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HW1sol

# HW1sol - 1 A regression analysis relating test scores(Y to...

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1. A regression analysis relating test scores (Y) to training hours (X) produced the following fitted equation: ˆ 15 0.9 y x . (a) What is the fitted value of the response variable corresponding to x = 6?   ˆ 15 0.9 6 15 5.4 20.4 y (b) What is the residual corresponding to the data point with x = 5 and y = 17?   ˆ 15 0.9 5 15 4.5 19.5 17 19.5 2.5 i y e   (c) If x increases 3 units, how does ˆ y change? For each increase of 1 in x, ˆ y changes by the slope. Therefore if x increases by 3 units, ˆ y will increase by 3 times the slope, i.e. by (3)(0.9) = 2.7 (d) Consider the data point in part (b). An additional test score is to be obtained for a new observation at x = 5. Would the test score for the new observation necessarily be 17? Explain. Not necessarily. The new observation is a random variable from a normal distribution with estimated mean 19.5. So you would not likely see 17 a second time.

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