For the house selling price data of Section 3.4, when we include size, new, and taxes as

Question:

For the house selling price data of Section 3.4, when we include size, new, and taxes as explanatory variables, we obtain

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> summary(lm(price ~ size + new + taxes))

Estimate Std. Error t value Pr(>|t|)

(Intercept) -21.3538 13.3115 -1.604 0.11196 size 0.0617 0.0125 4.937 3.35e-06 new 46.3737 16.4590 2.818 0.00588 taxes 0.0372 0.0067 5.528 2.78e-07

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Residual standard error: 47.17 on 96 degrees of freedom Multiple R-squared: 0.7896, Adjusted R-squared: 0.783 F-statistic: 120.1 on 3 and 96 DF, p-value: < 2.2e-16

> anova(lm(price ~ size + new + taxes)) # sequential SS, size first Analysis of Variance Table Response: price Df Sum Sq Mean Sq F value Pr(>F)

size 1 705729 705729 317.165 < 2.2e-16 new 1 27814 27814 12.500 0.0006283 taxes 1 67995 67995 30.558 2.782e-07 Residuals 96 213611 2225

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a. Report and interpret results of the global test of the hypothesis that none of the explanatory variables has an effect.

b. Report and interpret significance tests for the individual partial effects, adjusting for the other variables in the model.

c. What is the conceptual difference between the test of the size effect in the coefficients table and in the ANOVA table?

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