14_Regression and Diversification I_sol

14_Regression and Diversification I_sol - BM 410 HW#14 Free...

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BM 410 HW #14 Free Response 1) Assume the following: x , and e are random variables, each with their own PDFs Cov( x , e )=0 y=3x+e Var(x)=10 Var(e)=50 A) According to Stat Rule #3, what is the total variance of y ? Var(y)=9*10+50=140 B) What fraction of the variance of y is explained by variation in x ? 9*10/140=64% C) What is the correlation between x and y? In part B we calculated the R-square, which is the correlation squared. So the correlation could be +.80 or -.80. But then we see that the covariance between x and y is positive: b=+3=Cov(x,y)/var(x). Therefore, the correlation must be +.80. 2) Research Question: How much do patrol cars deter speeding? To answer this question, the Utah Highway Patrol varied the number of patrol cars on a specific stretch of I-15 across several days and measured the average speed of cars passing through this stretch of highway on each given day. A portion of the data they recorded is given below. Day # of patrol cars average speed 11-Oct 0 80 12-Oct 1 69 13-Oct 2 60 14-Oct 3 64 A) Let y = average speed, and x = # of patrol cars. Estimate a and b in the equation E[ y | x ]= a + bx . For practice, you should do this using only your calculator. You can check your answers in excel for accuracy. Covar(x,y)=-7.125 Please do not share these solutions with students who may be taking BusM 410 in the future. 1
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Var(x)=1.25 average(y)=68.25 average(x)=1.5 b =-7.125/1.25=-5.7 a=65.8-(-5.7)*2=76.8 B) Given you estimates in part (A), what is E[ y | x =4]? That is, if the UHP decided to employ 4 patrol cars, what would we expect the average speed to be? =76.8-5.7*4 = 54
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This note was uploaded on 03/17/2011 for the course BUS M 410 taught by Professor Brianboyer during the Fall '10 term at BYU.

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14_Regression and Diversification I_sol - BM 410 HW#14 Free...

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