# Question

A real estate agency collects the data in Table concerning

y = sales price of a house (in thousands of dollars)

x1 = home size (in hundreds of square feet)

x2 = rating (an overall “niceness rating” for the house expressed on a scale from 1 [worst] to 10 [best], and provided by the real estate agency)

Scatter plots of y versus x1 and y versus x2 are as follows:

The agency wishes to develop a regression model that can be used to predict the sales prices of future houses it will list. Figure gives the MINITAB output of a regression analysis of the real estate sales price data in Table 14.4 using the model

y = β0 + β1x1 + β2x2 = ε

a. Using the MINITAB output, identify and interpret b1 and b2, the least squares point estimates of b1 and b2.

b. Calculate a point estimate of the mean sales price of all houses having 2,000 square feet and a rating of 8, and a point prediction of the sales price of a single house having 2,000 square feet and a rating of 8. Find this point estimate (prediction), which is given at the bottom of the MINITAB output, and verify that it equals (within rounding) your calculated value.

y = sales price of a house (in thousands of dollars)

x1 = home size (in hundreds of square feet)

x2 = rating (an overall “niceness rating” for the house expressed on a scale from 1 [worst] to 10 [best], and provided by the real estate agency)

Scatter plots of y versus x1 and y versus x2 are as follows:

The agency wishes to develop a regression model that can be used to predict the sales prices of future houses it will list. Figure gives the MINITAB output of a regression analysis of the real estate sales price data in Table 14.4 using the model

y = β0 + β1x1 + β2x2 = ε

a. Using the MINITAB output, identify and interpret b1 and b2, the least squares point estimates of b1 and b2.

b. Calculate a point estimate of the mean sales price of all houses having 2,000 square feet and a rating of 8, and a point prediction of the sales price of a single house having 2,000 square feet and a rating of 8. Find this point estimate (prediction), which is given at the bottom of the MINITAB output, and verify that it equals (within rounding) your calculated value.

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