These data track monthly performance of stock in Apple Computer since 1990. The data include 264 monthly returns on Apple Computer, as well as returns on the entire stock market, the S&P 500 index, stock in IBM, and Treasury Bills (short-term, 30-day loans to the government). (The column Whole Market Return is the return on a value-weighted portfolio that purchases stock in the three major US markets in proportion to the size of the company rather than one of each stock.) Formulate the regression with excess returns on Apple as the response and excess returns on the whole market, the S&P 500, and IBM as explanatory variables. (Excess returns are the same as excess percentage changes, only without being multiplied by 100. Just subtract the return on Treasury Bills from each.)
(a) Do any of these excess returns have linear patterns over time? Use timeplots of each one to see. (A scatterplot matrix becomes particularly useful.) Do any months stand out as unusual?
(b) Fit the indicated multiple regression. Does the estimated multiple regression explain statistically significant variation in the excess returns on Apple?
(c) Does collinearity affect the estimated effects of these explanatory variables in the estimated equation? In particular, do the partial effects create a different sense of importance from what is suggested by marginal effects?
(d) Which explanatory variable has the largest VIF?
(e) How would you suggest improving this model, or would you just leave it as is?
(f) Interpret substantively the fit of your model (which might be the one the question starts with).