Question

The following is the recent historical sales of Sony HDTV at a local BestBuy store.

Month	Jan	Feb	Mar	April	May
Actual HDTV sales	60	65	70	50	62

• Solution inputs are numbers only, no symbols or letters such as "$, (2.3), dollar".
• Numbers can be in the format of either 3000 or 3,000; 0.95 or .95
• Keep two decimals if not exact, do not round. For example, 3.24923... will be kept as 3.24, but the exact value of 0.625 will be kept as 0.625

1. Use the naive approach to forecast sales for June.  
2. Use a 4-month simple moving average to forecast sales for June.  
3. Using weighted moving average method, with weights of 0.5 one period ago, 0.3 two periods ago, and 0.2 three periods ago, to forecast sales for June.  
4. Assuming the forecast for April is 60. Use exponential smoothing, with a smoothing constant of 0.2, to forecast sales for June.  
5. Use simple linear regression y=a+bx, to first calculate the parameter value of b , then the parameter value of a  , and finally to forecast sales for June.  

Please evaluate Forecasting Method A, in terms of MAD and TS, based on the following forecasted sales, comparing to the realized actual sales.

Actual sales	20	34	25	31	35
Forecasted sales	23	32	24	36	29

• Solution inputs are number and letter only, no symbols such as "A., or (2.3)"
• Numbers can be in the format of either 3000 or 3,000; 0.95 or .95; negative number should be in the format of -0.8 instead of (0.8).
• Keep two decimals if not exact, do not round. For example, 3.24923... will be kept as 3.24, but the exact value of 0.625 will be kept as 0.625

1. The MAD value of forecasting method A is:  
2. The TS value of forecasting method A is:  
3. If another forecasting method B has the MAD = 4, and TS = 0.2, then which forecasting method (A or B) is better in terms of MAD value?   and which forecasting method (A or B) is better in terms of TS value?  

Answer 1

First question

Naive forecast for June = Actual sales of May = 62

4-month simple moving average forecast for Une = average(65,70,50,62) = 61.75

Weighted moving average forecast for June = 0.5*62+0.3*50+0.2*70 = 60

Formula

Regression

Month	Period (x)	Actual HDTV sales (y)	xy	x2
Jan	1	60	60	1
Feb	2	65	130	4
Mar	3	70	210	9
Apr	4	50	200	16
May	5	62	310	25
Total	15	307	910	55

x-bar = 15/5 = 3
y-bar = 307/5 = 61.4

b = (sum(xy)-n*x-bar*y-bar)/(sum(x2)-n*x-bar^2)

=(910-5*3*61.4)/(55-5*3^2) = -1.1

a=y-bar*b*x-bar = 61.40-(-1.1)*3 = 64.7

So, regression equation y =a+bx = 64.7-1.1x

Forecast for June = 64.7-1.1*6 = 58.1