F IL E 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 ten years of quarterly data. A portion is shown in the accompanying table; the complete data set can be found on the text website, labeled Retail Sales.

Year Quarter Retail Sales

(in $ millions)

GNP

(in $ billions) d1 d2 d3 2001 1 696,048 9,740.5 1 0 0 2 753,211 9,983.5 0 1 0

⋮ ⋮ ⋮ ⋮ ⋮ ⋮

2009 4 985,649 14,442.8 0 0 0 So u r c e: Retail sales obtained from www.census.gov; GNP obtained from research.

stlouisfed.org.

a. Estimate y = β 0 + β1 x + β 2d1 + β 3d2 + β 4d3 + ε where y is retail sales, x is GNP, d1 is a dummy variable that equals 1 if quarter 1 and 0 otherwise, d2is 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.

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. Use the partial F test to determine if the three seasonal dummy variables used in the model are jointly significant at the 5% level.