Consider the following to answer the question(s) below:
The average monthly residential mortgage lending rate in Canada is available monthly beginning in 1951. A scatterplot of the residuals against time for 747 months from January 1951 to March 2013 is shown below. The rate peaked in September of 1981 at 21.46%. The Durbin-Watson statistic has a value of 0.01.
-The critical values for the Durbin-Watson statistic for α = 0.05 and n = 750 are: dL= 1.87736 and dU = 1.88270. What does this tell us about the assumption of the independence of the errors?
A) The assumption of independent errors is violated.
B) The assumption of independent errors is not violated.
C) The errors are not related to one another over time.
D) This test is not valid for time series data.
E) This evidence does not allow us to draw any conclusions in this regard.

Question

Consider the following to answer the question(s) below:
The average monthly residential mortgage lending rate in Canada is available monthly beginning in 1951. A scatterplot of the residuals against time for 747 months from January 1951 to March 2013 is shown below. The rate peaked in September of 1981 at 21.46%.  The Durbin-Watson statistic has a value of 0.01.
-The critical values for the Durbin-Watson statistic for α = 0.05 and n = 750 are: dL= 1.87736 and dU = 1.88270. What does this tell us about the assumption of the independence of the errors?
A) The assumption of independent errors is violated. 
B) The assumption of independent errors is not violated. 
C) The errors are not related to one another over time. 
D) This test is not valid for time series data. 
E) This evidence does not allow us to draw any conclusions in this regard.

Quizplus · Accepted Answer

The Durbin-Watson statistic has a value close to 0, which indicates that there is very strong positive autocorrelation among the residuals. The critical values for the Durbin-Watson statistic for α = 0.05 and n = 750 are given as dL= 1.87736 and dU = 1.88270. The calculated Durbin-Watson statistic indicates that the residuals are significantly autocorrelated at the 5% significance level, suggesting that the assumption of independent errors is being violated. Thus, the best answer is A.

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