Companion: Chapter 8
library(poliscidata)## Registered S3 method overwritten by 'gdata':
## method from
## reorder.factor gplotsQ1
Q1A
wtd.cor(cbind(states$demhr11, states$demstate13, states$union10))## Warning in summary.lm(lm(stdz(y, weight = weight) ~ stdz(x, weight = weight), :
## essentially perfect fit: summary may be unreliable
## Warning in summary.lm(lm(stdz(y, weight = weight) ~ stdz(x, weight = weight), :
## essentially perfect fit: summary may be unreliable
## Warning in summary.lm(lm(stdz(y, weight = weight) ~ stdz(x, weight = weight), :
## essentially perfect fit: summary may be unreliable## $correlation
## V1 V2 V3
## V1 1.0000000 0.8101339 0.4889759
## V2 0.8101339 1.0000000 0.6107600
## V3 0.4889759 0.6107600 1.0000000
##
## $std.err
## V1 V2 V3
## V1 9.432950e-17 8.461717e-02 1.259053e-01
## V2 8.461717e-02 4.988511e-17 1.142888e-01
## V3 1.259053e-01 1.142888e-01 7.610520e-17
##
## $t.value
## V1 V2 V3
## V1 1.060114e+16 9.574108e+00 3.883681e+00
## V2 9.574108e+00 2.004606e+16 5.344008e+00
## V3 3.883681e+00 5.344008e+00 1.313971e+16
##
## $p.value
## V1 V2 V3
## V1 0.000000e+00 1.032423e-12 3.142987e-04
## V2 1.032423e-12 0.000000e+00 2.474964e-06
## V3 3.142987e-04 2.474964e-06 0.000000e+00Q1B
IncreasesQ1C
Decreases
Q1D
Yes. The percentage of workers who are union members is more highly correlated with percent state legislators who are Democratic (0.61) than it is with U.S. representatives who are Democratic (0.49).
Q2
Q2A
A negative sign on permit’s regression coefficient. (The more the public thinks abortion should be always be permitted the fewer restrictions the legislature should pass).
Q2B
summary(lm(states$abortlaw10 ~ states$permit))##
## Call:
## lm(formula = states$abortlaw10 ~ states$permit)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.768 -1.126 0.066 1.108 3.717
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 13.1709 1.0900 12.083 1.38e-14 ***
## states$permit -0.1839 0.0287 -6.407 1.57e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.785 on 38 degrees of freedom
## (10 observations deleted due to missingness)
## Multiple R-squared: 0.5193, Adjusted R-squared: 0.5067
## F-statistic: 41.05 on 1 and 38 DF, p-value: 1.575e-07Q2C
summary(lm(states$abortlaw10 ~ states$permit + states$womleg_2015))##
## Call:
## lm(formula = states$abortlaw10 ~ states$permit + states$womleg_2015)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.6642 -1.1509 0.2625 1.1423 3.1513
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 13.63712 1.14677 11.892 3.33e-14 ***
## states$permit -0.15608 0.03634 -4.295 0.000121 ***
## states$womleg_2015 -0.06388 0.05182 -1.233 0.225448
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.773 on 37 degrees of freedom
## (10 observations deleted due to missingness)
## Multiple R-squared: 0.5383, Adjusted R-squared: 0.5133
## F-statistic: 21.57 on 2 and 37 DF, p-value: 6.18e-07Q2D
0.0001, 0.23
Q2E
No. Controlling for the percentage of women in the state legislature, the percentage of the public that thinks abortion should be always be permitted still has a significantly negative effect on the number of abortion restrictions passed into law.
Q3
Q3A
summary(svyglm(femrole ~ age, design=gssD))##
## Call:
## svyglm(formula = ..1, design = ..2)
##
## Survey design:
## survey::svydesign(id = ~1, data = gss, weights = ~wtss)
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.04604 0.18060 33.477 < 2e-16 ***
## age -0.01279 0.00351 -3.644 0.000279 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 3.635285)
##
## Number of Fisher Scoring iterations: 2fit.svyglm(svyglm(femrole ~ age, design=gssD))## R-Squared Adjusted R-Squared
## 0.013 0.012
Q3B
summary(svyglm(femrole ~ age + authoritarianism, design=gssD))##
## Call:
## svyglm(formula = ..1, design = ..2)
##
## Survey design:
## survey::svydesign(id = ~1, data = gss, weights = ~wtss)
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.873458 0.273175 25.161 < 2e-16 ***
## age -0.015206 0.004893 -3.107 0.00197 **
## authoritarianism -0.251422 0.044381 -5.665 2.22e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 3.319108)
##
## Number of Fisher Scoring iterations: 2fit.svyglm(svyglm(femrole ~ age + authoritarianism, design=gssD))## R-Squared Adjusted R-Squared
## 0.080 0.077Correct. The regression coefficient for the age variable in the bivariate regression above is negative and statistically significant. As age increases, support for non-traditional female roles tends to decrease.
Q3C
Q3D
Correct. The regression coefficient for the authoritarianism variable in the bivariate regression above is negative and statistically significant. As support for authoritarianism increases, support for non-traditional female roles tends to decrease.
Q3E
Incorrect. The partial regression coefficient for the age variable in the multiple regression shows the effect of age on support for non-traditional female roles controlling for support for authoritarianism. The partial regression coefficient for age is negative and statistically significant
Q4
Q4A
# Note: The directions don't say whether the regression should be weighted
# so code for both unweighted and weighted regressions appears below.
summary(lm(fedspend_scale ~ owngun_owngun, data=nes))##
## Call:
## lm(formula = fedspend_scale ~ owngun_owngun, data = nes)
##
## Residuals:
## Min 1Q Median 3Q Max
## -10.729 -2.135 0.271 2.271 6.865
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.13498 0.07993 114.29 <2e-16 ***
## owngun_owngun2. No 1.59401 0.09701 16.43 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.37 on 5536 degrees of freedom
## (378 observations deleted due to missingness)
## Multiple R-squared: 0.04651, Adjusted R-squared: 0.04633
## F-statistic: 270 on 1 and 5536 DF, p-value: < 2.2e-16# Expected support of non-gun owner = 9.13 + 1.59 = 10.72
summary(svyglm(fedspend_scale ~ owngun_owngun, design=nesD))##
## Call:
## svyglm(formula = ..1, design = ..2)
##
## Survey design:
## survey::svydesign(id = ~1, data = nes, weights = ~wt)
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.0366 0.1038 87.05 <2e-16 ***
## owngun_owngun2. No 1.3401 0.1259 10.64 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 10.84832)
##
## Number of Fisher Scoring iterations: 2# Expected support of non-gun owner = 9.04 + 1.34 = 10.38
Q4B
Weighted: support for spending = 10.38 – 1.34*(own gun)
Unweighted: support for spending = 10.73 – 1.59*(own gun)
Q4C
Yes. According to the bivariate regression results, gun owners have significantly lower support for federal spending than non-gun owners. Based on the sample weighted regression results, the probability of observing a 1.34 point difference on the federal spending scale by random chance when the null hypothesis is true is less than 0.001.
Q4D
# Note: This is only needed for weighted regression, the unweighted
# lm summary reports the R-squared statistic
fit.svyglm(svyglm(fedspend_scale ~ owngun_owngun, design=nesD))## R-Squared Adjusted R-Squared
## 0.036 0.036