aianjie

 

2、A regression equation with 4 independent variables is estimated using 20 data points. The R2 is 0.46. An analyst is testing to see whether all of the coefficients are equal to zero. The p-value for the test is:

A) lower than 0.025.

B) between 0.05 and 0.10.

C) greater than 0.10.

D) between 0.025 and 0.05.

aianjie

 

The correct answer is D

To solve this problem, one can assume any value for the total sum of squares. In this case, assume its 1. The regression sum of squares is R2 multiplied by the total sum of squares, which is 0.46. The residual sum of squares is the difference between the total sum of squares and the regression sum of squares, which is 1 ? 0.46 = 0.54. The numerator degrees of freedom is equal to the number of independent variables, which is 4, and the mean regression sum of squares is the regression sum of squares divided by the numerator degrees of freedom, which is 0.46 / 4 = 0.115. The denominator degrees of freedom is the number of observations minus the number of independent variables, minus 1, which is 20 ? 4 ? 1 = 15. The mean squared error is the residual sum of squares divided by the denominator degrees of freedom, which is 0.54 / 15 = 0.036. The F-statistic is the ratio of the mean regression sum of squares to the mean squared error, which is 0.115 / 0.036 = 3.19, which is in between the F-values (with four numerator degrees of freedom and 15 denominator degrees of freedom) of 3.06 for a p-value of 0.05 (calculated using the F-table at 5%) and 3.80 for a p-value of 0.025 (calculated using the F-table at 2.5%).

aianjie

 

3、A dependent variable is regressed against a single independent variable across 100 observations. The mean squared error is 2.807, and the mean regression sum of squares is 117.9. What is the correlation coefficient between the two variables?

A) 0.55.

B) 0.30.

C) 0.99.

D) 0.65.

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.

 

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.