The following table shows the quarterly demand, in thousands of cases, for a national beer distributor over the past $4$ years.

Year Quarter Demand $($in thousands of cases$)$

$1$ I $289$

$1$ II $501$

$1$ III $441$

$1$ IV $348$

$2$ I $346$

$2$ II $516$

$2$ III $539$

$2$ IV $289$

$3$ I $434$

$3$ II $519$

$3$ III $496$

$3$ IV $488$

$4$ I $279$

$4$ II $525$

$4$ III $534$

$4$ IV $532$

The data can also be found in the Excel file: Beer Data Download Beer Data. $($If the file failed to download, please manually enter the numbers in the table above to your spreadsheet.$)$

A$.$ Forecast the demand for the first quarter of Year $5$ by using a $4-$period moving average model. Answer $=$

$($to $2$ decimals$).$ Calculate the RMSE using only the actual data and the fitted values in Years $2,3$ and $4.$ RMSE $=$

$($to $2$ decimals$)$

B$.$ Forecast the demand for the first quarter of Year $5$ by using an exponential smoothing model with

$.$ Answer $=$

$($to $2$ decimals$).$ Calculate the RMSE using the actual data and the fitted values in all $4$ years. RMSE $=$

$($to $2$ decimals$)$

C$.$ Forecast the demand for the first quarter of Year $5$ by using a linear trend model. Answer $=$

$($to $2$ decimals$).$ Calculate the RMSE using the actual data and the fitted values in all $4$ years. RMSE $=$

$($to $2$ decimals$)$

D$.$ Forecast the demand for the first quarter of Year $5$ by using a quadratic trend model. Answer $=$

$($to $2$ decimals$).$ Calculate the RMSE using the actual data and the fitted values in all $4$ years. RMSE $=$

$($to $2$ decimals$)$