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Group Exercise: Bivariate Linear Regression

Identify a numeric IV that you think could explain our DV, favorability toward big business. Compute the linear model. Interpret the results, as appropriate. We'll see which group has the best fitting model (explains the most variation in our DV). Paste your R code below your interpretation.

Comments

> summary(lm(V162100~V162099))

Call:
lm(formula = V162100 ~ V162099)

Residuals:
Min 1Q Median 3Q Max
-351.58 -15.67 -1.17 13.33 947.83

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 25.49366 1.86200 13.69 <2e-16 ***
V162099 0.36682 0.02224 16.50 <2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 52.85 on 3574 degrees of freedom
(695 observations deleted due to missingness)
Multiple R-squared: 0.07075, Adjusted R-squared: 0.07049
F-statistic: 272.1 on 1 and 3574 DF, p-value: < 2.2e-16

>

- For every 10 degree change in favorability toward poor people, you can expect a 3.7 degree change in favorability toward big business. We can explain 7% of explained variation for big business.

> summary(lm(V162100~V162110))

Call:
lm(formula = V162100 ~ V162110)

Residuals:
Min 1Q Median 3Q Max
-239.51 -14.49 -0.96 11.97 954.10

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 34.47621 1.89774 18.17 <2e-16 ***
V162110 0.23550 0.02181 10.80 <2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 53.74 on 3608 degrees of freedom
(661 observations deleted due to missingness)
Multiple R-squared: 0.03132, Adjusted R-squared: 0.03105
F-statistic: 116.6 on 1 and 3608 DF, p-value: < 2.2e-16

There is a significant difference, we reject the null hypothesis, for a ten degree change in favorability toward police there would be a 2.4 degree change in favorability toward big business.

we can only explain 3 percent of variation in this model.

> summary(lm(V162100~V162097))

Call:
lm(formula = V162100 ~ V162097)

Residuals:
Min 1Q Median 3Q Max
-161.52 -15.03 -1.67 12.94 948.96

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 45.08619 1.12587 40.05 <2e-16 ***
V162097 0.13169 0.01194 11.03 <2e-16 *** .13 x 10degrees
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 53.83 on 3586 degrees of freedom
(683 observations deleted due to missingness)
Multiple R-squared: 0.03283, Adjusted R-squared: 0.03256
F-statistic: 121.7 on 1 and 3586 DF, p-value: < 2.2e-16

10 degree favorability change in liberals and there is a 1.30 degree increase in favorability towards big business

summary(lm(V162100~V162096))

Call:
lm(formula = V162100 ~ V162096)

Residuals:
Min 1Q Median 3Q Max
-205.29 -14.70 -0.02 13.36 949.67

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 41.575339 1.040657 39.95 <2e-16 ***
V162096 0.168885 0.009672 17.46 <2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 50.32 on 3585 degrees of freedom
(684 observations deleted due to missingness)
Multiple R-squared: 0.07838, Adjusted R-squared: 0.07812
F-statistic: 304.9 on 1 and 3585 DF, p-value: < 2.2e-16
Result : For every 10 degree favor-ability change in republican party. There is a 1.7 degrees increase increase favor ability towards big business.