Freight car loading over an $8-$week period at a busy port are as follows; $(40$ pts$)$

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Week $12345678$

Number $220250260280300330310340$

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a$)$ Forecast week $9,$ by using exponential soothing, use a$($alpha$)=0\mathrm{.}6,$

forecast of week $5=310.$

b$)$ Develop the trend equation for the forecast and how many for week $20$

and $25.$

c$)$ The manager intends to install new equipment when the volume exceeds $750$ loadings per week. Assuming the current trend continues, the loading volume will reach that level in approximately what week?

d$)$ Compute MAD and MSE for the trend equation for periods $1-8.$