A bear market in the stock market is defined as a condition in which the market declines by 20% or more over the course of at least two months. The following data represent the number of months and percentage change in the S&P500 (a group of 500 stocks).

(a) Treating the length of the bear 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 bear market and market performance?

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Months Percent Months Percent Change Change 12.1 -20.57 1.9 -44.57 8.3 -44.29 14.9 -21.63 -32.86 3.3 6.5 -27.97 -42.54 3.4 8. -22.18 -61.81 6.8 18.1 -36.06 -48.20 5.8 -40.60 21 -27.11 3.1 -29.43 20.7 13.4 -31.81 3.4 -33.51 12.9 -54.47 18.2 -36.77 5.1 -24.44 9.3 -33.75 -28.69 -51.93 7.6 13.6 -34.42 -27.62 17.9 2.1 -28.47 11.8