Case $4$:

A hospital pharmacy would like to develop a budget for allergy medications that is based on patient days. Cost and patient days data were collected over a $17-$month period. Data are shown as below:

$\backslash$table$[[$Period$,$Cost $($$$),$Patient Days$],[$Year $1,$ October,$32996,516],[$Year $1,$ November,$34242,530],[$Year $1,$ December,$27825,528],[$Year $2,$ January,$29807,517],[$Year $2,$ February,$28692,500],[$Year $2,$ March,$34449,514],[$Year $2,$ April,$33335,515],[$Year $2,$ May,$38217,509],[$Year $2,$ June,$36690,524],[$Year $2,$ July,$35303,524],[$Year $2,$ August,$33780,539],[$Year $2,$ September,$32843,551],[$Year $2,$ October,$37781,543],[$Year $2,$ November,$27761,528],[$Year $2,$ December,$31876,531],[$Year $3,$ January,$31463,542],[$Year $3,$ February,$29829,558]]$

Answer the following questions:

Develop a linear$-$regression$-$based forecasting model to predict costs. $($What is the linear regression equation?$)$

Predict costs when patient days are $520,530,540$ and $550.$

What would be predicted costs for March of year $3($eighteenth month$),$ using a four$-$period moving average?