Question 1

If the value of the Durbin-Watson statistic d is small (d < 2),this indicates a(n)____________________ (positive/negative)first-order autocorrelation exists.

Accepted Answer

The answer of If the value of the Durbin-Watson statistic...

Question 2

If the value of the Durbin-Watson test statistic,d,satisfies the inequality d > 4 −d_L,we conclude that positive first-order autocorrelation exists.

Accepted Answer

The Durbin-Watson test statistic ranges from 0 to 4, where a value around 2 suggests no autocorrelation, values significantly less than 2 suggest positive autocorrelation, and values significantly greater than 2 suggest negative autocorrelation. The condition described does not correctly determine positive first-order autocorrelation.

Question 3

If the Durbin-Watson statistic has a value close to 0,which assumption is violated?
A)Homoscedasticity.
B)Normality of the errors.
C)Independence of errors.
D)None of these choices.

Accepted Answer

The Durbin-Watson statistic tests for autocorrelation or dependence of errors. A value close to 0 indicates positive autocorrelation, which means that errors at one time point are correlated with errors at the next time point. This violates the assumption of independence of errors. Homoscedasticity and normality of the errors are not directly tested by the Durbin-Watson statistic.

Question 4

To use the Durbin-Watson test to test for negative first-order autocorrelation,the null hypothesis will be H₀: ____________________ (there is/there is no)first-order autocorrelation.

Accepted Answer

The answer of To use the Durbin-Watson test to test...

Question 5

Test the hypotheses H₀: no first-order autocorrelation vs.H₁: first-order autocorrelation,given that: Durbin-Watson Statistic d = 1.89,n = 28,k = 3,and α = 0.01.

Accepted Answer

The answer of Test the hypotheses H₀: no first-order autocorrelation...

Question 6

In testing the significance of a multiple regression model with three independent variables,the null hypothesis is  .

Accepted Answer

The null hypothesis in testing the significance of a multiple regression model with three independent variables is that all of the regression coefficients are equal to zero, indicating that the independent variables do not have a significant effect on the dependent variable. Therefore, the statement is true.

Question 7

If the Durbin-Watson statistic d has values smaller than 2,this indicates
A)a positive first-order autocorrelation
B)a negative first-order autocorrelation
C)no first-order autocorrelation at all
D)None of these choices.

Accepted Answer

The Durbin-Watson statistic measures the presence of autocorrelation in the residuals of a regression model. If the value of d is less than 2, it indicates the presence of positive first-order autocorrelation. If the value of d is greater than 2, it indicates the presence of negative first-order autocorrelation. If the value of d is close to 2, it indicates no first-order autocorrelation. Therefore, the best choice for this question is A, which corresponds to the presence of positive first-order autocorrelation.

Question 8

If the residuals in a regression analysis of time ordered data are not correlated,the value of the Durbin-Watson d statistic should be near ____________________.

Accepted Answer

The answer of If the residuals in a regression analysis...

Question 9

If the value of the Durbin-Watson statistic d is large (d > 2),this indicates a(n)____________________ (positive/negative)first-order autocorrelation exists.

Accepted Answer

The answer of If the value of the Durbin-Watson statistic...

Question 10

Test the hypotheses H₀: There is no first-order autocorrelation vs.H₁: There is positive first-order autocorrelation,given that: Durbin-Watson Statistic d = 1.12,n = 45,k = 5,and α = 0.05.

Accepted Answer

The answer of Test the hypotheses H₀: There is no...

Question 11

Given that the Durbin-Watson test is conducted to test for positive first-order autocorrelation with α = .05,n = 20,and there are two independent variables in the model,the critical values for the test are d_L = __________ and d_U = __________,respectively.

Accepted Answer

The answer of Given that the Durbin-Watson test is conducted...

Question 12

The following is the regression output for a regression of calories on fiber and sugars for 10 popular types of cereal.Fill in the missing information,indicated by the boldface lettersa to f (up to three decimal places).
​
​  Analysis of variance table for multiple regression model:  ​

Accepted Answer

The answer of The following is the regression output for...

Question 13

To use the Durbin-Watson test to test for positive first-order autocorrelation,the null hypothesis will be H₀: ____________________ (there is/there is no)first-order autocorrelation.

Accepted Answer

The answer of To use the Durbin-Watson test to test...

Question 14

The range of the values of the Durbin-Watson statistic d is:
A)−4 ≤d≤ 4
B)−2 ≤d≤ 2
C)0 ≤d≤ 2
D)0 ≤d≤ 4

Accepted Answer

The Durbin-Watson statistic d is a test statistic used to detect the presence of autocorrelation at lag 1 in the residuals from a regression analysis. Its range is from 0 to 4, where a value of 2 indicates no autocorrelation, values approaching 0 indicate positive autocorrelation, and values approaching 4 indicate negative autocorrelation.

