Question 1

Exhibit 13-6
Below you are given a partial Excel output based on a sample of 16 observations.
 
-Refer to Exhibit 13-6. The degrees of freedom for the sum of squares explained by the regression (SSR) are
A)2
B)3
C)13
D)15

Accepted Answer

The answer of Exhibit 13-6
Below you are given a partial...

Question 2

Exhibit 13-6 Below you are given a partial Excel output based on a sample of 16 observations. -Refer to Exhibit 13-6. We want to test whether the parameter $\beta$₁ is significant. The test statistic equals A)-1.4 B)1.4 C)3.6 D)5

Accepted Answer

The answer of Exhibit 13-6
Below you are given a partial...

Question 3

Exhibit 13-7
A regression model involving 4 independent variables and a sample of 15 periods resulted in the following sum of squares.
SSR = 165
SSE = 60
-Refer to Exhibit 13-7. The test statistic from the information provided is
A)2.110
B)3.480
C)4.710
D)6.875

Accepted Answer

The answer of Exhibit 13-7
A regression model involving 4 independent...

Question 4

Exhibit 13-5
Below you are given a partial Excel output based on a sample of 25 observations.
 
-Refer to Exhibit 13-5. The t value obtained from the table to test an individual parameter at the 5% level is
A)2.06
B)2.069
C)2.074
D)2.080

Accepted Answer

The answer of Exhibit 13-5
Below you are given a partial...

Question 5

Exhibit 13-8
The following estimated regression model was developed relating yearly income (y in $1,000s) of 30 individuals with their age (xS1U1B11S1U1B0) and their gender (xS1U1B12S1U1B0) (0 if male and 1 if female).  = 30 + 0.7xS1U1B11S1U1B0 + 3xS1U1B12S1U1B0
Also provided are SST = 1,200 and SSE = 384.
-Refer to Exhibit 13-8. From the above function, it can be said that the expected yearly income of
A)males is $3 more than females
B)females is $3 more than males
C)males is $3,000 more than females
D)females is $3,000 more than males

Accepted Answer

The answer of Exhibit 13-8
The following estimated regression model was...

Question 6

Exhibit 13-6
Below you are given a partial Excel output based on a sample of 16 observations.
 
-Refer to Exhibit 13-6. Carry out the test to determine if there is a relationship among the variables at the 5% level. The null hypothesis should
A)be rejected
B)not be rejected
C)revised
D)None of these alternatives is correct.

Accepted Answer

The output shows a p-value of 0.000181, which is less than 0.05 (the significance level), indicating strong evidence against the null hypothesis of no relationship among the variables. Therefore, the null hypothesis should be rejected.

Question 7

Exhibit 13-6 Below you are given a partial Excel output based on a sample of 16 observations. -Refer to Exhibit 13-6. The interpretation of the coefficient of x₁ is that A)a one unit change in x₁ will lead to a 3.682 unit decrease in y B)a one unit increase in x₁ will lead to a 3.682 unit decrease in y when all other variables are held constant C)a one unit increase in x₁ will lead to a 3.682 unit decrease in x₂ when all other variables are held constant D)It is impossible to interpret the coefficient.

Accepted Answer

The answer of Exhibit 13-6
Below you are given a partial...

Question 8

Exhibit 13-7
A regression model involving 4 independent variables and a sample of 15 periods resulted in the following sum of squares.
SSR = 165
SSE = 60
-Refer to Exhibit 13-7. The coefficient of determination is
A)0.3636
B)0.7333
C)0.275
D)0.5

Accepted Answer

The coefficient of determination, R-squared, is the proportion of the total variation in the dependent variable explained by the independent variables. It ranges from 0 to 1.

R-squared = SSR / (SSR + SSE)
R-squared = 165 / (165 + 60)
R-squared = 0.7333

Therefore, the coefficient of determination is 0.7333 or approximately 0.73. Choice B is the correct answer.

Question 9

Exhibit 13-6
Below you are given a partial Excel output based on a sample of 16 observations.
 
-Refer to Exhibit 13-6. The test statistic used to determine if there is a relationship among the variables equals
A)-1.4
B)0.2
C)0.77
D)5

Accepted Answer

The answer of Exhibit 13-6
Below you are given a partial...

Question 10

Exhibit 13-8
The following estimated regression model was developed relating yearly income (y in $1,000s) of 30 individuals with their age (xS1U1B11S1U1B0) and their gender (xS1U1B12S1U1B0) (0 if male and 1 if female).  = 30 + 0.7xS1U1B11S1U1B0 + 3xS1U1B12S1U1B0
Also provided are SST = 1,200 and SSE = 384.
-Refer to Exhibit 13-8. The yearly income of a 24-year-old male individual is
A)$13.80
B)$13,800
C)$46,800
D)$49,800

Accepted Answer

The answer of Exhibit 13-8
The following estimated regression model was...

