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 D ₁ + c ₂ D ₂ + c ₃ D ₃

where

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

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

D ₁ = 1 if t is quarter I ; 0 otherwise

D ₂ = 1 if t is quarter II ; 0 otherwise

D ₃ = 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

1. Is there a sufficient statistical evidence of an upward trend in t-shirt sales?
2. 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?
3. Using the estimated forecast equation, forcast sales of Shirtco t-shirts for 2008(III) and 2009(II).
4. How might you improve this forecast equation?

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