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 deviation of the x-variable: 4.95%
• mean of the y-variable: 10.7%
• standard deviation of the y-variable: 21.23%
• correlation between the two variables: 0.502

Suppose that the mean change in January is 16.53%.

What is the predicted value of the change in the stock market index for the year?

Enter your answer to 2 decimal places in percent format; do not type the % symbol. (Observe that if you leave the means and standard deviations in percent format when you carry out your calculations, then your final answer will be in percent format.) If the intercept is negative, include the minus sign.

Correct Answer: 40.37 margin of error +/- 0.02

Answer 1

Given : = 2.75 , σ_x = 4.95 and = 10.7, σ_x = 21.23, r = 0.502

Slope ( b₁ ) = = = 2.1530

Intercept ( b₀ ) = - b₁ * = 10.7 - ( 2.1530*2.75 ) = 4.7792

Equation of regression line

= b₀ + b₁ *x

= 4.7792  + 2.1530 *x

We are asked to predict for x = 16.53

= 4.7792 + ( 2.1530 *16.53 )

= 40.36