Question 15

If the value of the Durbin-Watson test statistic,d,satisfies the inequalities d < d_L or d > 4 −d_L,where d_L and d_U are the critical values of d,we conclude that autocorrelation exists.

Accepted Answer

The statement is true. The Durbin-Watson test statistic measures the presence of autocorrelation in the residuals of a regression analysis. The critical values of the test statistic depend on the sample size and the number of independent variables in the regression model. If the calculated value of the test statistic falls below the lower critical value or above the upper critical value, we reject the null hypothesis of no autocorrelation and conclude that autocorrelation exists.

Question 16

The range of the values of the Durbin-Watson statistic d is ____________________.

Accepted Answer

The answer of The range of the values of the...

Question 17

In testing the significance of a multiple regression model with three independent variables,the null hypothesis is  .
​
​

Accepted Answer

The answer of In testing the significance of a multiple...

Question 18

If the Durbin-Watson statistic has a value close to 4,which assumption is violated?
A)Homoscedasticity
B)Normality of the errors
C)Independence of errors
D)None of these choices.

Accepted Answer

The Durbin-Watson statistic measures autocorrelation or dependence of errors. The statistic has a value between 0 and 4, with a value of 2 indicating no autocorrelation. If the statistic has a value close to 4, it suggests negative autocorrelation, while a value close to 0 suggests positive autocorrelation. Therefore, a value close to 4 violates the assumption of independence of errors. Homoscedasticity and normality are not related to the Durbin-Watson statistic.

Question 19

If the Durbin-Watson statistic,d,has values greater than 2,this indicates
A)a positive first-order autocorrelation
B)a negative first-order autocorrelation
C)no first-order autocorrelation at all
D)None of these choices.

Accepted Answer

A Durbin-Watson statistic value greater than 2 suggests a negative first-order autocorrelation because it indicates that the residuals from an ordinary least squares regression are inversely related across consecutive observations.

Question 20

Test the hypotheses: H₀: There is no first-order autocorrelation vs.H₁: There is negative first-order autocorrelation,given that: Durbin-Watson Statistic d = 1.75,n = 20,k = 2,and α = 0.01.

Accepted Answer

The answer of Test the hypotheses: H₀: There is no...

Quiz 17: Multiple Regression

If the value of the Durbin-Watson statistic d is small (d < 2),this indicates a(n)____________________ (positive/negative)first-order autocorrelation exists.

If the value of the Durbin-Watson test statistic,d,satisfies the inequality d > 4 −d_L,we conclude that positive first-order autocorrelation exists.

If the Durbin-Watson statistic has a value close to 0,which assumption is violated?

To use the Durbin-Watson test to test for negative first-order autocorrelation,the null hypothesis will be H₀: ____________________ (there is/there is no)first-order autocorrelation.

Test the hypotheses H₀: no first-order autocorrelation vs.H₁: first-order autocorrelation,given that: Durbin-Watson Statistic d = 1.89,n = 28,k = 3,and α = 0.01.

In testing the significance of a multiple regression model with three independent variables,the null hypothesis is .

If the Durbin-Watson statistic d has values smaller than 2,this indicates

If the residuals in a regression analysis of time ordered data are not correlated,the value of the Durbin-Watson d statistic should be near ____________________.

If the value of the Durbin-Watson statistic d is large (d > 2),this indicates a(n)____________________ (positive/negative)first-order autocorrelation exists.

Test the hypotheses H₀: There is no first-order autocorrelation vs.H₁: There is positive first-order autocorrelation,given that: Durbin-Watson Statistic d = 1.12,n = 45,k = 5,and α = 0.05.

Given that the Durbin-Watson test is conducted to test for positive first-order autocorrelation with α = .05,n = 20,and there are two independent variables in the model,the critical values for the test are d_L = __________ and d_U = __________,respectively.

The following is the regression output for a regression of calories on fiber and sugars for 10 popular types of cereal.Fill in the missing information,indicated by the boldface lettersa to f (up to three decimal places). Analysis of variance table for multiple regression model:

To use the Durbin-Watson test to test for positive first-order autocorrelation,the null hypothesis will be H₀: ____________________ (there is/there is no)first-order autocorrelation.

The range of the values of the Durbin-Watson statistic d is:

If the value of the Durbin-Watson test statistic,d,satisfies the inequalities d < d_L or d > 4 −d_L,where d_L and d_U are the critical values of d,we conclude that autocorrelation exists.

The range of the values of the Durbin-Watson statistic d is ____________________.

In testing the significance of a multiple regression model with three independent variables,the null hypothesis is .

If the Durbin-Watson statistic has a value close to 4,which assumption is violated?

