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

Q_t = a + bt + c₁D₁ + c₂D₂ + c₃D₃

where 

Q_t = sales of athletic shoes in the tth quarter 

t = 1, 2, . . . . , 28 [2007(I), 2007(II), . . . . , 2013(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:

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 2014(III) and 2015(II). 

d. How might you improve this forecast equation?

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DEPENDENT VARIABLE: QT R-SQUARE F-RATIO P-VALUE ON F OBSERVATIONS: 28 0.9651 159.01 0.0001 PARAMETER ESTIMATE STANDARD ERROR VARIABLE T-RATIO P-VALUE INTERCEPT D1 D2 D3 184500 2100 3280 6250 7010 10310 340 1510 2220 1580 17.90 6.18 2.17 2.82 4.44 0.0001 0.0001 0.0404 0.0098 0.0002