Question

Historical demand for a product is as follows:

	DEMAND
April	61
May	56
June	81
July	61
August	86
September	81

a. Using a simple four-month moving average, calculate a forecast for October. (Round your answer to 2 decimal places.)

b. Using single exponential smoothing with α = 0.30 and a September forecast = 64, calculate a forecast for October. (Round your answer to 2 decimal places.)

c. Using simple linear regression, calculate the trend line for the historical data. Say the X axis is April = 1, May = 2, and so on, while the Y axis is demand. (Round your intercept value to the nearest whole number and slope value to 2 decimal places.)

d. Calculate a forecast for October using your regression formula. (Round your answer to 2 decimal places.)

Answer 1

a) A four months moving average method averages the actual value for the previous four months to generate the forecast for the next month. This can be calculated as the sum of the actual value for the previous four months / 4

So forecast for October = (81+61+86+81)/4

= 309/4

= 77.25

b) Using the exponential smoothing method the formula to calculate the forecast is as follows :

Ft = F(t-1) + [A(t-1) - F(t-1)]

Where Ft = forecast for period t

A(t-1)= actual value for period previous to t

F(t - 1)= forecast for period previous to t

= smoothing constant

So using the above formula with =0.30 and September forecast of 64 the forecast for October = 64 + 0.30(81 - 64) = 64 + (0.30 × 17) = 64 + 5.10 = 69.10

C)

Month period(X) sales(Y) XY X^2 (square of X)

April 1 61 61 1

May 2 56 112 4

June 3 81 243 9

July 4 61 244 16

August 5 86 430 25

September 6 81 486 36

X = 1+2+3+4+5+6 = 21

Y = 61+56+81+61+86+81 = 426

XY = 61+112+243+244+430+486 = 1576

X^2 = 1+4+9+16+25+36 = 91

Number of periods = n = 6

X-bar = X/n = 21/6 = 3.5

Y-bar = Y/n = 426/6 = 71

b = [ XY - (n. X-bar. Y-bar)] / [ X^2 - (n. Square of X-bar)]

= [1576- (6 x 3.5 x 71)] / [91 - (6 x 3.5 x 3.5)]

= (1576-1491) / (91 - 73.5)

= 85/ 17.5

= 4.86

a= Y-bar - (b x X-bar) = 71 - (4.86 x 3.5) = 71-17.01 = 53.99 or rounded to 54

So the regression equation is Yt = a+bx => Yt= 54+4.86x

d) October is period 7,so x= 7

Forecast for October Yt = 54 + 4.86x = 54 + (4.86 x 7) = 54+34.02 = 88.02