ismch11 - 190 Solutions Manual for Statistics for Business...

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190 Solutions Manual for Statistics for Business & Economics, 5 th Edition Chapter 11: Multiple Regression 11.1 The estimated regression slope coefficients are interpreted as follows: b 1 = .661: All else equal, an increase in the plane’s top speed by one mph will increase the expected number of hours in the design effort by an estimated .661 million worker-hours. b 2 = .065: All else equal, an increase in the plane’s weight by one ton will increase the expected number of hours in the design effort by an estimated .065 million worker-hours b 3 = -.018: All else equal, an increase in the percentage of parts in common with other models will result in a decrease in the expected number of hours in the design effort by an estimated .065 million worker-hours 11.2 The estimated regression slope coefficients are interpreted as follows: b 1 = .057: All else equal, an increase of one unit in the change over the quarter in equity purchases by financial institutions results in an estimated .057 increase in the change over the quarter in the Financial Times stock price index b 2 = -.065: All else equal, an increase of one unit in the change over the quarter in equity sales by financial institutions results in an estimated .065 decrease in the change over the quarter in the Financial Times stock price index 11.3 a. b 1 = .052: All else equal, an increase of one hundred dollars in weekly income results in an estimated .052 quarts per week increase in milk consumption. b 2 = 1.14: All else equal, an increase in family size by one person will result in an estimated increase in milk consumption by 1.14 quarts per week b. The intercept term b 0 of -.025 is the estimated milk consumption of quarts of milk per week given that the family’s weekly income is 0 dollars and there are 0 members in the family. This is likely extrapolating beyond the observed data series and is not a useful interpretation. 11.4 a. b 1 = .653: All else equal, a one unit increase in the average number of meals eaten per week will result in an estimated .653 pounds gained during freshman year. b 2 = -1.345: All else equal, a one unit increase in the average number of hours of exercise per week will result in an estimated 1.345 pound weight loss. b 3 = .613: All else equal, a one unit increase in the average number of beers consumed per week will result in an estimated .613 pound weight gain. 11-5 a. When the correlation is = 0 the slope coefficient of the X 1 term simplifies to the slope coefficient of the bivariate regression: Start with equation 11.4: 1 1 2 2 1 2 1 1 2 ( ) (1 ) y x y x x x y x x x S r r r b S r - = - . Note that if the correlation between X 1 and X 2 is zero, then the second terms in both the numerator and denominator are zero and the formula algebraically reduces to 1 1 1 y x y x S r b S = which is the equivalent of the bivariate slope coefficient (see box on bottom of page 380).

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191 Solutions Manual for Statistics for Business & Economics, 5 th Edition b. When the correlation between X 1 and X 2 is = 1, then the second term in the denominator goes to 0 and the slope coefficient is undefined.
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