |
3.531 |
.001 |
.200 |
5.009 |
|---|
| Rate of serious crimes per 1000 population |
3.012E-02 |
.013 |
.303 |
2.317 |
.024 |
.299 |
3.344 |
|---|
| Percentage poor |
-.178 |
.085 |
-.324 |
-2.101 |
.040 |
.216 |
4.625 |
|---|
| Percentage having difficulty speaking or writing English |
.215 |
.092 |
.214 |
2.333 |
.023 |
.611 |
1.636 |
|---|
| Percentage age 25 or older who had not finished high school |
6.129E-02 |
.045 |
.211 |
1.369 |
.176 |
.216 |
4.619 |
|---|
| Percentage of housing in small, multiunit buildings |
-3.496E-02 |
.025 |
-.139 |
-1.419 |
.161 |
.534 |
1.872 |
|---|
| City 1=yes, 0=no |
1.160 |
.771 |
.203 |
1.505 |
.138 |
.283 |
3.538 |
|---|
| Percentage of households counted by conventional personal enumeration |
3.699E-02 |
.009 |
.372 |
3.997 |
.000 |
.591 |
1.691 |
|---|
| a Dependent Variable: Preliminary estimate of percentage undercount
|
page 343 Table 13.2 Correlations among eight predictors of the 1980 U.S.
census undercount.
CORRELATIONS
/VARIABLES=perc_min crimrate poverty diffeng hsgrad housing city countprc.
Correlations
|
Percentage black or Hispanic |
Rate of serious crimes per 1000 population |
Percentage poor |
Percentage having difficulty speaking or writing English |
Percentage age 25 or older who had not finished highschool |
Percentage of housing in small, multiunit buildings |
City 1=yes, 0=no |
Percentage of households counted by conventional personal enumeration |
|---|
| Percentage black or Hispanic |
Pearson Correlation |
1 |
.655 |
.738 |
.395 |
.535 |
.357 |
.758 |
-.334 |
|---|
| Sig. (2-tailed) |
. |
.000 |
.000 |
.001 |
.000 |
.003 |
.000 |
.006 |
|---|
| N |
66 |
66 |
66 |
66 |
66 |
66 |
66 |
66 |
|---|
| Rate of serious crimes per 1000 population |
Pearson Correlation |
.655 |
1 |
.369 |
.512 |
.067 |
.532 |
.729 |
-.233 |
|---|
| Sig. (2-tailed) |
.000 |
. |
.002 |
.000 |
.595 |
.000 |
.000 |
.060 |
|---|
| N |
66 |
66 |
66 |
66 |
66 |
66 |
66 |
66 |
|---|
| Percentage poor |
Pearson Correlation |
.738 |
.369 |
1 |
.152 |
.751 |
.335 |
.538 |
-.157 |
|---|
| Sig. (2-tailed) |
.000 |
.002 |
. |
.224 |
.000 |
.006 |
.000 |
.208 |
|---|
| N |
66 |
66 |
66 |
66 |
66 |
66 |
66 |
66 |
|---|
| Percentage having difficulty speaking or writing English |
Pearson Correlation |
.395 |
.512 |
.152 |
1 |
-.116 |
.340 |
.480 |
-.108 |
|---|
| Sig. (2-tailed) |
.001 |
.000 |
.224 |
. |
.352 |
.005 |
.000 |
.387 |
|---|
| N |
66 |
66 |
66 |
66 |
66 |
66 |
66 |
66 |
|---|
| Percentage age 25 or older who had not finished high school |
Pearson Correlation |
.535 |
.067 |
.751 |
-.116 |
1 |
.235 |
.315 |
-.414 |
|---|
| Sig. (2-tailed) |
.000 |
.595 |
.000 |
.352 |
. |
.058 |
.010 |
.001 |
|---|
| N |
66 |
66 |
66 |
66 |
66 |
66 |
66 |
66 |
|---|
| Percentage of housing in small, multiunit buildings |
Pearson Correlation |
.357 |
.532 |
.335 |
.340 |
.235 |
1 |
.566 |
-.086 |
|---|
| Sig. (2-tailed) |
.003 |
.000 |
.006 |
.005 |
.058 |
. |
.000 |
.491 |
|---|
| N |
66 |
66 |
66 |
66 |
66 |
66 |
66 |
66 |
|---|
| City 1=yes, 0=no |
Pearson Correlation |
.758 |
.729 |
.538 |
.480 |
.315 |
.566 |
1 |
-.269 |
|---|
| Sig. (2-tailed) |
.000 |
.000 |
.000 |
.000 |
.010 |
.000 |
. |
.029 |
|---|
| N |
66 |
66 |
66 |
66 |
66 |
66 |
66 |
66 |
|---|
| Percentage of households counted by conventional personal enumeration |
Pearson Correlation |
-.334 |
-.233 |
-.157 |
-.108 |
-.414 |
-.086 |
-.269 |
1 |
|---|
| Sig. (2-tailed) |
.006 |
.060 |
.208 |
.387 |
.001 |
.491 |
.029 |
. |
|---|
| N |
66 |
66 |
66 |
66 |
66 |
66 |
66 |
66 |
|---|
page 355 Table 13.3 B. Fox's Canadian women's labor force participation data. T is year; L is women's labor force participation rate, in percent; F is
the total fertility rate, per 1000; M is men's average weekly wages in 1935 dollars; W is women's average weekly wages; D is per-capita
consumer debt; and P is the percentage of part-time workers.
