Question 1

Exhibit 15-6 Below you are given a partial Excel output based on a sample of 16 observations. -Refer to Exhibit 15-6. 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 15-6
Below you are given a partial...

Question 2

Exhibit 15-6
Below you are given a partial Excel output based on a sample of 16 observations. 
-Refer to Exhibit 15-6. 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 15-6
Below you are given a partial...

Question 3

Exhibit 15-6 Below you are given a partial Excel output based on a sample of 16 observations. -Refer to Exhibit 15-6. 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 represented by the formula y = a + bx, where a is the intercept and b is the slope. In choice C, the estimated regression equation is given with the values of a, b1, and b2. Therefore, C is the best choice. Choices A and B are not in the correct format of a regression equation. Choice D has the incorrect values for the intercept and slope.

Question 4

Exhibit 15-4
a.y = $\beta$S1U1B10S1U1B0 + $\beta$S1U1B11S1U1B0xS1U1B11S1U1B0 + $\beta$S1U1B12S1U1B0xS1U1B12S1U1B0 + $\varepsilon$
b.E(y) = $\beta$S1U1B10S1U1B0 + $\beta$S1U1B11S1U1B0xS1U1B11S1U1B0 + $\beta$S1U1B12S1U1B0xS1U1B12S1U1B0
c.= bS1U1B1oS1U1B0 + bS1U1B11S1U1B0 xS1U1B11S1U1B0 + bS1U1B12S1U1B0 xS1U1B12S1U1B0
d.E(y) = $\beta$S1U1B10S1U1B0 + $\beta$S1U1B11S1U1B0xS1U1B11S1U1B0 + $\beta$S1U1B12S1U1B0xS1U1B12S1U1B0
-Refer to Exhibit 15-4. Which equation describes the multiple regression model?
A)equation a
B)equation b
C)equation c
D)equation d

Accepted Answer

The multiple regression model is described by equation a because it includes all of the independent variables (S1U1B10, S1U1B11, and S1U1B12) and the error term ($\varepsilon$).

Question 5

Exhibit 15-4
a.y = $\beta$S1U1B10S1U1B0 + $\beta$S1U1B11S1U1B0xS1U1B11S1U1B0 + $\beta$S1U1B12S1U1B0xS1U1B12S1U1B0 + $\varepsilon$
b.E(y) = $\beta$S1U1B10S1U1B0 + $\beta$S1U1B11S1U1B0xS1U1B11S1U1B0 + $\beta$S1U1B12S1U1B0xS1U1B12S1U1B0
c.= bS1U1B1oS1U1B0 + bS1U1B11S1U1B0 xS1U1B11S1U1B0 + bS1U1B12S1U1B0 xS1U1B12S1U1B0
d.E(y) = $\beta$S1U1B10S1U1B0 + $\beta$S1U1B11S1U1B0xS1U1B11S1U1B0 + $\beta$S1U1B12S1U1B0xS1U1B12S1U1B0
-Refer to Exhibit 15-4. Which equation gives the estimated regression line?
A)equation a
B)equation b
C)equation c
D)equation d

Accepted Answer

Equation c represents the estimated regression line, as it uses lowercase 'b' to denote estimated coefficients, which are typically used in regression analysis to represent the estimated values of the parameters.

Question 6

Exhibit 15-6
Below you are given a partial Excel output based on a sample of 16 observations. 
-A term used to describe the case when the independent variables in a multiple regression model are correlated is
A)regression
B)correlation
C)multicollinearity
D)None of the alternative answers are correct.

Accepted Answer

Multicollinearity is the term used to describe the situation when independent variables in a multiple regression model are correlated. This can lead to unreliable and unstable estimates of the regression coefficients.

Question 7

Exhibit 15-5 Below you are given a partial Excel output based on a sample of 25 observations. -Refer to Exhibit 15-5. 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 test statistic for testing the significance of a parameter is typically calculated as the estimated coefficient divided by its standard error. The value 2.8 is likely the result of this calculation, indicating the significance of $\beta$₁.

Question 8

Exhibit 15-6
Below you are given a partial Excel output based on a sample of 16 observations. 
-Refer to Exhibit 15-6. 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 15-6
Below you are given a partial...

Question 9

Exhibit 15-5 Below you are given a partial Excel output based on a sample of 25 observations. -Refer to Exhibit 15-5. 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 F1S1β is 0.016, which is less than the significance level of 0.05. Therefore, we reject the null hypothesis that the coefficient for F1S1β is equal to zero at the 5% level of significance.

