Chapter 12.3, Problem 20AYU

Bear Markets (Refer to Problem 32. Section 4.1) 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).

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

Source: Gold-Eagle

1. a. Treating months as the explanatory variable, x, determine the estimates for β₀ and β₁.
2. 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.
3. c. Assuming the residuals are normally distributed, construct a 95% confidence interval for the slope of the true least-squares regression line.
4. 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?