a)
Linear trend y = a+bx
a = intercept
b = slope
x = time period
y = forecast for demand for period x
b = (sum xy – nbar{x}bar{y})/(sum x^{2}-nbar{x}^{2})
a=bar{y}-bbar{x}
n = no of peiods
bar{x}=sum x/n = the mean of the x values
bar{y}=sum y/n = the mean of the y values
https://d2vlcm61l7u1fs.cloudfront.net/media%2Feaf%2Feafc365c-e796-4469-8a46-b7f682c3b780%2FphpOwiJOj.png
ope b = (75713-(18*388.94*9.5))/(2109-(18*9.5*9.5)) = 19
Intercept a = 388.94 – (9.5*19) = 208.44
Y = 208.44 + 19x
b)
Forecast for week 20 and 21
Y (x= 20) = 208.44 + 19* 20 = 588.44
Y (x= 21) = 208.44 + 19* 21 = 607.44
c)
Y = 800
800 = 208.44 + 19*x
x = 31.13 weeks
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