Could you help me to solve it?

4. (50pts) Using 14,752 observations on college graduates in the March 2013 Current Population Survey, the following regression results are obtained where log(Earnings) denotes the natural logarithm of hourly earnings [in dollars) and the standard errors are reported in parentheses. log[Er:--ariiings)YE = 2.811 + 0.0096149ng R2 =0.034 [0.018) (00004) (a) Test the null hypothesis that the slope parameter is zero using a test with a 1% signicance level (5pts). What do you conclude from your test about the relationship between Age and log[Earnings)? (5pts) (b) Test the null hypothesis that the slope parameter is equal to 0.01 using a test with a 5% signi- canoe level (5pts). (c) Suppose a researcher re-defines the age variable as Age; = Age:/100. Calculate the new slope coefficient estimate (denoted by b) if the researcher runs an OLS regression of log(Earnings) on Age instead of Age (5pts). Calculate the new standard error of the estimator b (5pts). Calculate the new t-statistic that tests the slope coefficient is equal to zero based on b (5pts). (d) Let e; denote the fitted residual from the regression. Calculate 1 , e; where n = 14, 752 denotes the sample size (5pts). (e) On average, based on the estimation results, how much are the hourly earnings (in level, not in log) of a college graduate expected to increase in 20 years if he or she is currently 25 years old (10pts)? (f) How much of the variation in log(Earnings) is explained by the variation in Age (5pts)