Using R for Introductory Statistics : John Verzani

Linear regression 269Extractor functions for lm()The lm () function is reticent, but we can coax out more information as needed. This isdone using extractor functions. Useful ones are summarized in Table 10.1.These functions are called with the result of a modeling function, such as lm(). Thereare other types of modeling functions in R; these so-called “generic functions” may beused with them to return similar information.To illustrate, the estimate for σ 2 can be found using the resid() function to retrieve theresiduals from the model fitting:> sum( resid(res.mhr)^2 ) / (length(age) − 2) #RSS/(n−2)[1] 14.15Or, the RSS part can be found directly with deviance ():Table 10.1 Extractor functions for the result of1m ()summary () returns summary information about the regressionplot () makes diagnostic plotscoef() returns the coefficientsresiduals () returns the residuals (can be abbreviated resid())fitted ()returns the residualsdeviance() returns RSSpredict () performs predictionsanova () finds various sums of squaresAIC () is used for model selection> deviance(res.mhr)/ (length(age) −2)[1] 14.1510.1.5 Problems10.1 For the Cars93 (MASS) data set, answer the following:1. For MPG. highway modeled by Horsepower, find the simple regressioncoefficients. What is the predicted mileage for a car with 225 horsepower?2. Fit the linear model with MPG. highway modeled by Weight. Find the predictedhighway mileage of a 6,400 pound HUMMER H2 and a 2,524 pound MINI Cooper.3. Fit the linear model Max .Price modeled by Min .Price. Why might you expect theslope to be around 1 ?Can you think of any other linear relationships among the variables?