3. To predict the outcome of Presidential elections in the US Fair (2002) collected data the percentage vote share of the incumbent party candidate (Vote), the economic growth rate (Growth) and inflation rate in the year prior to the election (Inflation), both measured in percentages. In addition Person is a dummy variable taking the value 1 if the incumbent party candidate is running for re-election and zero otherwise and War is a dummy variable taking the value 1 if there was a war in the year prior to the election and zero otherwise. These data a were used to estimate the following regression Vote = Be + B2Persone+B3War + B.Growth + BeInflation + e The results of this regression are provided below. SUMMARY OUTPUT Regression Statistics Multiple R 0.698621 R Square 0.488071 Adjusted R 0.409313 Standard E 4.740951 Observatio 31 ANOVA Regression Residual Total SS MS F graficance 4 557.1574 1392894 6.197079 0.001218 26 584,392 22.47661 30 1141549 Intercept person Coefficientsandard Em Star Pale Lower 959Upper 95%-ower 95 per 95.0% 52.76635 1.759672 29 98647 1.07E-21 19.54929 56 38341 49 14929 56.38.341 3.187483 1.806754 1754195 0.089447 52637 6.901338-052637 6.901338 6.7326 3.272919 -2.05706 0.049841 -13.450200502 -13.4602 0.00502 0.530492 0.563076 3253039 0,003158 0.195285 0.565099 0.195285 0.885699 -0.73.007 0.461127 -1.58323 0.125453 -1.67793_021779 -1.67793 021779 growth inflation (a) Interpret these results. (b) Test the hypothesis that the true effect of an incumbent running for re-election on vote share is equal to the last digit of your student number (e.g. if your student number is 1839446, then test the hypothesis that the true effect of incumbency is equal to 6). (e) Predict the vote share an incumbent running for re-election in a year with no war, economic growth equal to 3% and inflation equal to 4%. (d) Suppose you are interested in testing the conjecture that neither the growth rate nor the inflation rate has any impact on vote share. Write down the restricted regression corresponding to these conjectures. (e) Suppose the sum of squared residuals from this restricted regression is equal to the first four digits of your student number. Use this and the information from the above regression to test the conjecture in part (d). (Make sure to show and explain your calculations carefully). 3. To predict the outcome of Presidential elections in the US Fair (2002) collected data the percentage vote share of the incumbent party candidate (Vote), the economic growth rate (Growth) and inflation rate in the year prior to the election (Inflation), both measured in percentages. In addition Person is a dummy variable taking the value 1 if the incumbent party candidate is running for re-election and zero otherwise and War is a dummy variable taking the value 1 if there was a war in the year prior to the election and zero otherwise. These data were used to estimate the following regression Vote = B1 + BPerson +B3War + BGrowth+ BeInflation + er The results of this regression are provided below. SUMMARY OUTPUT Regression Statistics Multiple R 0.698621 R Square 0.488071 Adjusted R 0.409313 Standard E 4.740951 Observatio 31 ANOVA of Regressior Residual Total SS MS F nificance 4 557. 1574 139.2894 6.197079 0.001218 26 584.392 22.47661 30 1141.549 Intercept person Wir growth inflation Coefficientsandard Em 1 Star P.value Lower 95% Ugger 95%ower 95.0%pper 95.02 52.76635 1.759672 29.98547 1.07E-21 49.14929 56,38341 49.14929 56.38341 3.187483 1.806764 1764195 0.089447 -0.52637 6.901338 -0.52637 6.901338 -6.7326 3.272919 -2.05706 0.049841 -13.4602 -0.00502 -13.4602 -0.00502 0.530492 0.163076 3.253039 0.003158 0.195285 0.865699 0.195285 0.865699 -0.73007 0461127 -1.58323 0.125458 -1.67793 021779 -1.67793 0.21779 (a) Interpret these results. (b) Test the hypothesis that the true effect of an incumbent running for re-election on vote share is equal to the last digit of your student number (e.g. if your student number is 1839446, then test the hypothesis that the true effect of incumbency is equal to 6). (c) Predict the vote share an incumbent running for re-election in a year with no war, economic growth equal to 3% and inflation equal to 4%