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3. Rubax, a United States producer of athletic shoes, estimates the following linear trend model for shoe sales:Qt= a + bt + c1D1 + c2D2 + c3D3WhereQt= sales of athletic shoes in the tth quartert = 1,2,3, ......., 28 (2001(I), 2001(II), ........., 2007(IV) )D1 = 1 if t is quarter I (winter); 0 otherwiseD2 = 1 if t is quarter II (spring); 0 otherwiseD3 = 1 if t is quarter III (summer); 0 otherwiseThe 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 = 159.01a. 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?
Explain why this model violates the assumption of no perfect collinearity. Write the t statistic for testing the null hypothesis
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