HW6sol - Stat 512 1 Solutions to Homework #6 Dr. Levine 1....

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Stat 512 – 1 Solutions to Homework #6 Dr. Levine 1. In this exercise you will illustrate some of the ideas described in Chapter 7 of the text related to the extra sums of squares. (a) Create a new variable called SAT which equals SATM + SATV and run the following two regressions: (i) predict GPA using HSM , HSS , and HSE ; Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 3 27.71233 9.23744 18.86 <.0001 Error 220 107.75046 0.48977 Corrected Total 223 135.46279 (ii) predict GPA using SAT , HSM , HSS and HSE . Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 4 27.88746 6.97187 14.19 <.0001 Error 219 107.57533 0.49121 Corrected Total 223 135.46279 Calculate the extra sum of squares for the comparison of these two analyses. Use it to construct the F statistic (i.e., general linear test statistic) for testing the null hypothesis that the coefficient of the SAT variable is zero in the model with all four predictors. What are the degrees of freedom for this test statistic? Using the SSE definition, () ( ) ( ) |, , , , ,, , 107.75046 107.57533 0.17513 SSM sat hsm hss hse SSE hsm hss hse SSE sat hsm hss hse =− =−= or, using the SSM definition, ( ) ( ) , , , , 27.88746 27.71223 0.17513 SSM sat hsm hss hse SSM sat hsm hss hse SSM hsm hss hse The numerator df is (220 – 219) = (4 – 3) = 1. ( ) , / 1 0.17513/1 0.35653 0.49121 SSM sat hsm hss hse F MSE full = == , df = (1,219)
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(b) Use the TEST statement in PROC REG to obtain the same test statistic. Give the statistic, degrees of freedom, P value and conclusion. Test nosat Results for Dependent Variable gpa Mean Source DF Square F Value Pr > F Numerator 1 0.17513 0.36 0.5511 Denominator 219 0.49121 F = 0.36, P = 0.5511, do not reject H 0 . There is no evidence of a linear relationship with SAT when HSM, HSE, and HSS are in the model.
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This note was uploaded on 02/05/2011 for the course STAT 512 taught by Professor Staff during the Spring '08 term at Purdue University-West Lafayette.

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HW6sol - Stat 512 1 Solutions to Homework #6 Dr. Levine 1....

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