Scatterplot of HR YS BA Exercise 1. Consider the homerun (HR), batting average (BA) data. The least-squares (best-fit) 80 line for predicting HR using BA is: HR = 133.72 280.8 BA (see the scatterplot). 70 60 50 4 40 . 30 20 10 (b) Compute the residual corresponding to the first observation (BA(Barry Larkin), HR(Barry Larkin)) = (0.319, 15). 0 0.30 0.31 0.32 0.34 0.35 0.36 0.37 0.33 BA (c) Based on this LSQ line, what is the predicted number of home runs for an MVP who hits 0.500? Explain why this prediction is ill-advised. (d) It turns out that p2 = 0.084. Interpret this value in the words of the problem. Would you say batting average is useful for predicting number of home runs. Explain. (e) Use the value of r2 to compute the correlation coefficient r. Does this number align with your eye-ball estimate based on the scatterplot? (f) Interpret the slope of the LSQ line, HR = 133.72 280.8 BA, in the words of the problem. (Make sure you use a reasonable increment in BA.] 280.8 BA, are Exercise 2. Consider the setting of Exercise 1. The residuals corresponding to the LSQ line, HR = 133.72 plotted in the graph below. Residuals Versus the Order of the Data (response is HR) 30 20 10 Residual 0 -10 -20 -30 2 3 4 5 13 14 6 7 8 9 10 11 12 Observation Order (a) Using the residual graph only, estimate how far the fitted/predicted number of home runs (fitted s) is from the observed number of home runs (observed ys value) for the 5th observation in the data set. (b) Give an approximate 95% prediction interval for the number of homeruns hit by an MVP who has a batting average of 0.350. Explain your reasoning