Question

Problem 3-20 An analyst must decide between two different forecasting techniques for weekly sales of roller blades: a linear trend equation and the naive approach. The linear trend equation is Ft 122+2.0t, and it was developed using data from periods 1 through 10. Based on data for periods 11 through 20 as shown in the table, which of these two methods has the greater accuracy if MAD and MSE are used? (Round your answers to 2 decimal places) Units Sold 147 148 151 146 155 152 156 157 158 167 12 13 14 15 17 19 20 MAD (Naive) MAD (Linear) MSE (Naive) MSE (Linear) (Click to select) provides forecasts with less average error and less average squared error
Please show work.

Answer 1

In case of naive method, the actual demand of present period is taken as the forecast of the next period. Thus the actual demand of 11th period will be taken as the forecast value of the 12th period and so on.

While in case of linear forecasting method, the linear equation is given as Ft=122+2*t thus in order to find out the forecast of any period, we have to replace t with the value of that period.

For example forecast of 11th period will be =122+2*11 =144

Therefore from the above explanation, the calculations are as below:-

T	Unit Sold	Forecast (Naive)	Deviation (Naive)	Absolute Deviation (Naive)	Square Error (Naive)	Forecast (linear)	Forecast (linear)	Deviation (Linear)	Absolute Deviation (Linear)	Square Error (linear)
11	147					122+2*11	144	3	3	9
12	148	147	1	1	1	122+2*12	146	2	2	4
13	151	148	3	3	9	122+2*13	148	3	3	9
14	146	151	-5	5	25	122+2*14	150	-4	4	16
15	155	146	9	9	81	122+2*15	152	3	3	9
16	152	155	-3	3	9	122+2*16	154	-2	2	4
17	156	152	4	4	16	122+2*17	156	0	0	0
18	157	156	1	1	1	122+2*18	158	-1	1	1
19	158	157	1	1	1	122+2*19	160	-2	2	4
20	167	158	9	9	81	122+2*20	162	5	5	25

MAD = Sum(A-F)/n

MAD for Naive = 36/9=4

MAD for Linear = 25/10=2.5

MSE = [Sum of (A-F)^2]/n-1

MSE for Naive =224/(9-1) =28.5

MSE for Linear =81/(10-1)=9

Answer:- Linear Trend equation provides forecast with less average error and less average square error