In Exercise 10.23 on page 569 we fit a model predicting the price of a home (in $1000s), using size (in square feet), number of bedrooms, and number of bathrooms, based on data in HomesForSale. Output for fitting a slightly revised model is shown below where the Size variable is measured in 1000s of square feet (rather than just the raw square footage in SizeSqFt in the previous model):

Residual standard error: 507.7 on 116 degrees of freedom

Multiple R-squared: 0.4671, Adjusted R-squared: 0.4533

F-statistic: 33.89 on 3 and 116 DF, p-value: 8.383e-16

(a) Compare this output to the regression output in Exercise 10.23 and comment on how the coefficient, standard error, and t-statistic for Size change when we code the variable in 1000s of square feet rather than square feet as in SizeSqFt.
(b) Interpret the coefficient for Beds, the number of bedrooms in this fitted model.
(c) An architect (who has not taken statistics) sees this output and decides to build houses with fewer bedrooms so they will sell for more money. As someone who has taken statistics, help him to correctly interpret this output.

Exercise 10.23

Here is some output for fitting a model to predict the price of a home (in $1000s) using size (in square feet, SizeSqFt, different units than the variable Size in HomesForSale), number of bedrooms, and number of bathrooms. (The data are based indirectly on information in the HomesForSale dataset.)

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Coefficients: Estimate Std. Error t value -1.487 4.552 -2.359 2.534 Pr(> It) 0.1396 *** (Intercept) Size Beds Baths -217.00 330.58 145.90 72.62 57.03 1.32e-05 0.0200 * 0.0126 * -134.52 200.03 78.94 The regression equation is Price = - 217 + 0.331 SizeSqFt - 135 Beds + 200 Baths Predictor Coef SE Coef т Constant -217.0 145.9 -1.49 0.140 SizeSqFt Beds 0.33058 0.07262 4.55 0.000 -134.52 57.03 -2.36 0.020 Baths 200.03 78.94 2.53 0.013 S= 507.706 R-Sq = 46.7% R-Sq(adj) = 45.3% Analysis of Variance Source DF MS Regression 3 26203954 8734651 33.89 0.000 Residual Error 116 29900797 257765 Total 119 56104751