Question

Stock market analysts are continually looking for reliable predictors of stock prices. Consider the problem of modeling the price per share of electric utility stocks (Y). Two variables thought to influence such a stock price are return on average equity (X1) and annual dividend rate (X2). The stock price, returns on equity, and dividend rates on a randomly selected day for 16 electric utility stocks are provided in the file P10_19. Xlsx.

a. Estimate a multiple regression model using the given data. Include linear terms as well as an interaction term involving the return on average equity (X1) and annual dividend rate (X2).


b. Which of the three explanatory variables (X1, X2, and X1X2) should be included in a final version of this regression model? Explain. Does your conclusion make sense in light of your knowledge of corporate finance?

Answer 1

To estimate a multiple regression model, we need to include linear terms and an interaction term. The final version of the model will include variables that are significant and align with corporate finance knowledge.

Step-by-step explanation:

In order to estimate a multiple regression model using the given data, we need to include linear terms as well as an interaction term involving the return on average equity (X1) and annual dividend rate (X2). The multiple regression model can be written as follows:

Y = b0 + b1*X1 + b2*X2 + b3*(X1*X2)

To decide which explanatory variables to include in the final version of the regression model, we need to assess the significance of each variable. We can do this by examining the p-values associated with the coefficients of each variable. If the p-value is less than a predetermined significance level, typically 0.05, we can conclude that the variable is significant and should be included in the model. Additionally, the inclusion of variables should also align with our knowledge of corporate finance and their impact on stock prices.

Based on the significance of the p-values and knowledge of corporate finance, we can determine which explanatory variables should be included in the final version of the regression model.

Answer 2

To estimate a multiple regression model, we need to include linear terms and an interaction term. The final version of the model will include variables that are significant and align with corporate finance knowledge.

a. To estimate a multiple regression model using the given data, we can use the variables return on average equity (X1), annual dividend rate (X2), and an interaction term involving X1 and X2. The multiple regression equation can be written as:

Y = β0 + β1X1 + β2X2 + β3(X1X2)

Where Y is the price per share of electric utility stocks, X1 is the return on average equity, X2 is the annual dividend rate, and X1X2 is the interaction term.

By estimating the coefficients β0, β1, β2, and β3, we can determine the relationship between the explanatory variables and the stock price.

b. To determine which of the three explanatory variables (X1, X2, and X1X2) should be included in a final version of the regression model, we need to assess their statistical significance and practical relevance.

Statistical significance can be evaluated by performing hypothesis tests for each coefficient. If a coefficient is statistically significant, it means that it has a significant impact on the dependent variable (stock price). On the other hand, if a coefficient is not statistically significant, it suggests that it may not be necessary to include that variable in the model.

Practical relevance, on the other hand, requires considering the knowledge of corporate finance. For example, if X1 and X2 are known to be important factors in determining stock prices, it would make sense to include them in the model. Additionally, if the interaction term X1X2 captures a meaningful relationship between X1 and X2, it should also be included.

By analyzing the estimated coefficients, p-values, and considering the knowledge of corporate finance, we can determine which explanatory variables should be included in the final regression model.