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?