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The US real GDP growth data from Problem Set 1b and Project 1 were updated with three new explanatory variables, and the expanded data set is posted in an Excel file. LOCKDOWN is a dummy or binary variable that equals one for countries that imposed a national lockdown before April 1 (i.e., before the second quarter of 2020 started) and equals zero for all other countries. FIRSTCASE is the number of days into 2020 when the country identified its first COVID case. For example, FIRSTCASE = 25 if a country found its first COVID case on January 25. WORSTCASE is a dummy variable that equals one for those countries with the largest second-quarter COVID impacts on GDP (larger than a 13.5% decline) and equals zero for all other countries. The purpose of this variable is to allow the constant term (intercept b1) in the regression model to shift for the hardest hit countries. Please load the revised data into GRETL and answer these questions:
1. Please use the Ordinary Least Squares tool in GRETL to estimate an expanded regression model from the revised data. The base model from Project 1 had three statistically significant explanatory variables (BB, CHILD, and SERVICE), so our expanded model keeps these variables, drops the insignificant variables (BUSWEB and TOUR), and adds the new explanatory variables. Recall that GRETL provides a pop-up menu that allows you to select the dependent variable (Q2GDP) and the explanatory variables, and the window for the revised model should look like:
2. Please answer the following questions about the estimated version of the revised model:
a) Based on the R2 statistic for the expanded model, what share of the variation in Q2GDP is explained by this regression model?
b) Which coefficients in the revised model are significantly different from zero (i.e., have pvalues less than 0.10)?
c) Please explain how we should interpret the estimated values of the LOCKDOWN and WORSTCASE coefficients?
d) Based on the estimated value of the FIRSTCASE coefficient, what is the expected change in second-quarter GDP per capita if a country was able to delay the occurrence of its first COVID case by 10 days?
3. To visually evaluate how well the expanded regression model fits the data, we can plot the fitted (predicted) changes in Q2GDP along with the actual values. This graph may be formed by clicking on the Graphs menu item in the regression window and then selecting Fitted, actual plot and By observation number from the submenus. The actual observations of Q2GDP are plotted as open circles, and the predicted values from the model are plotted as solid circles. Please provide a copy of your actual-predicted plot. Based on this plot, how well does the model fit the data?
4. We have three explanatory variables in our dataset that are not included in the current model (BUSWEB, SOCEXP, and TOUR). Can you improve the fit of the expanded model by adding oneor more of these explanatory variables back into the model? Please add these variables to the regression model from Question 1 and provide a copy of the GRETL output. Do these new variables improve the model reported in Question 1?
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