Reading 12- LOS e (Part 2) : Q1- 4

1.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 lower coefficient of determination.

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

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

D)   should have a higher total sum of squares.

The correct answer was B)

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

2.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 necessarily TRUE?

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

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

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

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

The correct answer was B)

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.

3.Which of the following statements regarding the R² is FALSE?

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

B)   0 ≤ R² ≤ 1.0.

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

D)   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.

The correct answer was C)     

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

4.Which of the following statements regarding the R² is FALSE?

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

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

C)   Adding independent variables to the regression equation will increase the R².

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

The correct answer was A)

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