Question 11

Exhibit 13-6
Below you are given a partial Excel output based on a sample of 16 observations.
 
-Refer to Exhibit 13-6. The sum of squares due to error (SSE) equals
A)37.33
B)485.3
C)4,853
D)6,308.9

Accepted Answer

The answer of Exhibit 13-6
Below you are given a partial...

Question 12

Exhibit 13-5 Below you are given a partial Excel output based on a sample of 25 observations. -Refer to Exhibit 13-5. Carry out the test of significance for the parameter $\beta$₁ at the 5% level. The null hypothesis should be A)rejected B)not rejected C)revised D)None of these alternatives is correct.

Accepted Answer

The p-value for the test is 0.049, which is less than the 5% level of significance. Therefore, we reject the null hypothesis and conclude that there is evidence to suggest that the parameter F1S1β has a significant effect on the dependent variable.

Question 13

Exhibit 13-6
Below you are given a partial Excel output based on a sample of 16 observations.
 
-Refer to Exhibit 13-6. The F value obtained from the table used to test if there is a relationship among the variables at the 5% level equals
A)3.41
B)3.63
C)3.81
D)19.41

Accepted Answer

The answer of Exhibit 13-6
Below you are given a partial...

Question 14

Exhibit 13-5 Below you are given a partial Excel output based on a sample of 25 observations. -Refer to Exhibit 13-5. We want to test whether the parameter $\beta$₁ is significant. The test statistic equals A)0.357 B)2.8 C)14 D)1.96

Accepted Answer

The answer of Exhibit 13-5
Below you are given a partial...

Question 15

Exhibit 13-7
A regression model involving 4 independent variables and a sample of 15 periods resulted in the following sum of squares.
SSR = 165
SSE = 60
-Refer to Exhibit 13-7. If we want to test for the significance of the model at 95% confidence, the critical F value (from the table) is
A)3.06
B)3.48
C)3.34
D)3.11

Accepted Answer

The answer of Exhibit 13-7
A regression model involving 4 independent...

Question 16

Exhibit 13-6 Below you are given a partial Excel output based on a sample of 16 observations. -Refer to Exhibit 13-6. The estimated regression equation is A)y = $\beta$₀ + $\beta$₁x₁ + $\beta$₂x₂ + $\varepsilon$ B)E(y) = $\beta$₀ + $\beta$₁x₁ + $\beta$₂x₂ C)= 12.924 - 3.682 x₁ + 45.216 x₂ D)= 4.425 + 2.63 x₁ + 12.56 x₂

Accepted Answer

The estimated regression equation is in the form of y = a + bx, where a is the intercept, b is the slope, and x is the independent variable. Option C provides the equation in this format with the estimated coefficients for the intercept and the two independent variables ₁ and ₂. Option A includes the error term and option B gives only the expected value of y without the estimated coefficients. Option D provides a different equation with different coefficients.

Question 17

Exhibit 13-5 Below you are given a partial Excel output based on a sample of 25 observations. -Refer to Exhibit 13-5. The interpretation of the coefficient on x₁ is that A)a one unit change in x₁ will lead to a 25.625 unit change in y B)a one unit change in x₁ will lead to a 25.625 unit increase in y when all other variables are held constant C)a one unit change in x₁ will lead to a 25.625 unit increase in x₂ when all other variables are held constant D)It is impossible to interpret the coefficient.

Accepted Answer

The coefficient on x₁ represents the expected change in y for a one unit increase in that variable, holding all other variables constant. Therefore, the interpretation is that a one unit change in x₁ will lead to a 25.625 unit increase in y when all other variables are held constant.

Question 18

Exhibit 13-6 Below you are given a partial Excel output based on a sample of 16 observations. -Refer to Exhibit 13-6. Carry out the test of significance for the parameter $\beta$₁ at the 1% level. The null hypothesis should be A)rejected B)not rejected C)revised D)None of these alternatives is correct.

Accepted Answer

The p-value for the test is 0.0848 which is greater than the significance level of 0.01. Therefore, we do not have enough evidence to reject the null hypothesis at the 1% level of significance.

