stat512hw1sol - Statistics 512 Homework#1 Solution 1 A...

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Statistics 512: Homework#1 Solution 1. A regression analysis relating test scores ( Y ) to training hours ( X ) produced the following fitted question: ˆ y = 25 - 0 . 5 x . (a) What is the fitted value of the response variable corresponding to x = 7?
(b) What is the residual corresponding to the data point with x = 3 and y = 30?
(c) If x increases 3 units, how does ˆ y change?
(d) An additional test score is to obtained for a new observation at x = 6. Would the test score for the new observation necessarily be 22? Explain.
(e) The error sums of squares ( SSE ) for this model was found to be 7. If there were n = 16 observations, provide the best estimate for σ 2 .
(f) Rewrite the regression equation in terms of x * where x * is training time measured in seconds. Show that your answer makes sense, i.e., gives the same predictions as the original equation (an example is sufficient).

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