The data presented below are for retail sales in the United States quarterly from the period 1992Q1 through 2003Q4. Also included is disposable personal income per capita (DPIPC) (to use as a measure of the well-being of the economy).
a. Develop a regression model of retail sales as a function of the S&P 500. Comment on the relevant summary statistics.
b. Estimate a new multiple-regression model using seasonal dummy variables for quarters 2, 3, and 4. Additionally, add a time index to account for trend. Comment on the relevant statistics of this model. Is this model an improvement on the model above? What evidence is there that this second model provides an improvement (no improvement)?
c. Square the time index variable and add it to the multiple-regression model above. Does the resulting model perform better than either previous model? Explain your reasoning.