Posted by **Renee Williams** on Thursday, June 28, 2007 at 9:10pm.

Rubax, a US manufacturer of athletic shoes, estimates the following linear trend model for shoe sales.

Q1=a+bt+c1D1+c2D2+c3D3

where

Q1=sales of athletic shoes in the t-th quarter

t= 1,2,...,28{1998(I), 1998(II),...2004(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 F-Ratio P-Value of F

Observations: 28 R-Square 0.9651

F-Ratio 159.01 P-Value = 0.0001

Variable Parameter Standard T-Ratio

Intercept 184500 10310 17.90

T 2100 340 6.18

D1 3280 1510 2.17

D2 6250 2220 2.82

D3 7010 1580 4.44

P-Value

0.0001

0.0001

0.0404

0.0098

0.0002

(a) is there sufficient statistical evidence of an upward trend in shoe sales?

(b) Do this 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 2005(III) and 2006 (II).

(d) how might you improve this forecase equation?

a) Look at the parameter and T-ratio for the T variable. The parameter is positive and the T-ratio is significant(as the P-value is .0001) so.....

b) Hummm. The appropriate test for multiple dummy variables, like your equation, is an F-test. Here, one would test whether the parameters for D1 D2 and D3, as a combination, are significantly different from zero. However, since the parameters for each D1,D2,D3 are each significant, then almost certainly, combined they would be different.

As for the seasonal pattern summer is the best quarter, autum is the worst.

c) Plug the appropriate values into the equation and solve....

d) There are a plethora of variables one could use to improve the forecast. How bout price, price of competitors, advertising expenses, advertising by competitors, population of young adults, number of retailers, number of shoe styles produced, etc.

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