Economyst, please help
Rubax__ a U.S. manufacturer of athletic shoes, estimates the following linear trend model for shoe sales:
Qt= a + bt + c1D1 + c2D2 + c3D3
Where
Qt= sales of athletic shoes in the tth quarter
t= 1, 2,…., 28[2001(I), 2001(II), …., 2007(IV)]
D1= 1 if t is quarter I (winter); 0 otherwise
D2= 1 if t is quarter II (spring); 0 otherwise
D3= 1 if t is quarter III (summer); 0 otherwise
The regression analysis produces the following results:
Dependent Variable QT
R-Square 0.9651
F-Ratio 159.01
P-Value on F 0.0001
Intercept: Parameter Estimate 184500, Standard Error 10310, T-Ratio 17.90, P-Value 0.0001
T: Parameter Estimate 2100, Standard Error 340, T-Ratio 6.18, PValue 0.0001
D1: Parameter Estimate 3280, Standard Error 1510, T-Ratio 2.17, P-Value 0.0404
D2: Parameter Estimate 6250, Standard Error 2220, T-Ratio 2.82, P-Value 0.0098
D3: Parameter Estimate 7010, Standard Error 1580, T-Ratio 4.44, P-Value 0.0002
a. Is there sufficient statistical evidence of an upward trend in shoe sales?
b. Do these data indicate a statistically significant seasonal pattern of sales for Rubax shoes? If so, what is the seasonal pattern exhibited by the data?
c. Using the estimated forecast equation, forecast sales of Rubax shoes for 2008(II) and 2009(II).
d. How might you improve this forecast question?