If the Durbin-Watson statistic,d,has values greater than 2,this indicates

Test the hypotheses: H₀: There is no first-order autocorrelation vs.H₁: There is negative first-order autocorrelation,given that: Durbin-Watson Statistic d = 1.75,n = 20,k = 2,and α = 0.01.

Quiz 17: Multiple Regression

If the value of the Durbin-Watson statistic d is small (d < 2),this indicates a(n)____________________ (positive/negative)first-order autocorrelation exists.

If the value of the Durbin-Watson test statistic,d,satisfies the inequality d > 4 −dL,we conclude that positive first-order autocorrelation exists.

If the Durbin-Watson statistic has a value close to 0,which assumption is violated?

To use the Durbin-Watson test to test for negative first-order autocorrelation,the null hypothesis will be H0: ____________________ (there is/there is no)first-order autocorrelation.

Test the hypotheses H0: no first-order autocorrelation vs.H1: first-order autocorrelation,given that: Durbin-Watson Statistic d = 1.89,n = 28,k = 3,and α = 0.01.

In testing the significance of a multiple regression model with three independent variables,the null hypothesis is .

If the Durbin-Watson statistic d has values smaller than 2,this indicates

If the residuals in a regression analysis of time ordered data are not correlated,the value of the Durbin-Watson d statistic should be near ____________________.

If the value of the Durbin-Watson statistic d is large (d > 2),this indicates a(n)____________________ (positive/negative)first-order autocorrelation exists.

Test the hypotheses H0: There is no first-order autocorrelation vs.H1: There is positive first-order autocorrelation,given that: Durbin-Watson Statistic d = 1.12,n = 45,k = 5,and α = 0.05.

Given that the Durbin-Watson test is conducted to test for positive first-order autocorrelation with α = .05,n = 20,and there are two independent variables in the model,the critical values for the test are dL = __________ and dU = __________,respectively.

The following is the regression output for a regression of calories on fiber and sugars for 10 popular types of cereal.Fill in the missing information,indicated by the boldface lettersa to f (up to three decimal places). ​ ​ Analysis of variance table for multiple regression model: ​

To use the Durbin-Watson test to test for positive first-order autocorrelation,the null hypothesis will be H0: ____________________ (there is/there is no)first-order autocorrelation.

The range of the values of the Durbin-Watson statistic d is:

If the value of the Durbin-Watson test statistic,d,satisfies the inequalities d < dL or d > 4 −dL,where dL and dU are the critical values of d,we conclude that autocorrelation exists.

The range of the values of the Durbin-Watson statistic d is ____________________.

In testing the significance of a multiple regression model with three independent variables,the null hypothesis is . ​ ​

If the Durbin-Watson statistic has a value close to 4,which assumption is violated?

If the Durbin-Watson statistic,d,has values greater than 2,this indicates

Test the hypotheses: H0: There is no first-order autocorrelation vs.H1: There is negative first-order autocorrelation,given that: Durbin-Watson Statistic d = 1.75,n = 20,k = 2,and α = 0.01.

If the value of the Durbin-Watson test statistic,d,satisfies the inequality d > 4 −d_L,we conclude that positive first-order autocorrelation exists.

To use the Durbin-Watson test to test for negative first-order autocorrelation,the null hypothesis will be H₀: ____________________ (there is/there is no)first-order autocorrelation.

Test the hypotheses H₀: no first-order autocorrelation vs.H₁: first-order autocorrelation,given that: Durbin-Watson Statistic d = 1.89,n = 28,k = 3,and α = 0.01.

Test the hypotheses H₀: There is no first-order autocorrelation vs.H₁: There is positive first-order autocorrelation,given that: Durbin-Watson Statistic d = 1.12,n = 45,k = 5,and α = 0.05.

Given that the Durbin-Watson test is conducted to test for positive first-order autocorrelation with α = .05,n = 20,and there are two independent variables in the model,the critical values for the test are d_L = __________ and d_U = __________,respectively.

The following is the regression output for a regression of calories on fiber and sugars for 10 popular types of cereal.Fill in the missing information,indicated by the boldface lettersa to f (up to three decimal places). Analysis of variance table for multiple regression model:

To use the Durbin-Watson test to test for positive first-order autocorrelation,the null hypothesis will be H₀: ____________________ (there is/there is no)first-order autocorrelation.

If the value of the Durbin-Watson test statistic,d,satisfies the inequalities d < d_L or d > 4 −d_L,where d_L and d_U are the critical values of d,we conclude that autocorrelation exists.

In testing the significance of a multiple regression model with three independent variables,the null hypothesis is .

Test the hypotheses: H₀: There is no first-order autocorrelation vs.H₁: There is negative first-order autocorrelation,given that: Durbin-Watson Statistic d = 1.75,n = 20,k = 2,and α = 0.01.