13.8 A real estate agency collects data concerning the sales price of
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13.8 A real estate agency collects data concerning the sales price of a house ( in thousands of dollars), and the home size ( in hundreds of square feet). The data are given in the table below. The MINITAB output from fitting a least squares regression line to the data is on the next page. x y
Sales price(y) home size(x) sales price(y) home size(x)
180 23 165.9 21
98.1 11 193.5 24
173.1 20 127.8 13
136.5 17 163.5 19
141 15 172.5 25
Fitted line plot
Sales price= 48.2 +5.700 home size
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A By using the formulas illustrated in Example 13.2 ( see page 497) and the data provided, verify that ( within rounding) b0 48.02 and b1 5.700, as shown on the MINITAB output. b Interpret the meanings of b0 and b1 . Does the interpretation of b0 make practical sense?
c Write the least squares prediction equation. d Use the least squares line to obtain a point estimate of the mean sales price of all houses having 2,000 square feet and a point prediction of the sales price of an individual house having 2,000 square feet.
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Accu- Copiers, Inc., sells and services the Accu- 500 copying machine. As part of its standard service contract, the company agrees to perform routine service on this copier. To obtain information about the time it takes to perform routine service, Accu- Copiers has collected data for 11 service calls. The data and Excel output from fitting a least squares regression line to the data follow on the next page.
Service call number of copier service(x) number of minute require(y)
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3 5
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138
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103
134
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copier line fit plot
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Minutes =11.4641 +24.6022* copier a Find the least squares point estimates b0 and b1 on the computer output and report their values.
Interpret b0 and b1 . Does the interpretation of b0 make practical sense? b Use the least squares line to compute a point estimate of the mean time to service four copiers and a point prediction of the time to service four copiers on a single call.
