Question: 7. Consider again the data and output from question 5 together with the following further R code: > anova(1m1) Analysis of Variance Table Response: Price

7. Consider again the data and output from question 5 together with the following further R code: > anova(1m1) Analysis of Variance Table Response: Price Df Sum Sq Mean Sq F value Pr(>F) Beds 1 5781051 5781051 102.0204 1.145e-10 *** Baths 1 874101 874101 15.4256 0.0005359 *** Receps 1 213183 213183 3.7621 0.0629397 AvPrice 1 340992 340992 6.0176 0.0209068 * Residuals 27 1529972 56666 > 1m2 anova (1m2) Analysis of Variance Table Response: Price Df Sum Sq Mean Sq F value Pr>F) Baths 1 6085955 6085955 88.4765 2.598e-10 *** Receps 1 658547 658547 9.5738 0.004342 ** Residuals 29 1994797 68786 (a) Using the R output, calculate the value of the test statistic for testing the hypoth- esis that variables Beds and AvPrice together have no significant effect on Price. in the presence of the other variables. [3] (b) What is the distribution of this statistic, assuming the null hypothesis is true? [1] (C) Writing X for a random variable with this distribution, draw conclusions regarding the hypothesis test in part (a) based on the following probabilities: [1] P(X > 3.35) = 0.05, P(X> 5.49) = 0.01. 7. Consider again the data and output from question 5 together with the following further R code: > anova(1m1) Analysis of Variance Table Response: Price Df Sum Sq Mean Sq F value Pr(>F) Beds 1 5781051 5781051 102.0204 1.145e-10 *** Baths 1 874101 874101 15.4256 0.0005359 *** Receps 1 213183 213183 3.7621 0.0629397 AvPrice 1 340992 340992 6.0176 0.0209068 * Residuals 27 1529972 56666 > 1m2 anova (1m2) Analysis of Variance Table Response: Price Df Sum Sq Mean Sq F value Pr>F) Baths 1 6085955 6085955 88.4765 2.598e-10 *** Receps 1 658547 658547 9.5738 0.004342 ** Residuals 29 1994797 68786 (a) Using the R output, calculate the value of the test statistic for testing the hypoth- esis that variables Beds and AvPrice together have no significant effect on Price. in the presence of the other variables. [3] (b) What is the distribution of this statistic, assuming the null hypothesis is true? [1] (C) Writing X for a random variable with this distribution, draw conclusions regarding the hypothesis test in part (a) based on the following probabilities: [1] P(X > 3.35) = 0.05, P(X> 5.49) = 0.01

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