14.5 Exercises

1. WDI and Heteroscedasticity (***): Using the data in wdi, estimate the following equation for the year 2018 and report the results: $$fertrate = \beta_0 + \beta_1 \cdot gdp+ \beta_2 \cdot litrate$$ Conduct a test for heteroscedasticity of your choice. Is there heteroscedasticity present in the model? If yes, execute additional calculations to correct for it and report the results.

2. Indy Homes III (***): The data indyhomes contains home values of two ZIP codes in Indianapolis. The model estimates the home value (dependent variable) based on a set of independent variables. The variables levels and garage refers to the number of stories and garage spots, respectively. The remaining variables are self-explanatory.

   1. Create a dummy variable called northwest for the 46268 ZIP code.
   2. Report and interpret the results of the regression equation that uses $\ln(price)$ as the dependent variables and the folloing as independent variables: $\ln(sqft)$, $northwest$, $\ln(lot)$, $bed$, $garage$, and $levels$. In addtion, include an interaction between northwest and levels.
   3. What is the expected home value of a house in the 46228 ZIP code area with the following characteristics: 1900 sqft, 0.65 acres lot, 3 bedrooms, 3 bathrooms, 2 garage spots, and 2 story.
   4. Conduct a Breusch-Pagan-Godfrey test for heteroscedasticity. What do you conclude?
   5. Estimate the above model with heteroscedasticity-consistent (HC) standard errors. What changes compared to the model from Part b?

3. WDI and Multicollinearity (***): Use the command subset() on the WDI data and to select the variables fertrate, gdp, litrate, lifeexp, and mortrate for the year 2015. Estimate the following model $$fertrate=\beta_0+\beta_1 \cdot gdp+\beta_2 \cdot litrate+\beta_3 \cdot lifeexp+\beta_4 \cdot mortrate$$ Interpret the results. What do you conclude in terms of statistical significance and the value of $R^2$? Use the function vif from the package car. What can you say about the issue of multicollinearity in this case? Correct the issue of multicollinearity by adjusting your model.

5. Wages, Productivity, and Autocorrelation (***):