6 a real estate agent is interested in developing a

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Unformatted text preview: n the accuracy and completeness of your results and explanations. 6. A real estate agent is interested in developing a model to estimate the prices of houses in a particular part of a large city. She takes a random sample of 25 recent sales and, for each house, records the price (in thousands of dollars), the size of the house (in square feet), and whether or not the house has a swimming pool. This information, along with regression output for a linear model using size to predict price, is shown below and on the next page. © 2010 The College Board. Visit the College Board on the Web: www.collegeboard.com. GO ON TO THE NEXT PAGE. -9- 2010 AP® STATISTICS FREE-RESPONSE QUESTIONS (Form B) (a) Interpret the slope of the least squares regression line in the context of the study. © 2010 The College Board. Visit the College Board on the Web: www.collegeboard.com. GO ON TO THE NEXT PAGE. -10- 2010 AP® STATISTICS FREE-RESPONSE QUESTIONS (Form B) (b) The second house in the table has a residual of 49. Interpret this residual value in the context of the study. The real estate agent is interested in investigating the effect of having a swimming pool on the price of a house. (c) Use the residuals from all 25 houses to estimate how much greater the price for a house with a swimming pool would be, on average, than the price for a house of the same size without a swimming pool. To further investigate the effect of having a swimming pool on the price of a house, the real estate agent creates two regression models, one for houses with a swimming pool and one for houses without a swimming pool. Regression output for these two models is shown below. (d) The conditions for inference have been checked and verified, and a 95 percent confidence interval for the true difference in the two slopes is ( − 0.099, 0.110 ) . Based on this interval, is there a significant difference in the two slopes? Explain your answer. (e) Use the regression model for houses with a swimming pool and the regression model for houses without a swimming pool to estimate how much greater the price for a house with a swimming pool would be...
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