A forecaster used the regression equation Q_t = a + bt + c_1 D_1 + c_2D_2 + c_3D

Question

A forecaster used the regression equation Q_t = a + bt + c_1 D_1 + c_2D_2 + c_3D_3 and quarterly sales data for Q1 1993 through Q4 2008 (t = 1, ..., 64) for an appliance manufacturer to obtain the results shown below. Q is quarterly sales, and D_1, D_2 and D_3 are dummy variables for quarters I, II, and III. a. Is there an upward or downward trend in sales over time? Is this trend statistically significant? Justify your answer using regression statistics. b. In any given year, which ranking of quarterly sales tends to be true (mark the # of your choice on the answer sheet): 1. Q_I > Q_II > Q_III > Q_IV 2. Q_I > Q_II > Q_IV > Q_III 3. Q_II > Q_III > Q_IV > Q_I 4. Q_III > Q_II > Q_III > Q_IV 5. Q_III > Q_IV > Q_II > Q_I c. Calculate the estimated sales forecasts for the 1^st, 2^nd, 3^rd and 4^th quarter of 2009.

Explanation / Answer

Part-a

There is an upward trend as coefficient of T is positive. Also this is statistically significant with p-value=0.0362<0.05

Part-b

Option-5

Part-c

For 2009, t=65

1st quarter sale=30.0+1.5*65-30.0*1-15.0*0+20.0*0=97.5

2nd quarter sale=30.0+1.5*65-30.0*0-

15.0*1+20.0*0=112.5

Third quarter sale=30.0+1.5*65-30.0*0-15.0*0+20.0*1=147.5

4th quarter sale=30.0+1.5*65-30.0*0-15.0*0+20.0*0=127.5

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