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ECON2P91_ReviewQuestions_No2_Solutions_Fall2009

ECON2P91_ReviewQuestions_No2_Solutions_Fall2009 - 1ECON2P91...

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1ECON2P91: Review Questions No. 2 1. Textbook Chapter 4 Page 137 q. 4.1 (a) The predicted average test score is · 520 4 5 82 22 392 36 TestScore = . - . × = . (b)The predicted change in the classroom average test score is · ( 5 82 19) ( 5 82 23) 23 28 TestScore = - . × - - . × = . (c)Using the formula for 0 ˆ β in Equation (4.8), we know the sample average of the test scores across the 100 classrooms is 0 1 ˆ ˆ 520 4 5 82 21 4 395 85 TestScore CS β β = + × = . - . × . = . . (d)Use the formula for the standard error of the regression (SER) in Equation (4.19) to get the sum of squared residuals: 2 2 ( 2) (100 2) 11 5 12961 SSR n SER = - = - × . = . Use the formula for 2 R in Equation (4.16) to get the total sum of squares: 2 2 12961 13044 1 1 0 08 SSR TSS R = = = . - - . The sample variance is 2 Y s = TSS 13044 1 99 131 8. n - = = . Thus, standard deviation is 2 11 5. Y Y s s = = . 2. Textbook Chapter 4 Page 137 q. 4.2 The sample size 200. n = The estimated regression equation is · 2 (2 15) 99 41 (0 31) 3 94 0 81 SER 10 2 Weight Height R = . - . + . . , = . , = . . (a)Substituting 70, 65, and 74 Height = inches into the equation, the predicted weights are 176.39, 156.69, and 192.15 pounds. (b) · 3 94 3 94 1 5 5 91. Weight Height = . × ∆ = . × . = . (c)We have the following relations: 1 2 54 and1 0 4536 . in cm lb kg = . = . Suppose the regression equation in the centimeter-kilogram space is · 0 1 ˆ ˆ Weight Height γ γ = + . The coefficients are 0 ˆ 99 41 0 4536 45 092 ; kg γ = - . × . = - . 0 4536 2 54 1 ˆ 3 94 0 7036 kg γ .
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