GET FILE='D:\bfox.sav'.
list year womwork fertil mwage fwage debt parttime.
YEAR WOMWORK FERTIL MWAGE FWAGE DEBT PARTTIME
1946 25.30 3748 25.35 14.05 18.18 10.28
1947 24.40 3996 26.14 14.61 28.33 9.28
1948 24.20 3725 25.11 14.23 30.55 9.51
1949 24.20 3750 25.45 14.61 35.81 8.87
1950 23.70 3669 26.79 15.26 38.39 8.54
1951 24.20 3682 26.33 14.58 26.52 8.84
1952 24.10 3845 27.89 15.66 45.65 8.60
1953 23.80 3905 29.15 16.30 52.99 5.49
1954 23.60 4047 29.52 16.57 54.84 6.67
1955 24.30 4043 32.05 17.99 65.53 6.25
1956 25.10 4092 32.98 18.33 72.56 6.32
1957 26.20 4168 32.25 17.64 69.49 7.30
1958 26.60 4073 32.52 18.16 71.71 8.65
1959 26.90 4100 33.95 18.58 78.89 8.80
1960 27.90 4119 34.63 18.95 84.99 9.39
1961 29.10 4159 35.14 18.78 87.71 10.23
1962 29.90 4134 34.49 18.74 95.31 10.77
1963 29.80 4017 35.99 19.71 104.40 10.84
1964 30.90 3886 36.68 20.06 116.80 11.70
1965 32.10 3467 37.96 20.94 130.99 12.33
1966 33.20 3150 38.68 21.20 135.25 12.18
1967 34.50 2879 39.65 21.95 142.93 13.67
1968 35.10 2681 41.20 22.68 155.47 13.82
1969 36.10 2563 42.44 23.75 165.04 14.91
1970 36.90 2571 42.02 25.63 164.53 15.52
1971 37.00 2503 45.32 26.79 169.63 15.47
1972 37.90 2302 45.61 27.51 190.62 15.85
1973 40.10 2931 45.59 27.35 209.60 15.40
1974 40.60 1875 48.06 29.64 216.66 16.23
1975 42.20 1866 46.12 29.33 224.34 16.71
Number of cases read: 30 Number of cases listed: 30
page 358 Figure 13.6 Plot of C(p)-p against p for the census undercount
regression. Only subsets for which C(p)-p < 10 are shown. The following capitalized letter are employed to label the predictors in each subset:
Minority, Crime, Poverty, Language, High school, hOusing, cIty, and
coNventaional. Ericksen, et al. (1989) selected the predictor subset MCN . (i.e., Minority, Crime and coNventaional).
NOTE: We do not know how to make this table in SPSS.
page 359 Table 13.4 "Best" subset regression models for Ericksen et. al.'s
census undercount data. Coefficient standard errors are in parentheses.
GET FILE='D:\ericksen.sav'.
regression
/statistics=defaults selection
/dep=undcount /method=enter perc_min crimrate countprc
/method=enter diffeng
/method=enter poverty
/method=enter hsgrad housing city.
