Some people think that the behavior of the stock market in January predicts its

Question

Some people think that the behavior of the stock market in January predicts its behavior for the rest of the year. Define the independent variable x to be the percent change in January and the dependent variable y to be the change in the index for the entire year.

Calculation based on 35 years of data gives: ¯x = 1.25, sx = 4.2, ¯y = 6.,3 sy = 10.92, r = 0.41.

(a). What proportion of the variation in yearly changes in the index is explained by its linear relationship with the change during January?

(b). What is the equation of the least squares line for predicting full-year change from January change? ˆy = ( ) + ( ) x

Explanation / Answer

a) We have

r = 0.41

R-Square = 0.41*0.41 = 0.1681

So, 0.1681 proportion of the variation in yearly changes in the index is explained by its linear relationship with the change during January

b) Slope = (0.41*10.92)/4.2 = 1.066

Intercept = 6.3-1.066*1.25 = 4.9675

y = 4.9675+1.066x

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.