# managerial economics

posted by
**queen** on
.

rubax, a u.s manufacturer of athletic shoes, estiamtes the following linear trend model for shoe sales

Qt=a+bt+c1D1+c2D2+c3D3

where

Qt=sales of athletic shoes in the t-th quater

t=1,2,...,28[1998(I),1998(II),...,2004(IV)]

D1=1 if t is quater I (winter); 0 otherwisw

D2=1 if t is quater II (spring); o otherwise

D3=1 if t is quater III (summer); o 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

p-value on f 0.0001

variable parameter ESt. standarderror

intercept 184500 10310

T 2100 340

D1 3280 1510

D2 6250 2220

D3 7010 1580

T-ratio p-value

17.90 0.0001

6018 0.0001

2.17 0.0404

2.82 0.0098

4.44 0.0002

A. is there sufficient statiscal 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 2005 (III) and 2006(II)

D.how might you improve this forecast equation?

I tried to line up the regression analysis i hope whom ever help me will see to make the regresssion line you correctly on their paper. thank you , signed the desperate Queen

On June 28, a Renee Williams posted this very question. Below is and was my response. Plz repost if you have questions.....

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.