Variables Entered/Removed(b)
| Model |
Variables Entered |
Variables Removed |
Method |
|---|
| 1 |
Percentage of households counted by conventional personal enumeration, Rate of serious crimes per 1000 population, Percentage black or Hispanic(a) |
. |
Enter |
|---|
| 2 |
Percentage having difficulty speaking or writing English(a) |
. |
Enter |
|---|
| 3 |
Percentage poor(a) |
. |
Enter |
|---|
| 4 |
Percentage of housing in small, multiunit buildings, City 1=yes, 0=no, Percentage age 25 or older who had not finished high school(a) |
. |
Enter |
|---|
| a All requested variables entered. |
| b Dependent Variable: Preliminary estimate of percentage undercount
|
Model Summary
|
R |
R Square |
Adjusted R Square |
Std. Error of the Estimate |
Selection Criteria |
|---|
| Model |
Akaike Information Criterion |
Amemiya Prediction Criterion |
Mallows' Prediction Criterion |
Schwarz Bayesian Criterion |
|---|
| 1 |
.798(a) |
.638 |
.620 |
1.52302 |
59.405 |
.409 |
12.676 |
68.164 |
|---|
| 2 |
.818(b) |
.669 |
.647 |
1.46699 |
55.385 |
.385 |
8.515 |
66.333 |
|---|
| 3 |
.828(c) |
.686 |
.659 |
1.44207 |
54.032 |
.377 |
7.320 |
67.170 |
|---|
| 4 |
.841(d) |
.708 |
.667 |
1.42647 |
55.211 |
.385 |
9.000 |
74.918 |
|---|
| a Predictors: (Constant), Percentage of households counted by conventional personal enumeration, Rate of serious crimes per 1000 population, Percentage black or Hispanic |
| b Predictors: (Constant), Percentage of households counted by conventional personal enumeration, Rate of serious crimes per 1000 population, Percentage black or Hispanic, Percentage having difficulty speaking or writing English |
| c Predictors: (Constant), Percentage of households counted by conventional personal enumeration, Rate of serious crimes per 1000 population, Percentage black or Hispanic, Percentage having difficulty speaking or writing English, Percentage poor |
| d Predictors: (Constant), Percentage of households counted by conventional personal enumeration, Rate of serious crimes per 1000 population, Percentage black or Hispanic, Percentage having difficulty speaking or writing English, Percentage poor, Percentage of housing in small, multiunit buildings, City 1=yes, 0=no, Percentage age 25 or older who had not finished high school
|
ANOVA(e)
| Model |
Sum of Squares |
df |
Mean Square |
F |
Sig. |
|---|
| 1 |
Regression |
252.966 |
3 |
84.322 |
36.352 |
.000(a) |
|---|
| Residual |
143.814 |
62 |
2.320 |
|
|
|---|
| Total |
396.780 |
65 |
|
|
|
|---|
| 2 |
Regression |
265.504 |
4 |
66.376 |
30.843 |
.000(b) |
|---|
| Residual |
131.276 |
61 |
2.152 |
|
|
|---|
| Total |
396.780 |
65 |
|
|
|
|---|
| 3 |
Regression |
272.006 |
5 |
54.401 |
26.160 |
.000(c) |
|---|
| Residual |
124.774 |
60 |
2.080 |
|
|
|---|
| Total |
396.780 |
65 |
|
|
|
|---|
| 4 |
Regression |
280.795 |
8 |
35.099 |
17.249 |
.000(d) |
|---|
| Residual |
115.985 |
57 |
2.035 |
|
|
|---|
| Total |
396.780 |
65 |
|
|
|
|---|
| a Predictors: (Constant), Percentage of households counted by conventional personal enumeration, Rate of serious crimes per 1000 population, Percentage black or Hispanic |
| b Predictors: (Constant), Percentage of households counted by conventional personal enumeration, Rate of serious crimes per 1000 population, Percentage black or Hispanic, Percentage having difficulty speaking or writing English |
| c Predictors: (Constant), Percentage of households counted by conventional personal enumeration, Rate of serious crimes per 1000 population, Percentage black or Hispanic, Percentage having difficulty speaking or writing English, Percentage poor |
| d Predictors: (Constant), Percentage of households counted by conventional personal enumeration, Rate of serious crimes per 1000 population, Percentage black or Hispanic, Percentage having difficulty speaking or writing English, Percentage poor, Percentage of housing in small, multiunit buildings, City 1=yes, 0=no, Percentage age 25 or older who had not finished high school |
| e Dependent Variable: Preliminary estimate of percentage undercount
|
Coefficients(a)
|
Unstandardized Coefficients |
Standardized Coefficients |
t |
Sig. |
|---|
| Model |
B |
Std. Error |
Beta |
|---|
| 1 |
(Constant) |
-2.224 |
