Historical demand for a produc

Historical demand fora 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 forOctober. (Round your answer to 2 decimalplaces.)

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

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

a) A four months moving average method averages the actual valuefor the previous four months to generate the forecast for the nextmonth. This can be calculated as the sum of the actual value forthe 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 tocalculate 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 theforecast 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 orrounded 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

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