These data give the prices (in dollars) for gold link chains at the Web site of a discount jeweler. The data include the length of the chain (in inches) and its width (in millimeters). All of the chains are 14-carat gold in a similar link style. Use the price as the response.
(a) Examine the scatterplots of the response versus the two explanatory variables as well as the scatterplot between the explanatory variables. Do you notice any unusual features in the data? Do the relevant plots appear straight enough for multiple regression?
(b) Find the correlation between each pair of variables. Which correlation is largest? Explain why this correlation is so much larger than the others.
(c) Fit the multiple regression of price on length and width. Show a summary of the fitted model. (Save the diagnostics for part (d).)
(d) Even though the equation fit in part (c) has a large R2 and both slopes are significantly different from zero, the estimated regression does not meet the conditions of the MRM. Explain why.
(e) You can obtain a better model by combining the two explanatory variables in a way that captures an important omitted variable. Do this, and see if the model improves. (Hint: Concentrate on identifying the obvious missing variable from this model. You can build a very good proxy for this variable using the given columns.)(f) Summarize the fit of your improved model.