Question 10

Exhibit 15-4
a.y = $\beta$S1U1B10S1U1B0 + $\beta$S1U1B11S1U1B0xS1U1B11S1U1B0 + $\beta$S1U1B12S1U1B0xS1U1B12S1U1B0 + $\varepsilon$
b.E(y) = $\beta$S1U1B10S1U1B0 + $\beta$S1U1B11S1U1B0xS1U1B11S1U1B0 + $\beta$S1U1B12S1U1B0xS1U1B12S1U1B0
c.= bS1U1B1oS1U1B0 + bS1U1B11S1U1B0 xS1U1B11S1U1B0 + bS1U1B12S1U1B0 xS1U1B12S1U1B0
d.E(y) = $\beta$S1U1B10S1U1B0 + $\beta$S1U1B11S1U1B0xS1U1B11S1U1B0 + $\beta$S1U1B12S1U1B0xS1U1B12S1U1B0
-Refer to Exhibit 15-4. Which equation describes the multiple regression equation?
A)equation a
B)equation b
C)equation c
D)equation d

Accepted Answer

The multiple regression equation is given by equation d, which includes the intercept and the coefficients for each of the independent variables.

Question 11

Exhibit 15-5 Below you are given a partial Excel output based on a sample of 25 observations. -Refer to Exhibit 15-5. 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 change in y for every one unit change in x₁ when all other variables are held constant. Therefore, the interpretation of the coefficient is "a one unit change in x₁ will lead to a 25.625 unit increase in y when all other variables are held constant."

Question 12

Exhibit 15-5 Below you are given a partial Excel output based on a sample of 25 observations. -Refer to Exhibit 15-5. The estimated regression equation is A)y = $\beta$₀ + $\beta$₁x₁ + $\beta$₂x₂ + $\beta$₃x₃ + $\varepsilon$ B)E(y) = $\beta$₀ + $\beta$₁x₁ + $\beta$₂x₂ + $\beta$₃x₃ C)= 145.321 + 25.625x₁ - 5.720x₂ + 0.823x₃ D)= 48.682 + 9.15x₁ + 3.575x₂ + 0.183x₃

Accepted Answer

The answer of Exhibit 15-5
Below you are given a partial...

Question 13

Exhibit 15-6
Below you are given a partial Excel output based on a sample of 16 observations. 
-Refer to Exhibit 15-6. 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 p-value (0.0005) is less than the significance level (0.05), indicating that we reject the null hypothesis and conclude there is a relationship among the variables.

Question 14

Exhibit 15-6
Below you are given a partial Excel output based on a sample of 16 observations. 
-Refer to Exhibit 15-6. 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 15-6
Below you are given a partial...

Question 15

Exhibit 15-6 Below you are given a partial Excel output based on a sample of 16 observations. -Refer to Exhibit 15-6. 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 answer of Exhibit 15-6
Below you are given a partial...

Question 16

Exhibit 15-6
Below you are given a partial Excel output based on a sample of 16 observations. 
-Refer to Exhibit 15-6. 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 test statistic used to determine if there is a relationship among the variables is given by the F-statistic, which in this case is 5.

Question 17

Exhibit 15-5
Below you are given a partial Excel output based on a sample of 25 observations. 
-Refer to Exhibit 15-5. 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 15-5
Below you are given a partial...

Question 18

Exhibit 15-6
Below you are given a partial Excel output based on a sample of 16 observations. 
-A regression model in which more than one independent variable is used to predict the dependent variable is called
A)a simple linear regression model
B)a multiple regression model
C)an independent model
D)None of these alternatives is correct.

Accepted Answer

A multiple regression model is used when more than one independent variable is used to predict the dependent variable, as opposed to a simple linear regression model which only uses one independent variable. An independent model does not exist in regression analysis.

Question 19

Exhibit 15-6 Below you are given a partial Excel output based on a sample of 16 observations. -Refer to Exhibit 15-6. 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 test statistic is calculated as $\frac{\hat{\beta}_1}{SE(\hat{\beta}_1)}$, which is equal to $\frac{-1}{0.714}$ = -1.4.

Question 20

Exhibit 15-6
Below you are given a partial Excel output based on a sample of 16 observations. 
-Refer to Exhibit 15-6. 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 15-6
Below you are given a partial...

