(25) 3. The estimated regression equation below is based on a data set that includes 50 di????erent countries, and is intended to explain di????erences across countries in the aggregate saving rate. The variables are averages over 1960-1970 to remove business cycles or other short-term ????uctuations.
s????av = 28.5666 −.4612p15 −1.6915p75 −.0003inc +.4009gro
(7.3544) (.1446) (1.0835) (.0009) (.1961)
n=50, R2 =.3385
where inc is the country’s per-capita disposable income in U.S. dollars, gro is the percent rate of change in per capita disposable income over the previous decade, sav is aggregate personal saving divided by aggregate disposable income (measured on a scale from zero to one), p15 is the share of the country’s population under 15 (measured on a scale from 0 to 1), and p75 is the share of the country’s population over 75 (measured on a scale from 0 to 1). The standard errors are in parentheses under the coe????cient estimates. In addition, assume that the assumptions MLR.1 through MLR.6 hold in this question unless indicated otherwise. (Each question part is worth 5 points.)
a. Using the 5% signi????cance level, test the hypothesis that, other things equal, the per-capita disposable income has a negative impact on the saving rate. Speci????cally state the null and alternative hyptoheses, the relevant test statistic, associated critical value or p-value, your decision rule, and your conclusion, i.e. reject or fail to reject the null. (Round your answers to four decimal places.)