𝑆𝑈𝑉𝑠 elastic with respect to gas prices

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.
𝑆𝑈𝑉𝑡 = 𝛽0 + 𝛽1𝐺𝑎𝑠𝑡 + 𝛽2𝑈𝑡 + 𝛽3𝑆𝑃𝑡
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 the 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.
𝐻0: 𝛽2 = 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 (𝑆𝑈𝑉𝑡 − 𝑆𝑈𝑉 ̂𝑡
) 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:
𝑙𝑛𝑆𝑈𝑉𝑡 = 𝛽0 + 𝛽1𝑙𝑛𝐺𝑎𝑠𝑡 + 𝛽2𝑙𝑛𝑈𝑡 + 𝛽3𝑙𝑛𝑆𝑃𝑡
Is the demand fo𝑟 𝑆𝑈𝑉𝑠 elastic with respect to gas prices? 𝑃𝑙𝑒𝑎𝑠𝑒 𝑒𝑥𝑝𝑙𝑎𝑖𝑛.