Suppose you model the relationship between used car prices (measured in dollars) and mileage (measured in miles) and estimate the relationship by OLS in STATA. The result is as follows: Source SS df MS Number of obs 69 F(1, 67) 20.01 Model 132650620 1 132650620 Prob > F 0.0000 Residual 444146339 67 6629049.84 R-squared 0.2300 Adj R-squared 0.2185 Total 576796959 68 8482308.22 Root MSE 2574.7 price Coef Std. Err. t P>It! (95% Conf. Intervall mileage 1 cons! - 115804 11692.5 .0258878 B -4.47 9.15 0.000 0.000 -. 1674762 9141.49 A 14243.51 1. 6 points) Precisely interpret the estimated intercept and slope in the model. Does the intercept have a useful interpretation in this context? 2. (6 points) Describe how well the regression line fits the data. Be precise about the measure(s) you the 3.6 points) Test the null hypothesis that the slope equals -0.18 versus the alternative that it does not equal -0.18 at the 1% significance level. 4.6 points) You want to test the null hypothesis that the effect of mileage on price is smaller than-0.15 versus the alternative that it is larger than -0.15. Formulate the null and alterna- tive hypotheses, find the corresponding t-statistic and show, in a graph of the t-distribution density, which region represents the p-value. Explain what is the decision rule, given your p-value. Note: You do not have to calculate the p-value. 5. (5 points) Find the values of A and B in the regression output above. 6.6 points) Construct a 90% confidence interval for the effect of a 100-mile change in the price of used cars. 7. (10 points) In the previous questions we used the homoskedastic standard errors for inference (since we did not use the robust option). a. If we recomputed them assuming heteroskedastic errors, what would you expect to happen to your answer in 4.3? b. If the error term is heteroskedastic, is 1 unbiased? Explain.