A government researcher is analyzing the relationship between retail sales and the gross national product (GNP). He also wonders whether there are significant differences in retail sales related to the quarters of the year. He collects 10 years of quarterly data. A portion is shown in the accompanying table; the entire data set, labeled Retafl_Sales, can be found on the text website

a. Estimate y = β0 + β1x + β2d1 + β3d2 + β4d3 + where y is retail sales, x is GNP, d1 is a dummy variable that equals 1 if quarter 1 and 0 otherwise, d2 is a dummy variable that equals 1 if quarter 2 and 0 otherwise, and d3 is a dummy variable that equals 1 if quarter 3 and 0 otherwise. Here the reference category is quarter 4.
b. Predict retail sales in quarters 2 and 4 if GNP equals $13,000 billion.
c. Which of the quarterly sales are significantly different from those of the 4th quarter at the 5% level?
d. Re-formulate the model to determine, at the 5% significance level, if sales differ between quarter 2 and quarter 3. Your model must account for allquarters.

Transcribed Image Text:

Retail Sales GNP Year Quarter (in $ millions) (in $billions) d d d d 9,7405 1 0 0 0 9,9835 01 0 0 20011 696,048 753,211 2009 4 985,649 14A42.8 0 0 0 1