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Consider the setting of Exercise 1. The residuals corresponding to the LSQ line, HR = 133.72 – 280.8 BA, are ne graph below. Residuals Versus the Order of the Data (response is HR) 30 20 10

Consider the setting of Exercise 1. The residuals corresponding to the LSQ line, HR = 133.72 – 280.8 BA, are ne graph below. Residuals Versus the Order of the Data (response is HR) 30 20 10

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.4: Mathematical Models And Least Squares Analysis
Problem 39E
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Please solve Exercise 2

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 -10 -20 -30 3 4 6. 8 10 11 12 13 14 Observation Order (a) Using the residual graph only, estimate how far the fitted/predicted number of home runs (fitted ŷ5) is from the observed number of home runs (observed y, 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. Residual
Transcribed Image Text: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 -10 -20 -30 3 4 6. 8 10 11 12 13 14 Observation Order (a) Using the residual graph only, estimate how far the fitted/predicted number of home runs (fitted ŷ5) is from the observed number of home runs (observed y, 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. Residual
Exercise 1. Scatterplot of HR vs BA 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 皇 40 30 20 (b) Compute the residual corresponding to the first observation 10 (BA(Barry Larkin), HR(Barry Larkin)) = (0.319, 15). 0.30 0.31 0.32 0.33 0.34 0.35 0.36 0.37 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 r? useful for predicting number of home runs. Explain. = 0.084. Interpret this value in the words of the problem. Would you say batting average is (e) Use the value of r2 to compute the correlation coefficient r. based on the scatterplot? Does this number align with your eye-ball estimate (f) Interpret the slope of the LSQ line, HR = 133.72 reasonable increment in BA.] 280.8 BA, in the words of the problem. [Make sure you use a
Transcribed Image Text:Exercise 1. Scatterplot of HR vs BA 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 皇 40 30 20 (b) Compute the residual corresponding to the first observation 10 (BA(Barry Larkin), HR(Barry Larkin)) = (0.319, 15). 0.30 0.31 0.32 0.33 0.34 0.35 0.36 0.37 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 r? useful for predicting number of home runs. Explain. = 0.084. Interpret this value in the words of the problem. Would you say batting average is (e) Use the value of r2 to compute the correlation coefficient r. based on the scatterplot? Does this number align with your eye-ball estimate (f) Interpret the slope of the LSQ line, HR = 133.72 reasonable increment in BA.] 280.8 BA, in the words of the problem. [Make sure you use a
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