A bear market is a market condition in which the price of the security falls. A bear market in the stock market is defined as a condition in which 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 months as the explanatory variable, x, determine the estimates for ß0 and ß1.
(b) Assuming the residuals are normally distributed, test whether a linear relation exists between the number of months of a bear market and percent change at the α = 0.05
level of significance.
(c) Assuming the residuals are normally distributed, construct a 95% confidence interval for the slope of the true leastsquares regression line.
(d) Based on your results to parts (b) and (c), would you recommend using the least-squares regression line to predict the percent change in the S&P500 during a bear market? Why? What would be a good estimate of the percent change in the S&P500 during a bear market?

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Months Percent Change Months Percent Change 1.9 12.1 -44.57 -20.57 8.3 -44.29 14.9 -21.63 3.3 -32.86 6.5 -27.97 3.4 -42.54 8.0 -22.18 6.8 -61.81 18.1 -36.06 5.8 -40.60 21.0 -48.20 -29.43 3.1 20.7 -27.11 -33.51 13.4 -31.81 3.4 12.9 -54.47 18.2 -36.77 9.3 5.1 -24.44 -33.75 7.6 -28.69 13.6 -51.93 -34.42 17.9 2.1 -27.62 11.8 -28.47