The California school data set from class actually contains the results on two tests: a math test and a reading test. You regress average reading score (readscr) in each school district on the percent of students in the district who have English as a second language (elpet) and obtain: readser = 666.93 0.76elpet R = 0.4765, sa = 14.57 (0.01) (0.96) Heteroskedasticity-robust standard errors are displayed in parentheses beneath each coefficient. You can assume that assumptions 2 and 3 of the OLS are satisfied. (a) Do you think that assumption 1 is satisfied for the proposed regression model? Argue. (b) Interpret the estimate of the slope coeficient 31. Does this estimate capture a causal effect? (c) If you were given another sample, would you expect to find a negative point estimate of 31? (Hint: First, try to generalize from the sample to the population. Then, answer the question) (d) Suppose you want to test for a positive relationship between the two variables with a 5% significance level. Can you use a symmetric 95% confidence interval to reach a conclusion about this test? If yes, construct the confidence interval and make a decision. If not, state the mull and alternative hypotheses you would use, compute the t-statistic, and draw a graph to show how you would calculate the p-value. (e) A policy-maker comes to you and asks you to evaluate the effects of a policy change which would increase clpct by 10 percent in each school district. Assume that the estimated coef- ficient reflects a causal effect and provide him with a range of predictions on the change in average reading score resulting from the policy change. Choose the range so that you have high-confidence that you are giving her the right answer.