# Question

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. For one explanatory variable, use the width of the chain. For the second, calculate the “volume” of the chain as p times its length times the square of half the width, Volume = p Metric Length × (Width / 2)2. To make the units of volume mm3, first convert the length to millimeters (25.4 mm = 1 inch).

(a) The explanatory variable Volume includes Width. Are these explanatory variables perfectly correlated? Can we use them both in the same multiple regression?

(b) Fit the multiple regression of Price on Width and Volume. Do both explanatory variables improve the ft of the model?

(c) Find the variance inflation factor and interpret the value that you obtain.

(d) What is the interpretation of the coefficient of Volume?

(e) The marginal correlation between Width and Price is 0.95, but its slope in the multiple regression is negative. How can this be?

(a) The explanatory variable Volume includes Width. Are these explanatory variables perfectly correlated? Can we use them both in the same multiple regression?

(b) Fit the multiple regression of Price on Width and Volume. Do both explanatory variables improve the ft of the model?

(c) Find the variance inflation factor and interpret the value that you obtain.

(d) What is the interpretation of the coefficient of Volume?

(e) The marginal correlation between Width and Price is 0.95, but its slope in the multiple regression is negative. How can this be?

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