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, â?¦.,28 [2004(I), 2004(II), â?¦., 2010(IV)]
D1 = 1 if t is quarter I (winter); 0 otherwise
D2= 1 if it is t 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 F-Ratio P-Value on F
Observations 28 0.9651 159.01 0.0001
Variable Parameter Estimate Standard Error T-Ratio P-Value
Intercept 184500 10310 17.9 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 sufficient statistical evidence of an upward trend in shoe sales?
b) Do these data indicate a statistically significant seasonal pattern of sales of 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 2011 (III) and 2012 (II).
d) how might you improve this forecast equation?
A Complete, Neat and Step-by-step Solution is provided in the attached file.