The consumer purchasing value of the dollar, from
1970 to 2004 is illustrated by the data in the next table.The
buying power of the dollar (compared with 1982) is listed
for each year.The first-order model
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
c. What assumption(s) must be satisfied in order for the
test of part b to be valid?
----------------------------------------------------------
Regression Analysis: Value Versus T
The regression equation is
VALUE = 1.99 - .0466 T
Predictor --------Coef -------SE Coef -------- T-------------- P
Constant -------1.99235 -----.09643---------20.66---------.0000
T ------------------( -.046632)---.004672-----(-9.98)---------.0000
S=0.279148--------R-Sq= 75.1%--------R-Sq(adj) = 74.4%
Analysis of Variance
Source-------DF------SS------- MS--------F---------P
Regression--1------7.7631---7.7631---99.62---.0000
Resid Error-33-----2.5715----.0779
Total----------34-----10.3346
Durbin-Watson Statistic= .0627189
1970 to 2004 is illustrated by the data in the next table.The
buying power of the dollar (compared with 1982) is listed
for each year.The first-order model
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
c. What assumption(s) must be satisfied in order for the
test of part b to be valid?
----------------------------------------------------------
Regression Analysis: Value Versus T
The regression equation is
VALUE = 1.99 - .0466 T
Predictor --------Coef -------SE Coef -------- T-------------- P
Constant -------1.99235 -----.09643---------20.66---------.0000
T ------------------( -.046632)---.004672-----(-9.98)---------.0000
S=0.279148--------R-Sq= 75.1%--------R-Sq(adj) = 74.4%
Analysis of Variance
Source-------DF------SS------- MS--------F---------P
Regression--1------7.7631---7.7631---99.62---.0000
Resid Error-33-----2.5715----.0779
Total----------34-----10.3346
Durbin-Watson Statistic= .0627189