Suppose we are interested in the effect that the length of a prison sentence has wages, and in particular whether that effect differs by race. Suppose we estimate the model Yi = Bo + BYrs; + BWhite; +B3Yrs; White;+ui, where y; is hourly wage in dollars, Yrs, is the number of years individual i has served in prison, and White, is a binary variable indicating whether individual i is white. Dependent Variable: Variables Yrsi White; Yrs; x White; (Intercept) Fit statistics Observations R Hourly Wage -1.43 (0.44) 4.14 (0.95) 0.30 (0.13) 20.12 (2.36) 987 0.058 Standard errors are reported in parenthesis. (a) (3 points) Interpret the coefficient on interaction term. (b) (2 points) Derive an expression for the marginal effect of Yrs on earnings y. (c) (2 points) Calculate the marginal effect of Yrs on y for both treated and untreated groups (d) (3 points) Is there statistical evidence that the effect of Yrs on y is different for white and non-white individuals? Specify the null and alternative hypotheses, the test statistic, the conclusion of the test, and the interpretation of that conclusion.