Predict the annual rate of return for a stock

Question

Solve the following problem:

1. An analyst for Phidelity Investments wants to develop a regression model to predict the annual rate of return for a stock based on the price-earnings (PE) ratio of the stock and a measure of the stock's risk.

PE Ratio	Risk	Return
7.4	1.0	7.6
11.1	1.3	13.0
8.7	1.1	8.9
11.2	1.2	10.9
11.6	1.7	12.1
12.2	1.3	12.8
12.5	1.2	11.3
12.5	1.3	14.1
13.0	1.6	14.8
13.4	1.4	16.7

a.    Prepare scatter plots for each independent variable versus the dependent variable. What type of model do these scatter plots suggest might be appropriate for the data?

b.    Let Y = Return, X₁ = PE Ratio, and X₂ = Risk. Obtain the regression results for the following regression model:
                  Y^ˆ = b_o +b₁X_1i    + b₂X_2i
Interpret the value of R2 for this model.

c.    Obtain the regression results for the following regression model:
                    Y^ˆ= b_o    + b₁X_1i    + b₂X_2i+b₃x_3i+b₄x_4i

where X_3i=x²_1i and x_4i=x²_2i. Interpret the value of R2 for this model.

d.    Which of the previous two models would you recommend that the analyst use?