Abstract
This coding exercise consists of an analysis of data from the 2020 Presidential elections in the United States. Using RStudio, the document provides answers to several coding questions.
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[...] The coefficient for `pct_unemp_rate` in each regression represents the expected change in Trump's percentage vote share for a one-unit increase in the percentage unemployment rate, holding all other variables constant. For example, in reg1, a 1 percentage point increase in unemployment rate is associated with a decrease of approximately 1.38 percentage points in Trump's vote share. Similarly, in reg5, this association is approximately -0.22, indicating a smaller effect when controlling for additional covariates. 10\. What is the interpretation of each of the coefficients in `reg5`? (Be precise about the magnitudes / units and what is held constant.) 10. [...]
[...] What do the coefficient estimates for `reg1` and `reg2` suggest regarding the association between the average household income `mean_income_thousands` (included in `reg2`, but omitted from `reg1`) and our main regressor, the percentage unemployment rate `pct_unemp_rate` (included in both `reg2` and 13. The coefficient for pct_unemp_rate increases from approximately -1.38 in reg1 to approximately -2.57 in reg2. This suggests that when controlling for mean_income_thousands in reg2, the negative association between unemployment rate and Trump's vote share strengthens, implying a potential multicollinearity effect between pct_unemp_rate and mean_income_thousands. 14\. Can you interpret the coefficient for `pct_unemp_rate` in `reg5` causally? Why What potential confounding variables could you think of? [...]
[...] `avg_rep_pct_votes_2012_2016`: A 1 percentage point increase in the average Republican vote percentage in the previous two presidential elections is associated with an increase of approximately 0.88 percentage points in Trump's vote share. 11\. Why does the number of observations not vary for each regression? 11. The same dataset is used for each of the regression, i.e., the same name of inputs/lines. 12\. What share of the variance in Donald Trump's vote percentage is each model able to explain? How does it vary across the four regressions? [...]
[...] 12. reg1: Explains approximately of the variance. reg2: Explains approximately 26% of the variance. reg3: Explains approximately 46% of the variance. reg4: Explains approximately 60% of the variance. reg5: Explains approximately 98% of the variance. The variance explained increases as more independent variables are added to the model. This suggests that the additional covariates in reg3, reg4, and reg5 contribute to a better understanding and explanation of the variability in Trump's vote percentage compared to simpler models (reg1 and reg2). [...]
[...] How would you go about trying to assess whether the unemployment rate at the county level has a causal impact on the vote percentage for Donald Trump? 14. Interpreting the coefficient for `pct_unemp_rate` in `reg5` causally is challenging due to the observational nature of the data and potential confounding factors. Establishing causality would require addressing confounding variables like economic, social, and political factors. Methods such as instrumental variable analysis, natural experiments, longitudinal data analysis, and causal inference techniques can be of use to assess the causal impact of county-level unemployment rate on Trump's vote percentage while addressing biases and confounding. [...]
