# 1 - Statistics 512 Problem Set No 0 Solutions 1 A...

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Statistics 512: Problem Set No. 0 Solutions 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? Solution: The ﬁtted value at x = 7 is ˆ y = 25 - (0 . 5)(7) = 25 - 3 . 5 = 21 . 5 . (b) What is the residual corresponding to the data point with x = 3 and y = 30? Solution: The ﬁtted value corresponding to the data point with x = 3 is ˆ y = 25 - (0 . 5)(3) = 25 - 1 . 5 = 23 . 5 . The residual corresponding to the data point with x = 3 and y = 30 is thus e i = 30 - 23 . 5 = 6 . 5 . (c) If x increases 3 units, how does ˆ y change? Solution: For increase of 1 in x , ˆ y changes by the slope. Therefore, if x increase by 3 units, ˆ y will decrease by 3 times the slope, i.e. by (3)( - 0 . 5) = - 1 . 5. (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.

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## This note was uploaded on 09/24/2010 for the course STAT 512 taught by Professor Staff during the Spring '08 term at Purdue.

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1 - Statistics 512 Problem Set No 0 Solutions 1 A...

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