The data frame table.b3 in the MPV package contains data on gas mileage and 11 other variables for a sample of 32 automobiles. (a) Construct a scatterplot of y (mpg) versus x1 (displacement). Is the...

The data frame table.b3 in the MPV package contains data on gas mileage and 11 other variables for a sample of 32 automobiles.

(a) Construct a scatterplot of y (mpg) versus x1 (displacement). Is the relationship between these variables non-linear?

(b) Use the xyplot() function, and x11 (type of transmission) as a group variable. Is a linear model reasonable for these data?

(c) Fit the model relating y to x1 and x11 which gives two lines having possibly different slopes and intercepts. Check the diagnostics. Are there any influential observations? Are there any influential outliers?

(d) Plot the residuals against the variable x7 (number of transmission speeds), again using x11 as a group variable. Is there anything striking about this plot?