Question: Shirtco, a U.S. manufacturer of t-shirts, estimates the following linear trend model for t-shirt sales:

Q _t = a + bt + c ₁ D₁ + c₂D₂ + c₃D₃

where

Q _t = sales of t-shirts in the tth quarter

t = 1,2,….,28,[2001(I), 2001(II),….., 2007(IV)]

D₁ = 1 if t is quarter I ; 0 otherwise

D₂ = 1 if t is quarter II ; 0 otherwise

D₃ = 1 if t is quarter III ; 0 otherwise

The regression analysis produces the following results:

Dependant Variable: QT R-Square F-Ratio P-Value on F

Observations: 28 0.9651 159.01 0.0001

Variable Paramter Standard T-Ratio P-Value

Estimate Error

Intercept 184500 10310 17.90 0.0001

T 2100 340 6.18 0.0001

D1 3280 1510 2.17 0.0404

D2 6250 2220 2.82 0.0098

D3 7010 1580 4.44 0.0002

a) Is there a sufficient statistical evidence of an upward trend in t-shirt sales?

b) Do these data indicate a statistically significant seasonal pattern of sales for Shirtco t-shirts? If so, what is the seasonal pattern exhibited by the data?

c) Using the estimated forecast equation, forcast sales of Shirtco t-shirts for 2008(III) and 2009(II).

d) How might you improve this forecast equation?