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Homework01Solns - Stat 512-2 Solutions to Homework#1 Dr...

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Stat 512-2 Solutions to Homework #1 Dr. Simonsen Due Wednesday August 31, 2005. A reminder – Please do not hand in any unlabelled or unedited SAS output. Include in your write-up only those results that are necessary to present a complete solution. In particular, questions must be answered in order (including graphs), and all graphs must be fully labeled (main title should include question number and all axes should be labelled). Don’t forget to put all necessary information (see course policies) on the first page. Include the SAS input for all questions at the very end of your homework. You will often be asked to continue problems on successive homework assignments, so save all your SAS code. 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 change? ˆ y For each increase of 1 in x, changes by the slope. Therefore if x increases by 3 units, will increase by 3 times the slope, i.e. by (3)(0.9) = 2.7 ˆ y ˆ y (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. (e) The error sums of squares (SSE) for this model was found to be 8. If there were n = 18 observations, provide the best estimate for 2 σ . 2 8 0.5 2 16 E SSE SSE s MSE df n = = = = = (f) Rewrite the regression equation in terms of x * where x * is training time measured in minutes. Show that your answer makes sense, i.e. gives the same predictions as the original equation (an example is sufficient).
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