Consider the following time series data. B. Use a multiple regression model with
ID: 3073603 • Letter: C
Question
Consider the following time series data.
B. Use a multiple regression model with dummy variables as follows to develop an equation to account for seasonal effects in the data. Qtr1 = 1 if Quarter 1, 0 otherwise; Qtr2 = 1 if Quarter 2, 0 otherwise; Qtr3 = 1 if Quarter 3, 0 otherwise
y= 6.6667 + -1 Qtr1+ -5 Dtr2 + -2 Qtr3
C. Compute the quarterly forecasts for next year based on the model you developed in part (b).
D. Use a multiple regression model to develop an equation to account for trend and seasonal effects in the data. Use the dummy variables you developed in part (b) to capture seasonal effects and create a variable t such that t = 1 for Quarter 1 in Year 1, t = 2 for Quarter 2 in Year 1,… t = 12 for Quarter 4 in Year 3.
y= 3.417 + 0.219 Qtr1+ -4.188 Dtr2 + -1.594 Qtr3 + 0.406 t
E. Compute the quarterly forecasts for next year based on the model you developed in part (d)
F. Is the model you developed in part (b) or the model you developed in part (d) more effective
I have already answered questions A-E I only need help finding the MSE in part F.
Quarter Year 1 Year 2 Year 3 1 4 6 7 2 0 1 4 3 3 5 6 4 5 7 8Explanation / Answer
b)
after regression on Quareter only
Value = 6.666666667 - Qtr1t - 3 Qtr2t -2 Qtr3t
c)
d)
when we include time also
Value = 3.416666667 + 0.21875* Qtr1t -2.1875* Qtr2t -1.59375 Qtr3t + 0.40625* t
f)
MSE
Model developed in part (b) 1.222233333
Model developed in part (d) 0.284722222
Model in d) is more effective as MSE is less
Actual Demand y t Q1 Q2 Q3 quarter 4 1 1 0 0 5.6666 2 2 0 1 0 3.6666 3 3 0 0 1 4.6666 5 4 0 0 0 6.6666 6 5 1 0 0 5.6666 3 6 0 1 0 3.6666 5 7 0 0 1 4.6666 7 8 0 0 0 6.6666 7 9 1 0 0 5.6666 6 10 0 1 0 3.6666 6 11 0 0 1 4.6666 8 12 0 0 0 6.6666 13 1 0 0 5.6666 14 0 1 0 3.6666 15 0 0 1 4.6666 16 0 0 0 6.6666