The following example is from the book Residuals and Influence in Regression (Cook and Weisberg, 1982). An experiment was conducted to investigate the amount of drug that is ­retained in the liver of a rat. In the experiment, rats were injected with a dose of a drug that was ­approximately proportional to the body weight of the rat. The amount of the drug injected into the rat was determined as approximately 40 mg of the drug per kilogram of body weight. After a set ­period of time, the rat was sacrificed, the animal€™s liver was weighed, and the fraction of the drug ­recovered in the liver was recorded. The experimenters wanted to relate the proportion of the drug in the rat€™s liver, y, to the explanatory variables: the body weight of the rat (gm), x1: liver weight of the rat (gm), x2: and relative dose level of the drug injected into the rat, x3. The data are given here.

a. Is there a problem with collinearity amongst the explanatory variables?
b. Fit the model y = β0 + β1x1 + β2x2 + β3x3 + ɛ to the data. Evaluate the fit of this model.
c. Is it possible to obtain essentially the same degree of fit as in part (b) using a model without some of the explanatory variables? Which subset of the variables yields the best fit?

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