Question

Some people think that the behavior of the stock market in January predicts its behavior for the rest of the year. Let the explanatory variable be the percent change in a stock market index in January. Let the response variable be the percent change in the stock market index for the entire year. You have a data set with 50 cases (where each case is a calendar year). Based on this data, you have the following statistics: mean of the x-variable: 2.75% standard devation of the x-variable: 4.48% mean of the y-variable: 8.17% standard devation of the y-variable: 22.31% correlation between the two variables: 0.655 Suppose that the mean change in January is 10.81%. What is the predicted value of the change in the stock market index for the year

Answer 1

1.95

Explanation:

Formula for slope is = γ Sy/Sx

γ = Correlation, Sy = S.D. of Y value, Sx= S.D. of X value

Sy = 8.17% = 0.0817

Sx = 2.75% = 0.0275

γ = 0.655

Slope = 0.655 *(0.0817/0.0275)

Slope = 1.94595

Slope = 1.94595

Slope = 1.95

Therefore, the slope of the regression line is 1.95