aianjie

 

2、A variable is regressed against three other variables, x, y, and z. Which of the following would NOT be an indication of multicollinearity? X is closely related to:

A) 3y + 2z.

B) 3.

C) y2.

D) 9y, and x is closely related to 4z.

aianjie

 

The correct answer is C

If x is related to y2, the relationship between x and y is not linear, so multicollinearity does not exist. If x is equal to a constant (3), it will be correlated with the intercept term.

aianjie

 

3、An analyst runs a regression of portfolio returns on three independent variables.  These independent variables are price-to-sales (P/S), price-to-cash flow (P/CF), and price-to-book (P/B).  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) multicollinearity.

D) unconditional heteroskedasticity.

aianjie

 

The correct answer is C

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.

aianjie

 

4、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)    Age should be excluded from the regression.

B)    Education may be unnecessary.

C)   Income is not needed.

D)   Experience may be a redundant variable.

aianjie

 

The correct answer is D

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.

aianjie

 

AIM 6: Define, calculate and interpret the variance and standard errors in a multilinear regression.

In the multivariable regression model: Y = B0 + B1 × Xli + B2 × X2i + εi, the formula for the standard errors of the estimated coefficients includes the variance of εi, which is represented by: σ2. Since the term is:

A) not known with certainty, the expression σ2 is replaced with: .

B) not known with certainty, the standard errors of the coefficients cannot be estimated.

C) not known with certainty, the expression σ2 is replaced with: .

D) known with certainty, the standard errors of the coefficients are known with certainty.

aianjie

 

The correct answer is C

The expression:  is an estimate of σ2 when there are two independent variables and n-3 degrees of freedom.

aianjie

 

AIM 8: Interpret regression results.

1、Consider the following analysis of variance (ANOVA) table:

Source	Sum of squares	Degrees of freedom	Mean square
Regression	556	1	556
Error	679	50	13.5
Total	1,235	51

The R² for this regression is:

A)    0.82.

B)    0.55.

C)   0.67.

D)   0.45.

aianjie

 

The correct answer is D

R2 = RSS/SST = 556/1,235 = 0.45.