Question 1

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 $\alpha$ = 0.01.

Accepted Answer

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

Question 2

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 3

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 4

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

A Durbin-Watson statistic with a value smaller than 2 indicates a positive first-order autocorrelation. If the value is between 0 and 2, this suggests a weak positive autocorrelation, and if it is between 2 and 4, it suggests a weak negative autocorrelation. However, in this question, we are only given the information that the value is smaller than 2, which indicates a positive autocorrelation.

Question 5

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 6

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 $\alpha$ = 0.01.

Accepted Answer

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

Question 7

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 tests for autocorrelation, or the presence of correlation between successive errors in a linear regression model. A value close to 4 suggests a negative autocorrelation, which means that the errors are negatively correlated with their lags. This violates the assumption of independence of errors, which states that the errors should be uncorrelated with each other. Homoscedasticity and normality of the errors are not related to the Durbin-Watson statistic.

Question 8

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 9

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, which is a violation of the assumption of independence of errors. A value close to 0 indicates strong positive autocorrelation, indicating that the errors in the model are not independent. Therefore, choice C is the correct answer.

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 $\alpha$ = 0.05.

Accepted Answer

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

Question 11

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 12

Given that the Durbin-Watson test is conducted to test for positive first-order autocorrelation with $\alpha$ = .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 13

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 14

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

This statement is true. The Durbin-Watson test is used to test for autocorrelation in the residuals of a regression model. The critical values of the test statistic depend on the sample size and the number of independent variables in the model. If the calculated value of the test statistic falls outside the critical value range, we can conclude that autocorrelation exists in the residuals.

Question 15

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 16

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

Accepted Answer

The Durbin-Watson statistic ranges from 0 to 4, where 0 indicates strong positive autocorrelation and 4 indicates strong negative autocorrelation. A value around 2 suggests no autocorrelation.

Quiz 17: Multiple Regression

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\alphaα = 0.01.

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

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

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: 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\alphaα = 0.01.

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

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

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

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\alphaα = 0.05.

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.

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