Reading 12- LOS h: Q1-5 style, black, class

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1．An analyst further studies the independent variables of a study she recently completed. The correlation matrix shown below is the result. Which statement best reflects possible problems with a multivariate regression?

	Age	Education	Experience	Income
Age	1.00
Education	0.50	1.00
Experience	0.95	0.55	1.00
Income	0.60	0.65	0.89	1.00

A)    Experience may be a redundant variable.
B)    Age should be excluded from the regression.
C)    Education may be unnecessary.
D)    Income is not needed.

2．An analyst runs a regression of portfolio returns on three independent variables.  These independent variables are Price to Sales, Price to Cash Flow, and Price to Book.  The analyst discovers that the p-values for each independent variable are relatively high.  However, the F-test has a very small p-value.  The analyst is puzzled and tries to figure out how the F-test can be statistically significant when the individual independent variables are not significant.  What violation of regression analysis has occurred? 
A)    serial correlation.
B)    conditional heteroskedasticity.
C)    unconditional heteroskedasticity.
D)    multicollinearity.

3．Which of the following statements regarding multicollinearity is FALSE?
A)    Multicollinearity may be a problem even if the Multicollinearity is not perfect.
B)    Multicollinearity makes it difficult to determine the contribution to explanation of the dependent variable of an individual explanatory variable.
C)    Multicollinearity may be present in any regression model.
D)    If the t-statistics for the individual independent variables are insignificant, yet he F-statistic is significant, this indicates the presence of Multicollinearity.

4．Which of the following is a potential remedy for multicollinearity?
A)    Take first differences of the dependent variable.
B)    Omit one or more of the collinear variables.
C)    Increase the sample size.
D)    Add dummy variables to the regression.

spaceedu

1．An analyst further studies the independent variables of a study she recently completed. The correlation matrix shown below is the result. Which statement best reflects possible problems with a multivariate regression?

	Age	Education	Experience	Income
Age	1.00
Education	0.50	1.00
Experience	0.95	0.55	1.00
Income	0.60	0.65	0.89	1.00

A)    Experience may be a redundant variable.
B)    Age should be excluded from the regression.
C)    Education may be unnecessary.
D)    Income is not needed.
The correct answer was A)
The correlation coefficient of experience with age and income, respectively, is close to +1.00. This indicates a problem of multicollinearity and should be addressed by excluding experience as an independent variable.

2．An analyst runs a regression of portfolio returns on three independent variables.  These independent variables are Price to Sales, Price to Cash Flow, and Price to Book.  The analyst discovers that the p-values for each independent variable are relatively high.  However, the F-test has a very small p-value.  The analyst is puzzled and tries to figure out how the F-test can be statistically significant when the individual independent variables are not significant.  What violation of regression analysis has occurred? 
A)    serial correlation.
B)    conditional heteroskedasticity.
C)    unconditional heteroskedasticity.
D)    multicollinearity.
The correct answer was D)
An indication of multicollinearity is when the independent variables individually are not statistically significant but the F-test suggests that the variables as a whole do an excellent job of explaining the variation in the dependent variable.

3．Which of the following statements regarding multicollinearity is FALSE?
A)    Multicollinearity may be a problem even if the Multicollinearity is not perfect.
B)    Multicollinearity makes it difficult to determine the contribution to explanation of the dependent variable of an individual explanatory variable.
C)    Multicollinearity may be present in any regression model.
D)    If the t-statistics for the individual independent variables are insignificant, yet he F-statistic is significant, this indicates the presence of Multicollinearity.
The correct answer was C)
Multicollinearity is not an issue in simple regression.

4．Which of the following is a potential remedy for multicollinearity?
A)    Take first differences of the dependent variable.
B)    Omit one or more of the collinear variables.
C)    Increase the sample size.
D)    Add dummy variables to the regression.
The correct answer was B)
The first differencing is not a remedy for the collinearity, nor is the inclusion of dummy variables. Increasing the sample size may improve the t-statistics associated with the estimates, but does is not a remedy to the problem. The best potential remedy is to attempt to eliminate highly correlated variables.