Multiple Regression: The data in apple.xlsx tracks monthly performance of stock inApple Computer since its reception in 1980. The data include 300 monthly returns on AppleComputer, IBM stock returns as well as returns on the entire stock market. Formulate the modelwith Apple Return as the response and Market Return and IBM Return as explanatory variables.
(A) Examine scatterplots of the response versus the two explanatory variables as well as the scatterplot between the responses. Do you notice any unusual features in the data? Do the relevant plots appear straight enough for multiple regression?
(B) Fit the indicated multiple regression and show a summary of the estimated features of the model.
(C) The regression of Apple returns on market returns estimates β for this stock to be about 1.5.Does the multiple regression suggest a different slope for the market?
(D) Give a confidence interval for the coefficient of IBM returns and carefully interpret thisestimate.
(E) Does the inclusion of IBM returns improve the fit of the model with just market returns by a statistically significant amount? Does this imply that we've found an improved trading scheme?
Non-linear Transformation: Influential wine critics such as Robert Parker publishtheir personal ratings of wines and many consumers pay close attention. Do these ratings affectthe price? The data in wine.xlsx are a sample of ratings and prices found online at the website ofan internet wine merchant.
(A) Does the scatterplot of the price of wine on the rating suggest a linear or nonlinear relationship?
(B) Fit a linear regression equation to the data, regressing price on the rating. Does this fitted model make substantive sense?
(C) Create a scatterplot for the natural logarithm of the price on the rating. Does the relationship seem more suited to regression?