Question 19

Exhibit 13-8
The following estimated regression model was developed relating yearly income (y in $1,000s) of 30 individuals with their age (xS1U1B11S1U1B0) and their gender (xS1U1B12S1U1B0) (0 if male and 1 if female).  = 30 + 0.7xS1U1B11S1U1B0 + 3xS1U1B12S1U1B0
Also provided are SST = 1,200 and SSE = 384.
-Refer to Exhibit 13-8. The yearly income of a 24-year-old female individual is
A)$19.80
B)$19,800
C)$49.80
D)$49,800

Accepted Answer

Plug in the values for a 24-year-old female:
y = 30 + 0.7(24) + 3(1)
y = 30 + 16.8 + 3
y = $49.80 (in thousands)
Therefore, the yearly income of a 24-year-old female individual is $49,800. Choice D is the correct answer.

Question 20

Exhibit 13-6
Below you are given a partial Excel output based on a sample of 16 observations.
 
-Refer to Exhibit 13-6. The t value obtained from the table which is used to test an individual parameter at the 1% level is
A)2.65
B)2.921
C)2.977
D)3.012

Accepted Answer

The answer of Exhibit 13-6
Below you are given a partial...

Quiz 13: Multiple Regression

Exhibit 13-6 Below you are given a partial Excel output based on a sample of 16 observations. -Refer to Exhibit 13-6. The degrees of freedom for the sum of squares explained by the regression (SSR) are

Exhibit 13-6 Below you are given a partial Excel output based on a sample of 16 observations. -Refer to Exhibit 13-6. We want to test whether the parameter β\betaβ 1 is significant. The test statistic equals

Exhibit 13-7 A regression model involving 4 independent variables and a sample of 15 periods resulted in the following sum of squares. SSR = 165 SSE = 60 -Refer to Exhibit 13-7. The test statistic from the information provided is

Exhibit 13-5 Below you are given a partial Excel output based on a sample of 25 observations. -Refer to Exhibit 13-5. The t value obtained from the table to test an individual parameter at the 5% level is

Exhibit 13-6 Below you are given a partial Excel output based on a sample of 16 observations. -Refer to Exhibit 13-6. Carry out the test to determine if there is a relationship among the variables at the 5% level. The null hypothesis should

Exhibit 13-6 Below you are given a partial Excel output based on a sample of 16 observations. -Refer to Exhibit 13-6. The interpretation of the coefficient of x1 is that

Exhibit 13-7 A regression model involving 4 independent variables and a sample of 15 periods resulted in the following sum of squares. SSR = 165 SSE = 60 -Refer to Exhibit 13-7. The coefficient of determination is

Exhibit 13-6 Below you are given a partial Excel output based on a sample of 16 observations. -Refer to Exhibit 13-6. The test statistic used to determine if there is a relationship among the variables equals

Exhibit 13-6 Below you are given a partial Excel output based on a sample of 16 observations. -Refer to Exhibit 13-6. The sum of squares due to error (SSE) equals

Exhibit 13-5 Below you are given a partial Excel output based on a sample of 25 observations. -Refer to Exhibit 13-5. Carry out the test of significance for the parameter β\betaβ 1 at the 5% level. The null hypothesis should be

Exhibit 13-6 Below you are given a partial Excel output based on a sample of 16 observations. -Refer to Exhibit 13-6. The F value obtained from the table used to test if there is a relationship among the variables at the 5% level equals

Exhibit 13-5 Below you are given a partial Excel output based on a sample of 25 observations. -Refer to Exhibit 13-5. We want to test whether the parameter β\betaβ 1 is significant. The test statistic equals

Exhibit 13-7 A regression model involving 4 independent variables and a sample of 15 periods resulted in the following sum of squares. SSR = 165 SSE = 60 -Refer to Exhibit 13-7. If we want to test for the significance of the model at 95% confidence, the critical F value (from the table) is

Exhibit 13-6 Below you are given a partial Excel output based on a sample of 16 observations. -Refer to Exhibit 13-6. The estimated regression equation is

Exhibit 13-5 Below you are given a partial Excel output based on a sample of 25 observations. -Refer to Exhibit 13-5. The interpretation of the coefficient on x1 is that

Exhibit 13-6 Below you are given a partial Excel output based on a sample of 16 observations. -Refer to Exhibit 13-6. Carry out the test of significance for the parameter β\betaβ 1 at the 1% level. The null hypothesis should be

Exhibit 13-6 Below you are given a partial Excel output based on a sample of 16 observations. -Refer to Exhibit 13-6. The t value obtained from the table which is used to test an individual parameter at the 1% level is

Exhibit 13-6 Below you are given a partial Excel output based on a sample of 16 observations. -Refer to Exhibit 13-6. The interpretation of the coefficient of x₁ is that

Exhibit 13-5 Below you are given a partial Excel output based on a sample of 25 observations. -Refer to Exhibit 13-5. The interpretation of the coefficient on x₁ is that