Question
This exercise gives you an opportunity to interpret the results of a regression analysis. The following public opinion data is taken from the 2020 ANES,
This exercise gives you an opportunity to interpret the results of a regression analysis. The following public opinion data is taken from the 2020 ANES, testing factors that potentially influence a voter's levels of hope for the United States prior to the 2020 Presidential Election. A researcher has outlined the following variables for a regression model: The dependent variable, Hope, is a scale that ranges from 1 to 4, with 1 meaning least hope for the United States and 4 the most. The independent variables are as follows: Local handling of COVID (Local): a scale that ranges from 1 to 4, with 1 least approval, and 4 meaning most approval Governor's handling of COVID (Governor): a scale that ranges from 1 to 4, with 1 least approval, and 4 meaning most approval Care about the Presidential election (PresCare): a scale that ranges from 1 to 5, with 1 meaning Respondent does not care and 5 meaning Respondent cares intensely Respondent Ideology (Ideology): a scale that ranges from 1 to 7, with 1 meaning Respondent identifies as extremely liberal to 7 meaning respondent identifies as extremely conservative The researcher's hypotheses are that approval of local government and one's governor's actions during the COVID pandemic should increase hope for the future of the United States, while caring about the Presidential election and ideology should be unrelated. The table below gives you the results of a regression analysis of Respondent hope on the above explanatory variables, in a format that commonly appears in scholarly journals. Not as much information seems to be supplied. But in fact you can reconstruct the significance tests. Assume that the null hypotheses pertaining to the regression parameters are that the s (coefficients) equal zero. Note that the standard errors appear in parentheses below the estimated coefficients.
Table 1: Regression Analysis of Hope on Respondent Characteristics
Estimate (Standard Error) | |
Local | 0.05 (0.01) |
Governor | -0.03 (0.01) |
Pres Care | -0.03 (0.016) |
Ideology | 0.27 (0.01) |
Constant | 1.49 (0.09) |
R2 | 0.14 |
N | 6991 |
1. Compute the test statistic for the regression coefficients. Which independent variables (if any) have a statistically significant effect on the dependent variable? 2. Of all the independent variables included in the model, which would you say has the largest effect on the dependent variable, and why? 3. What proportion of the variation in hope is explained by the model? 4. In sum, do the data support the researcher's hypotheses? Explain your answer for each variable in the model.
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