.561 |
|
-3.965 |
.000 |
|---|
| Percentage black or Hispanic |
7.861E-02 |
.015 |
.557 |
5.337 |
.000 |
|---|
| Rate of serious crimes per 1000 population |
3.630E-02 |
.010 |
.366 |
3.614 |
.001 |
|---|
| Percentage of households counted by conventional personal enumeration |
2.800E-02 |
.008 |
.282 |
3.473 |
.001 |
|---|
| 2 |
(Constant) |
-1.976 |
.550 |
|
-3.592 |
.001 |
|---|
| Percentage black or Hispanic |
7.519E-02 |
.014 |
.533 |
5.273 |
.000 |
|---|
| Rate of serious crimes per 1000 population |
2.715E-02 |
.010 |
.274 |
2.613 |
.011 |
|---|
| Percentage of households counted by conventional personal enumeration |
2.730E-02 |
.008 |
.275 |
3.512 |
.001 |
|---|
| Percentage having difficulty speaking or writing English |
.209 |
.087 |
.208 |
2.414 |
.019 |
|---|
| 3 |
(Constant) |
-.793 |
.860 |
|
-.921 |
.361 |
|---|
| Percentage black or Hispanic |
.101 |
.020 |
.716 |
4.992 |
.000 |
|---|
| Rate of serious crimes per 1000 population |
2.435E-02 |
.010 |
.245 |
2.355 |
.022 |
|---|
| Percentage of households counted by conventional personal enumeration |
2.933E-02 |
.008 |
.295 |
3.796 |
.000 |
|---|
| Percentage having difficulty speaking or writing English |
.184 |
.086 |
.183 |
2.126 |
.038 |
|---|
| Percentage poor |
-.110 |
.062 |
-.200 |
-1.768 |
.082 |
|---|
| 4 |
(Constant) |
-1.771 |
1.382 |
|
-1.282 |
.205 |
|---|
| Percentage black or Hispanic |
7.983E-02 |
.023 |
.566 |
3.531 |
.001 |
|---|
| Rate of serious crimes per 1000 population |
3.012E-02 |
.013 |
.303 |
2.317 |
.024 |
|---|
| Percentage of households counted by conventional personal enumeration |
3.699E-02 |
.009 |
.372 |
3.997 |
.000 |
|---|
| Percentage having difficulty speaking or writing English |
.215 |
.092 |
.214 |
2.333 |
.023 |
|---|
| Percentage poor |
-.178 |
.085 |
-.324 |
-2.101 |
.040 |
|---|
| Percentage age 25 or older who had not finished high school |
6.129E-02 |
.045 |
.211 |
1.369 |
.176 |
|---|
| Percentage of housing in small, multiunit buildings |
-3.496E-02 |
.025 |
-.139 |
-1.419 |
.161 |
|---|
| City 1=yes, 0=no |
1.160 |
.771 |
.203 |
1.505 |
.138 |
|---|
| a Dependent Variable: Preliminary estimate of percentage undercount
|
Excluded Variables(d)
|
Beta In |
t |
Sig. |
Partial Correlation |
Collinearity Statistics |
|---|
| Model |
Tolerance |
|---|
| 1 |
Percentage having difficulty speaking or writing English |
.208(a) |
2.414 |
.019 |
.295 |
.731 |
|---|
| Percentage poor |
-.240(a) |
-2.093 |
.040 |
-.259 |
.423 |
|---|
| Percentage age 25 or older who had not finished high school |
-.124(a) |
-1.158 |
.251 |
-.147 |
.506 |
|---|
| Percentage of housing in small, multiunit buildings |
-.068(a) |
-.747 |
.458 |
-.095 |
.715 |
|---|
| City 1=yes, 0=no |
.169(a) |
1.280 |
.206 |
.162 |
.331 |
|---|
| 2 |
Percentage poor |
-.200(b) |
-1.768 |
.082 |
-.223 |
.411 |
|---|
| Percentage age 25 or older who had not finished high school |
-.049(b) |
-.449 |
.655 |
-.058 |
.455 |
|---|
| Percentage of housing in small, multiunit buildings |
-.088(b) |
-1.002 |
.320 |
-.128 |
.709 |
|---|
| City 1=yes, 0=no |
.123(b) |
.949 |
.346 |
.122 |
.323 |
|---|
| 3 |
Percentage age 25 or older who had not finished high school |
.154(c) |
1.044 |
.301 |
.135 |
.239 |
|---|
| Percentage of housing in small, multiunit buildings |
-.053(c) |
-.591 |
.557 |
-.077 |
.664 |
|---|
| City 1=yes, 0=no |
.146(c) |
1.147 |
.256 |
.148 |
.320 |
|---|
| a Predictors in the Model: (Constant), Percentage of households counted by conventional personal enumeration, Rate of serious crimes per 1000 population, Percentage black or Hispanic |
| b Predictors in the Model: (Constant), Percentage of households counted by conventional personal enumeration, Rate of serious crimes per 1000 population, Percentage black or Hispanic, Percentage having difficulty speaking or writing English |
| c Predictors in the Model: (Constant), Percentage of households counted by conventional personal enumeration, Rate of serious crimes per 1000 population, Percentage black or Hispanic, Percentage having difficulty speaking or writing English, Percentage poor |
| d Dependent Variable: Preliminary estimate of percentage undercount
|
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