# Question

This dataset tracks the monthly performance of stock in Apple Computer since January 1990 through the end of 2011. The data include 264 monthly returns on Apple Computer, as well as returns on the entire stock market, returns on Treasury Bills (short-term, 30-day loans to Uncle Sam), and inflation. (The column Market Return is the return on a value-weighted portfolio that purchases stock in proportion to the size of the company rather than one from each company.)

(a) Create a scatterplot for Apple Return on Market Return. Does a line seem to be a good summary of the association between these variables?

(b) Estimate the least squares linear equation for Apple Return on Market Return. Interpret the fitted intercept and slope. Be sure to include their units. Note if either estimate represents a large extrapolation and is consequently not reliable.

(c) Interpret r2 and se associated with the fitted equation. Attach units to these summary statistics as appropriate.

(d) If months in which the market went down by 2% were compared to months in which the market went up by 2%, how would this equation suggest Apple stock would differ between these periods?

(e) Plot the residuals from the regression ft in part

(b) on Market Return. Does this plot suggest that the residuals possess simple variation? Do you recognize the dates of any of the outliers?

(f) Careful analyses of stock prices often subtract the so-called risk-free rate from the returns on the stock. After the risk-free rate has been subtracted, the returns are sometimes called “excess returns” to distinguish them. The risk-free rate is the interest rate returned by a very safe investment, one with no (or at least almost no) chance of default. The return on short-term Treasury Bills is typically used as the risk-free rate. Subtract the risk-free rate from returns on Apple stock and the market, and then refit the equation using these excess returns. Does the equation change from the previous estimate? Explain why it’s similar or different.

(a) Create a scatterplot for Apple Return on Market Return. Does a line seem to be a good summary of the association between these variables?

(b) Estimate the least squares linear equation for Apple Return on Market Return. Interpret the fitted intercept and slope. Be sure to include their units. Note if either estimate represents a large extrapolation and is consequently not reliable.

(c) Interpret r2 and se associated with the fitted equation. Attach units to these summary statistics as appropriate.

(d) If months in which the market went down by 2% were compared to months in which the market went up by 2%, how would this equation suggest Apple stock would differ between these periods?

(e) Plot the residuals from the regression ft in part

(b) on Market Return. Does this plot suggest that the residuals possess simple variation? Do you recognize the dates of any of the outliers?

(f) Careful analyses of stock prices often subtract the so-called risk-free rate from the returns on the stock. After the risk-free rate has been subtracted, the returns are sometimes called “excess returns” to distinguish them. The risk-free rate is the interest rate returned by a very safe investment, one with no (or at least almost no) chance of default. The return on short-term Treasury Bills is typically used as the risk-free rate. Subtract the risk-free rate from returns on Apple stock and the market, and then refit the equation using these excess returns. Does the equation change from the previous estimate? Explain why it’s similar or different.

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