3. Moneyball lite We run a regression trying to understand the impact of OBP (on base percentage) on RPG (runs per game). The results for each team in the American League are shown below. Coefficients : Estimate Std. Error t value Pr (>It!) (Intercept) -8. 247 1. 921 -4.294 0.00104 * = OBP [ League = "American"] 38 . 817 5. 506 7.050 1.34e-05 * . * Residual standard error: 0.2099 on 12 degrees of freedom. R-squared: 0.8055. (a) Verify the numbers in this table in R, using the baseball . cav data from the class web site. Use the subset option in the Im () command to restrict the analysis to the American League teams. (b) Give an approximate 90% confidence interval for the slope. (c) Test the hypothesis that OBP is unrelated to RPG at the 10% level. (d) What is the correlation between RPG and OBP? (e) Give the plug-in 95% prediction interval for RPG when OBP is 0.400. (f) Test the hypothesis that the true slope is exactly 30 at the 5% level. Count as extreme only values greater than the null hypothesis value of 30