R Programming Question:

alr4, data file: stopping

1. Using Speed as the only regressor, find an appropriate transformation for Distance that can linearize this regression.

2. Hald (1960) suggested on the basis of a theoretical argument using a quadratic mean function for Distance given Speed, with Var(Distance|Speed) = ²Speed². Draw the plot of Distance versus Speed, and add a line on the plot of the fitted curve from Halds model. Then obtain the fitted values from the fit of the trans- formed Distance on Speed, using the transformation you found above. Transform these fitted values to the Distance scale (for example, if you fit the regression sqrt(Distance) Speed, then the fitted values would be in square-root scale and you would square them to get the original Distance scale). Add to your plot the line corresponding to these transformed fitted values. Compare the fit of the two models.