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- From: Mathematics, Statistics and Probability
- Posted on: Fri 22 Jan, 2016
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13.21 In Problem 13.9 on page 482, an agent for a real estate company wanted to predict the monthly rent for apartment, based on the size of the apartment (stored in Rent). Using the results of that problem,
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a. determine the coefficient of determination, r^2, and interpret its meaning.
c. How useful do you think this regression model is for predicting the monthly rent?
13.79 An accountant for a large department store would like to develop a model to predict the amount of time if takes to process invoices. Data are collected from the past 32 working days, and the number of invoices processed and completion time (in hours) are stored in Invoice. (Hint: First, determine which are independent and dependent variables.)
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a. Assuming a linear relationship, use the least-squares method to compute the regression coefficients b0 and b1.
b.Interpret the meaning of the Y intercept, B0, and the slope, b1, in this problem.
c. Use the prediction line developed in (a) to predict the amount of time it would take to process 150 invoices.
d. Determine the coefficient of determination, r^2, and interpret its meaning.
14.5 A consumer organization wants to develop a regression model to predict mileage (as measured by miles per gallon) based on the horsepower of the car's engine and the weight of the car (in pounds). Date were collected from a sample of 50 recent car models, and the results are organized and stored in Auto.
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a. State the multiple regression equation.
b. Interpret the meaning of the slopes, b1 and b2, in this problem.
c. Explain why the regression coefficient, b0, has no practical meaning in the contest of this problem.
d. Predict the miles per gallon for cars that have 60 horsepower and weigh 2,000 pounds.
14.59 Professional basketball has truly become a sport that generates interest among fans around the world. More and more players come from outside the United States to play in the National Basketball Association (NBA). You want to develop a regression model to predict the number of wins achieved by each NBA team, based on field goal (shots made) percentage for the team and for the opponent. The data are stored in NBA2009.
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a. State the multiple regression equation.
b. Interpret the meaning of the slopes in this equation.
c. Predict the number of wins for a team that has a field goal percentage of 45% and an opponent field goal percentage of 44%.
e. Is there a significant relations between number of wins and the two independent variables ( field goal percentage for the team and for the opponent) at the 0.05 level of significance?
g. Interpret the meaning of the coefficient of multiple determination in this problem.
i. At the 0.05 level of significance, determine whether each independent variable makes a significant contribution to the regression model for this set of data.
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