A bull market is defined as a market condition in which the price of a security rises for an extended period of time. A bull market in the stock market is often defined as a condition in which a market rises by 20% or more without a 20% decline. The data on the next page represent the number of months and percentage change in the S&P500 (a group of 500 stocks) during the 25 bull markets dating back to 1929 (the year of the famous market crash).

(a) Treating the length of the bull market as the explanatory variable, draw a scatter diagram of the data.

(b) Determine the linear correlation coefficient between months and percent change.

(c) Does a linear relation exist between duration of the bull market and market performance?

(d) Find the least-squares regression line treating length of the bull market as the explanatory variable.

(e) Interpret the slope.

(f) Did the bull market that lasted 50.4 months have a percent change above or below what would be expected? Explain. 

(g) Draw a residual plot. Any outliers?

(h) Would you consider the bull market from December 4, 1987 through March 24, 2000, which lasted 149.8 months and saw a 582.15% rise in stock prices, influential? Explain. Note: After this bull market, the market entered a bear market that lasted 18.2 months and saw the stock market decline 37%. This era is often referred to as the "Tech Bubble."

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Bull Percent Bull Percent Months Change Months Change 46.77 4.9 86.9 267.08 25.83 86.35 2.3 50.4 0.8 25.82 44.1 79.78 1.2 30.61 26.1 48.05 2.3 111.59 32.0 73.53 4.7 120.61 74.9 125.63 61.3 228.81 3.7 37.28 131.64 24.2 149.8 582.15 21.40 7.4 62.24 3.5 26.78 6.6 60.9 101.50 20.91 5.0 1.6 24.22 49.7 157.70 48.6 127.85 13.1 23.89