Question $1.$ The spreadsheet "Question $1-$Assignment $1.$xlsx$"($uplosded to "Demand Mansgment $($Forecasting$)"$ module of Canvas$)$ has data for the past $30$ weels of sales for product $x.$ Baced on the data, do the following questions.

If you use Excel to solve this question, submit the excel file along with your solutions to the assignment. Note that you need to explain your answers to the following questions in detail, and just submitting the calculations done by excel is not enough.$]$

$($a$)$ Plot the data. Just by looking at the plot, do you think a $3-$week simple moving average wouk be a better forecast, or a $6-$week simple moving average? Just by looking at the plot, do you think an exponential smoothing with value of $=0\mathrm{.}2$ would be better forecast or would $=0\mathrm{.}6$ be better? Explain your reasoning.

$($b$)$ Which one of the four possible forecasts mentioned in part $($a$)(3-$week and $6-$week simple moving average and exponential smoothing with value of $=0\mathrm{.}2$ and $-0\mathrm{.}6$ is the best forecast? Justify your answer by calculating $($Mean Absolute Deviation$)($MAD$)$ and $($Mrant Squared Error$)$ MSE. According to the chosen $($method$,$ what will be the forecast of sales during Week $31?$

$($c$)$ Now, assume that we want to fit the best Linear trend to the data to estimate the average demand change every week considering it$.$ Fif this line to the data, and ad it to the plot of part $($a$).$ How much is the average demand change every week aceveling to it$?$ Compare the forecasting performance of this methich to the answer you got at part $($b$).$

$($Remark: For some of the above parts, different people could reach different conchasions but wont need to give good reasons for your condusions$)$