3. Rubax, a U.S. manufacturer of athletic shoes, estimates the following linear trend model for shoe sales:
Qt= a + bt + c1D1 + c2D2 + c3D3
Qt= sales of athletic shoes in the tth quarter
t = 1,2,3, ......., 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:
Qt = 184500 + 2,100t + 3280 D1 + 6250 D2 + 7010 D3
(17.90) (6.18) (2.17) (2.82) (4.44)
R2 = 0.9651 F = 159.01
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 1999(III) and 2000(II).
d. How might you improve this forecast equation?
A Complete, Neat and Step-by-step Solution is provided in the attached file.