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    Linear Trend Model-Regression analysis

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    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?

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