12: Multiple Regression and Issues in Regression Ana follow

土豆妮

Session 3: Quantitative Methods: Quantitative
Methods for Valuation
Reading 12: Multiple Regression and Issues in Regression Analysis

LOS e, (Part 2): Define, distinguish between, and interpret the R² and adjusted R² in multiple regression.

 

 

 

Which of the following statements regarding the R² is FALSE?

A) The adjusted-R2 not appropriate to use in simple regression.

B) The adjusted-R2 is greater than the R2 in multiple regression.

C) It is possible for the adjusted-R2 to decline as more variables are added to the multiple regression.

luqian55

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maxsimax

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土豆妮

An analyst is estimating a regression equation with three independent variables, and calculates the R², the adjusted R², and the F-statistic. The analyst then decides to add a fourth variable to the equation. Which of the following is most accurate?

A) The R2 and F-statistic will be higher, but the adjusted R2 could be higher or lower.

B) The adjusted R2 will be higher, but the R2 and F-statistic could be higher or lower.

C) The R2 will be higher, but the adjusted R2 and F-statistic could be higher or lower.

土豆妮

An analyst is estimating a regression equation with three independent variables, and calculates the R², the adjusted R², and the F-statistic. The analyst then decides to add a fourth variable to the equation. Which of the following is most accurate?

A) The R2 and F-statistic will be higher, but the adjusted R2 could be higher or lower.

B) The adjusted R2 will be higher, but the R2 and F-statistic could be higher or lower.

C) The R2 will be higher, but the adjusted R2 and F-statistic could be higher or lower.

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The R² will always increase as the number of variables increase. The adjusted R² specifically adjusts for the number of variables, and might not increase as the number of variables rise. As the number of variables increases, the regression sum of squares will rise and the residual T sum of squares will fall—this will tend to make the F-statistic larger. However, the number degrees of freedom will also rise, and the denominator degrees of freedom will fall, which will tend to make the F-statistic smaller. Consequently, like the adjusted R², the F-statistic could be higher or lower.

土豆妮

An analyst regresses the return of a S& 500 index fund against the S& 500, and also regresses the return of an active manager against the S& 500. The analyst uses the last five years of data in both regressions. Without making any other assumptions, which of the following is TRUE? The index fund:

A) should have a higher coefficient on the independent variable.

B) regression should have higher sum of squares regression as a ratio to the total sum of squares.

C) should have a lower coefficient of determination.

土豆妮

An analyst regresses the return of a S& 500 index fund against the S& 500, and also regresses the return of an active manager against the S& 500. The analyst uses the last five years of data in both regressions. Without making any other assumptions, which of the following is TRUE? The index fund:

A) should have a higher coefficient on the independent variable.

B) regression should have higher sum of squares regression as a ratio to the total sum of squares.

C) should have a lower coefficient of determination.

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The index fund regression should provide a higher R², which is the sum of squares regression divided by the total sum of squares.

土豆妮

Which of the following statements regarding the R² is FALSE?

A) The adjusted-R2 not appropriate to use in simple regression.

B) The adjusted-R2 is greater than the R2 in multiple regression.

C) It is possible for the adjusted-R2 to decline as more variables are added to the multiple regression.

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The adjusted-R² will always be less than R²in multiple regression.

土豆妮

Which of the following statements regarding the R² is FALSE?

A) The R2 is the ratio of the unexplained variation to the explained variation of the dependent variable.

B) The R2 of a regression will be greater than or equal to the adjusted-R2 for the same regression.

C) The F-statistic for the test of the fit of the model is the ratio of the mean squared regression to the mean squared error.

土豆妮

Which of the following statements regarding the R² is FALSE?

A) The R2 is the ratio of the unexplained variation to the explained variation of the dependent variable.

B) The R2 of a regression will be greater than or equal to the adjusted-R2 for the same regression.

C) The F-statistic for the test of the fit of the model is the ratio of the mean squared regression to the mean squared error.

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The R² is the ratio of the explained variation to the total variation.