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.

a. Estimate y = β0 + β1x + β2d1 + β3d2 + β4d3 + ɛ 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. Reformulate the model to determine, at the 5% significance level, if sales differ between quarter 2 and quarter 3. Your model must account for all quarters.

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Retail Sales GNP 20011 2 Year Quarter (in $ millions) (in $ billions) d d2 da d 9,740.5 1 0 0 0 9,983.50 1 0 0 696,048 753,211 2009 4 985,649 4,442.80 0 0 1