Question

Two different forecasting techniques, Linear Regression and Trend-Seasonal, were used to forecast demand for cases of bottled water. Actual demand and the two sets of forecasts are as follows.

Predicted Demand

Period Sales Regression Linear regression Trend-Seasonal

1 282 200 290

2 255 210 230

3 262 220 270

4 290 230 210

5 230 240 250

A) Compute the MAD and Bias for each technique.

B) Construct a sentence to describe what the MAD and Bias tell the average person about each forecasting technique.

C) Which forecasting technique, Linear Regression or Trend-Seasonal, gives the best results? How did you derive this conclusion?

Answer 1

	sales	linear regression	trend seasonal	abs(error) in linear	abs(Error) in trend	error linear	error trend
1	282	200	290	82	8	82	-8
2	255	210	230	45	25	45	25
3	262	220	270	42	8	42	-8
4	290	230	210	60	80	60	80
5	230	240	250	10	20	-10	-20
				MAD		Bias
				47.8	28.2	43.8	13.8

Formula

	sales	linear regression	trend seasonal	abs(error) in linear	abs(Error) in trend	error linear	error trend
1	282	200	290	=ABS(C2-B2)	=ABS(D2-B2)	=B2-C2	=B2-D2
2	255	210	230	=ABS(C3-B3)	=ABS(D3-B3)	=B3-C3	=B3-D3
3	262	220	270	=ABS(C4-B4)	=ABS(D4-B4)	=B4-C4	=B4-D4
4	290	230	210	=ABS(C5-B5)	=ABS(D5-B5)	=B5-C5	=B5-D5
5	230	240	250	=ABS(C6-B6)	=ABS(D6-B6)	=B6-C6	=B6-D6
				MAD		Bias
				=AVERAGE(E2:E6)	=AVERAGE(F2:F6)	=AVERAGE(G2:G6)	=AVERAGE(H2:H6)

a)

MAD for linear = 47.8

MAD for trend seasonal = 28.2

Bias for linear = 43.8

bias for trend seasonal = 13.8

b)

MAD - It is average distance between each data value and the mean. Mean absolute deviation is a way to describe variation in a data set.

c)

Trend seasonal gives the best result, as its MAD and bias is less than those of Linear