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The consumer purchasing value of the dollar, Yt, from 1970
Chapter 14, Problem 52E(choose chapter or problem)
The consumer purchasing value of the dollar, from 1970 to 2007 is illustrated by the data in the table in the next column. The buying power of the dollar (compared with 1982) is listed for each year and saved in the BUYPOWER file. The first-order model
Yt = β0 + β1t + ε
was fit to the data using the method of least squares. The Minitab printout and a plot of the regression residuals are shown below.
a. Examine the plot of the regression residuals against t. Is there a tendency for the residuals to have long positive and negative runs? To what do you attribute this phenomenon?
b. Locate the Durbin-Watson d-statistic on the printout and test the null hypothesis that the time series residuals are uncorrelated. Use ⍺ = .10.
c. What assumption(s) must be satisfied in order for the test of part b to be valid?
Questions & Answers
QUESTION:
The consumer purchasing value of the dollar, from 1970 to 2007 is illustrated by the data in the table in the next column. The buying power of the dollar (compared with 1982) is listed for each year and saved in the BUYPOWER file. The first-order model
Yt = β0 + β1t + ε
was fit to the data using the method of least squares. The Minitab printout and a plot of the regression residuals are shown below.
a. Examine the plot of the regression residuals against t. Is there a tendency for the residuals to have long positive and negative runs? To what do you attribute this phenomenon?
b. Locate the Durbin-Watson d-statistic on the printout and test the null hypothesis that the time series residuals are uncorrelated. Use ⍺ = .10.
c. What assumption(s) must be satisfied in order for the test of part b to be valid?
ANSWER:
Step 1 of 6
(a)
Yes, there is a tendency for the residuals in the plot of the regression residuals against the variable t.
Reason:
* The residuals have the long positive and negative runs.
* That is, the residuals from 1 through 7 are positive runs, the residuals from 8 through 28 are negative runs and the residuals from 29 through 41 are positive runs.
* This implies that the error terms (residuals) are correlated.