Question 1

Which of the following best describes the purpose of adding additional explanatory variables to a regression model for stock returns, beyond those suggested by the CAPM?

Accepted Answer

To improve the fit and predictive power of the model by including variables that explain additional variation

Question 2

Given the regression output for the initial model (Sony % Change vs. Market % Change), which variable is statistically significant at the 0.05 level?

Accepted Answer

Market % Change

Question 3

What does a high correlation (e.g., $$r = 0.91) $$between Market % Change and Dow % Change indicate in the context of multiple regression?

Accepted Answer

There is likely to be collinearity, which can inflate the variance of estimated coefficients

Question 4

Which of the following is a sign of collinearity in a multiple regression model?

Accepted Answer

Standard errors for partial slopes are larger than those for marginal slopes

Question 5

Suppose you have the following regression equation: $$Y = \$$beta_0$$ + \$$beta_1$$ X_1$ + \$$beta_2$$ X_2$ + \varepsilon. If$$ $$X_1$$ and $$X_2$$ are highly correlated, what is a likely consequence?

Accepted Answer

The variance inflation factor (VIF) for $$X_1$$ and $$X_2$$ will be high

Question 6

What is the formula for the Variance Inflation Factor (VIF) for an explanatory variable $$X_j$$?

Accepted Answer

$$VIF_j = \frac{1}{1 - R_j^2$}$$

Question 7

If the VIF for the variable High-Low is 1.25, what does this indicate?

Accepted Answer

Collinearity has little effect on High-Low

Question 8

In the multiple regression model with all four explanatory variables, which variable is statistically significant based on the t-statistics?

Accepted Answer

Small-Big

Question 9

Which of the following is NOT a recommended approach for dealing with collinearity?

Accepted Answer

Always remove all variables with low VIF

Question 10

A regression model for Sony stock returns includes Market % Change, Dow % Change, Small-Big, and High-Low. The F-statistic is highly significant, but only Small-Big is significant individually. What does this suggest?

Accepted Answer

The model explains significant variation, but some variables may be redundant due to collinearity

Question 11

If removing a non-significant explanatory variable from a regression model does not cause a significant drop in $$R^2$$, what is the best course of action?

Accepted Answer

Remove the variable unless it is of special interest and does not introduce collinearity

Question 12

Which of the following best describes the difference between marginal and partial slopes in multiple regression?

Accepted Answer

Marginal slopes are estimated without considering other variables, while partial slopes account for the presence of other variables

Question 13

A scatterplot matrix of the variables in a regression model shows linear associations between the response and each explanatory variable. What does this suggest?

Accepted Answer

Linear regression is an appropriate modeling choice

Question 14

Which of the following is a plausible reason for keeping a non-significant explanatory variable in a regression model?

Accepted Answer

The variable is of special interest and does not introduce substantial collinearity

Question 15

If the residual plot of a regression model shows residuals with similar variances and no pattern, what does this indicate?

Accepted Answer

The assumption of homoscedasticity is satisfied

Question 16

Which of the following is true about the F-statistic in multiple regression?

Accepted Answer

It tests whether at least one explanatory variable is significantly related to the response

Question 17

Suppose you are building a regression model for stock returns and find that adding a new variable increases the VIF for existing variables above 10. What should you consider doing?

Accepted Answer

Remove the new variable or combine correlated variables

Question 18

Which of the following best explains why the slope for Market % Change becomes less significant when other variables are added to the model?

Accepted Answer

Collinearity with other variables, especially Dow % Change, reduces the unique variation explained by Market % Change

Ch. 24 Building Regression Models: Identifying and Evaluating Explanatory Variables

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