Savings and income Your microeconomics professor gives you a dataset of 90 households that describes the savings behavior and economic characteristics (income, famsize) of a sample of families in South Bend. The dataset also contains demographic information about the head of household (age, educ). She asks you to investigate the relationship between savings and family income (both measured in USD). You estimate the following population model for households h. Savings,= Bo + BincomeIncomer + Bogeagen + Bagezagen + Beseduch + Befamsizen + un The output from your investigation is below (some of the STATA output is omitted for the purposes of this question): Regression 2 reg savings income age age2 educ size Source | Model | 74947229.8 Residual I 870066450 Total 945013680 savings I income I SS df .0198167 age | -261.5792 age2 | 3.947223 educ | 240.4716 size 127.6799 cons 1 2111.449 Coef. Std. Err. 5 14989446 10357933.9 84 89 10618131.2 .080943 521.9599 6.601421 123.8293 MS 240.8095 10032.21 Number of obs F(X, X) Prob > F R-squared Adj R-squared Root MSE t p>It x XXX -0.50 0.618 0.60 0.551 X xxx 0.53 0.597 0.21 0.834 -1299.554 -9.180426 X [95% Conf. Interval] -351.1963 -17838.71 90 X 0.0793 0.0245 3218.4 776.3954 17.07487 606.5561 22061.61 a) [2 points] Interpret the coefficient on income in words. b) [5 points] Set up a test of the hypothesis that income has no impact on savings in this model. Outline all of your steps. If you have enough information to complete this test, do so. If not, explain what additional information you need to complete the test. Now, before you ran this regression, you ran a simpler regression of savings on income alone, and got an R2 of 0.0331. c) [5 points] Set up a test of the hypothesis that foge Pope Bed and Blue are jointly zero. Outline all of your steps. If you have enough information to complete this test, do so. If not, explain what additional Information you need to complete the test.