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 A

The correlation coefficient is the square root of the R2, which can be found by dividing the regression sum of squares by the total sum of squares. The regression sum of squares is the mean regression sum of squares multiplied by the number of independent variables, which is 1, so the regression sum of squares is equal to 117.9. The residual sum of squares is the mean squared error multiplied by the denominator degrees of freedom, which is the number of observations minus the number of independent variables, minus 1, which is equal to 100 ? 1 ? 1 = 98. The residual sum of squares is then 2.807 × 98 = 275.1. The total sum of squares is the sum of the regression sum of squares and the residual sum of squares, which is 117.9 + 275.1 = 393.0. The R2 = 117.9 / 393.0 = 0.3, so the correlation is the square root of 0.3 = 0.55.

aianjie

 

4、Erica Basenj, CFA, has been given an assignment by her boss. She has been requested to review the following regression output to answer questions about the relationship between the monthly returns of the Toffee Investment Management (TIM) High Yield Bond Fund and the returns of the index (independent variable).

Regression Statistics	< >>	< >>	< >>	< >>	< >>
R2	??	< >>	< >>	< >>	< >>
Standard Error	??	< >>	< >>	< >>	< >>
Observations	20	< >>	< >>	< >>	< >>
< >>	< >>	< >>	< >>	< >>	< >>
ANOVA	< >>	< >>	< >>	< >>	< >>
< >>	df	SS	MS	F	Significance F
Regression	1	23,516	23,516	?	?
Residual	18	?	7	< >>	< >>
Total	19	23,644	< >>	< >>	< >>
< >>	< >>	< >>	< >>	< >>	< >>
Regression Equation	< >>	< >>	< >>	< >>	< >>
< >>	< >>	Coefficients	Std. Error	t-statistic	P-value
Intercept	< >>	5.2900	1.6150	?	?
Slope	< >>	0.8700	0.0152	?	?

What is the value of the correlation coefficient?

A)    ?0.9973.

B)    0.8700.

C)   0.9973.

D)   ?0.8700.

aianjie

 

The correct answer is C

R2 is the correlation coefficient squared, taking into account whether the relationship is positive or negative. Since the value of the slope is positive, the TIM fund and the index are positively related. R2 is calculated by taking the (RSS / SST) = 0.99459. (0.99459)1/2 = 0.9973.

aianjie

 

What is the sum of squared errors (SSE)?

A) 23,515.

B) 23,644.

C) 3,283.

D) 128.

aianjie

 

The correct answer is D

SSE = SST ? RSS = 23,644 ? 23,516 = 128

What is the value of R2?

A) 0.0055.

B) 5.2900.

C) 0.9946. 

D) 0.9471.

aianjie

 

The correct answer is D

SSE = SST ? RSS = 23,644 ? 23,516 = 128

aianjie

 

What is the value of R2?

A) 0.0055.

B) 5.2900.

C) 0.9946. 

D) 0.9471.