Stats Midterm 2 - Student Name Discussion Section Number or...

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Student Name: Discussion Section Number or TA Name: Student ID: Midterm 2: Form A 6E:071 Spring 2007 Please write legibly. There are two forms for this exam. If an answer from the other form appears on this exam, we will consider that evidence that you copied from another exam and you will receive a grade of zero on the entire exam. You may use any calculator that the College Board allows and one cheat sheet, 8.5 x 11. Please be sure to sign the honor pledge after you complete the exam. 1. Consider the data set from Assignment 5, which contained the return on Phillip Morris (MO) stock and the return on the S&P 500 (SP). If we regress MO on SP, we obtain the following results: Predictor Coef SE Coef T P Constant 0.3537 0.7612 0.46 0.643 S&P 1.1695 0.2106 5.55 0.000 If we regress SP on MO, we obtain Predictor Coef SE Coef T P Constant 0.8608 0.3286 2.62 0.011 MO 0.23575 0.04246 5.55 0.000 a. (6 points) If the linear regression line minimizes the squared difference between the data and the regression line, why is the slope coefficient in the first regression different from the slope coefficient in the second regression? b. (2 points) What is the predicted value of MO if the return on the S&P is 4% (use S&P=4)? c. (2 points) What is the predicted value of S&P if the return on MO is 4% (use MO=4)? The regression of MO on S&P minimizes the distance in a different direction than does the regression of S&P on MO. In each case, we’ve assumed that one variable depends on the other variable, and our assumption of which variable is dependent changes the regression coefficient. MO = .3537 + 1.1695(4) = 5.0317 S&P = .8608 + .23575(4) = 1.8038
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2. A person’s blood alcohol content (BAC) is determined by many factors, including how much alcohol has been consumed, the person’s weight, and recent food consumption. We wish to predict BAC from number of beers consumed. We have data on 16 people who drank between 1 and 9 beers. The Minitab output from a regression of BAC on Beer is: The regression equation is BAC = - 0.0127 + 0.0180 Beers Predictor Coef SE Coef T P Constant -0.01270 0.01264 -1.00 0.332 Beers 0.017964 0.002402 7.48 0.000 S = XXXXXXXX R-Sq = XXXX% R-Sq(adj) = 78.6% Analysis of Variance Source DF SS MS F P Regression 1 0.023375 0.023375 XXXXX 0.000 Residual Error 14 0.005850 0.000418 Total 15 0.029225 a. (4 points) Is the coefficient on Beers significantly different from zero? Explain how you reached your answer. b. (2 points each) Calculate the following values: F-statistic = MSR/MSE =55.921 Regression standard error, s = sqrt(MSE) = 0.0204 R 2 =SSR/SST = 79.98 Correlation(BAC, Beers)= (Sx/Sy)*b = (2.198/.0441)*.017964 = 0.8953 c. (4 points) Provide an English interpretation of the coefficient on Beers.
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