1. This question is worth 50 points—2 points each, except for subparts (a) and (i), which are
worth 6 points each, and subpart (j), which is worth 10 points.
Use the file “Data for Question 1.” This file contains 145 monthly observations (2006-1 to
2018-1) on the following variables:
SUV: Sales of new sport utility vehicles in the U.S. (seasonally adjusted, in millions of
dollars).
U: The civilian unemployment rate.
Gas: Average price per gallon of unleaded gasoline.
SP: Standard and Poor’s Index of 500 stock prices with dividend reinvestment, monthly
average.
a) Use regression to estimate the following model specification. Report the results of the
regression—that is, report your estimates of β0 , β1 , β2, and β3.
= 0 + 1 + 2 + 3
b) Are the signs of the (estimated) coefficients consistent with your (prior) expectations?
Explain.
c) Suppose that the unemployment rate (U) is projected to decline by 0.2 percentage
points next month. Based on the equation you have estimated, what is t
he predicted
effect on SUVin the next month, holding all other factors constant? Be precise.
d) Can the following null hypothesis be rejected at the 0.01 significance level? Explain.
0: 2 = 0
2
e) Use the equation you estimated above to obtain a fitted value of SUV for 2008-7.
Compute (and report) the ratio of the in-sample forecast error ( − ̂
) for this
month to the standard error of the regression (SE). Provide an interpretation of this
ratio.
f) Prepare a chart (not table or spreadsheet) illustrating actual and fitted values of SUV for
the period 2006-4 to 2018-1.
g) Report the value of R
2 and provide a (precise) interpretation.
h) Set up an F-test. Can you reject null hypothesis at the 1 percent (.01) significance level?
i) Use the data contained in “Forecast” of your spreadsheet to forecast the value of SUV
for 2023-02 t 2023-06. Report your results.
j) Estimate the following regression specification:
= 0 + 1 + 2 + 3
Is the demand fo elastic with respect to gas prices? .