Question $3[20$ Marks$]$

The historical demand for magwinya for Mr Mosepele$$s small Semausu is as given below

Item No Month Demand

$1$ April $60$

$2$ May $55$

$3$ June $75$

$4$ July $60$

$5$ August $80$

$6$ September $75$

a$)$ Using a simple four$-$month moving average, calculate the forecast for October.

$(4$ marks$)$

b$)$ Using single exponential smoothing with $\backslash$alpha $=0\mathrm{.}2$ and September forecast $=65,$

calculate the forecast for October. $(6$ marks$)$

c$)$ Using simple linear regression, calculate the trend line for historical data. The

following data are given to help in your calculations: The X axis is April $=1,$ May $=$

$2$ and so on as indicated in the table above. The Y axis is demand.

n $=6$

$\backslash$Sigma X $=21$

$\backslash$Sigma Y $=405$

$\backslash$Sigma X$2=91$

$\backslash$Sigma Y$2=27\mathrm{.}875$

$\backslash$Sigma XY $=1\mathrm{.}485$

$(6$ marks$)$

d$)$ Calculate the forecast for October $(4$ marks$)$

$($Total $20$ Marks$)$