Plotting Pick one of your explanatory variables to visualize. Make a scatter plot of this variable and mobility. On top of this scatter plot, fix the other two explanatory variables at their mean values and use your fitted multiple regression model to plot the estimated relationship between your chosen explanatory variable and mobility. Based on this plot, does homoscedasticity look to violated?
Remember to add an x-label, y-label, and plot title. Put all discussion below the code chunk. # Code for plotting below
Hypothesis Testing Use the model above to test the null hypothesis that the sum of all the slope coefficients is equal to one against the alternative that it is not equal to one. Do we reject the null hypothesis at level α = 0.05?
Hint: the vcov(regression) command may be useful here. Put all discussion below the code chunk. # Help for the ‘vcov’ command ?vcov # Code for hypothesis testing
Model Selection II Consider adding three more terms to this model. These terms could be new variables from the dataset, transformations of your existing terms, or interaction terms. For each additional term, provide a short justification for why you are considering adding this specific term. The justification could be based on the scatter plots above or some economic theory justification (diminishing marginal returns, etc.)
Re-run your regression with all these transformed terms (as well as the original terms). Is your adjusted Rˆ2 higher or lower than before? Run an F-test to determine whether adding these new terms significantly increased the explanatory power of the model. State your null hypothesis and alternative hypothesis in terms of the full model parameters. Use level α = 0.1 and interpret the conclusions of this test in context.