Quiz 15: Multiple Regression

Exhibit 15-6 Below you are given a partial Excel output based on a sample of 16 observations. -Refer to Exhibit 15-6. The interpretation of the coefficient of x1 is that

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

Exhibit 15-6 Below you are given a partial Excel output based on a sample of 16 observations. -Refer to Exhibit 15-6. The estimated regression equation is

Exhibit 15-4 a.y = β\betaβ 0 + β\betaβ 1x1 + β\betaβ 2x2 + ε\varepsilonε b.E(y) = β\betaβ 0 + β\betaβ 1x1 + β\betaβ 2x2 c.= bo + b1 x1 + b2 x2 d.E(y) = β\betaβ 0 + β\betaβ 1x1 + β\betaβ 2x2 -Refer to Exhibit 15-4. Which equation describes the multiple regression model?

Exhibit 15-4 a.y = β\betaβ 0 + β\betaβ 1x1 + β\betaβ 2x2 + ε\varepsilonε b.E(y) = β\betaβ 0 + β\betaβ 1x1 + β\betaβ 2x2 c.= bo + b1 x1 + b2 x2 d.E(y) = β\betaβ 0 + β\betaβ 1x1 + β\betaβ 2x2 -Refer to Exhibit 15-4. Which equation gives the estimated regression line?

Exhibit 15-6 Below you are given a partial Excel output based on a sample of 16 observations. -A term used to describe the case when the independent variables in a multiple regression model are correlated is

Exhibit 15-5 Below you are given a partial Excel output based on a sample of 25 observations. -Refer to Exhibit 15-5. We want to test whether the parameter β\betaβ 1 is significant. The test statistic equals

Exhibit 15-6 Below you are given a partial Excel output based on a sample of 16 observations. -Refer to Exhibit 15-6. The t value obtained from the table which is used to test an individual parameter at the 1% level is

Exhibit 15-5 Below you are given a partial Excel output based on a sample of 25 observations. -Refer to Exhibit 15-5. Carry out the test of significance for the parameter β\betaβ 1 at the 5% level. The null hypothesis should be

Exhibit 15-4 a.y = β\betaβ 0 + β\betaβ 1x1 + β\betaβ 2x2 + ε\varepsilonε b.E(y) = β\betaβ 0 + β\betaβ 1x1 + β\betaβ 2x2 c.= bo + b1 x1 + b2 x2 d.E(y) = β\betaβ 0 + β\betaβ 1x1 + β\betaβ 2x2 -Refer to Exhibit 15-4. Which equation describes the multiple regression equation?

Exhibit 15-5 Below you are given a partial Excel output based on a sample of 25 observations. -Refer to Exhibit 15-5. The interpretation of the coefficient on x1 is that

Exhibit 15-5 Below you are given a partial Excel output based on a sample of 25 observations. -Refer to Exhibit 15-5. The estimated regression equation is

Exhibit 15-6 Below you are given a partial Excel output based on a sample of 16 observations. -Refer to Exhibit 15-6. Carry out the test to determine if there is a relationship among the variables at the 5% level. The null hypothesis should

Exhibit 15-6 Below you are given a partial Excel output based on a sample of 16 observations. -Refer to Exhibit 15-6. The sum of squares due to error (SSE) equals

Exhibit 15-6 Below you are given a partial Excel output based on a sample of 16 observations. -Refer to Exhibit 15-6. Carry out the test of significance for the parameter β\betaβ 1 at the 1% level. The null hypothesis should be

Exhibit 15-6 Below you are given a partial Excel output based on a sample of 16 observations. -Refer to Exhibit 15-6. The test statistic used to determine if there is a relationship among the variables equals

Exhibit 15-5 Below you are given a partial Excel output based on a sample of 25 observations. -Refer to Exhibit 15-5. The t value obtained from the table to test an individual parameter at the 5% level is

Exhibit 15-6 Below you are given a partial Excel output based on a sample of 16 observations. -A regression model in which more than one independent variable is used to predict the dependent variable is called

Exhibit 15-6 Below you are given a partial Excel output based on a sample of 16 observations. -Refer to Exhibit 15-6. We want to test whether the parameter β\betaβ 1 is significant. The test statistic equals

Exhibit 15-6 Below you are given a partial Excel output based on a sample of 16 observations. -Refer to Exhibit 15-6. The F value obtained from the table used to test if there is a relationship among the variables at the 5% level equals

Exhibit 15-6 Below you are given a partial Excel output based on a sample of 16 observations. -Refer to Exhibit 15-6. The interpretation of the coefficient of x₁ is that

Exhibit 15-5 Below you are given a partial Excel output based on a sample of 25 observations. -Refer to Exhibit 15-5. The interpretation of the coefficient on x₁ is that