Exercise $5\mathrm{.}7($Algo$)$ THE FRESH DETERGENT CASE

Enterprise Industries produces Fresh, a brand of liquid laundry detergent. In order to manage its inventory more effectlvely and make revenue projections, the company would like to better predict demand for Fresh. To develop a prediction model, the company has gathered data concerning demand for Fresh over the last $30$ sales perlods $($each sales perlod is defined to be a four$-$week perlod$).$ The demand data are presented in $[.$jicture Excel Data File. For each sales perlod, let

$y=$ the dema$$d for the large size bottle of Fresh $($In hundreds of thousands of bottles$)$ In the sales period $($Demand$)$

$x_1=$ the price $($in dollars$)$ of Fresh as offered by Enterprise Industerles in the sales perlod

$x_2=$ the average industry price $($in dollars$)$ of competitors' similar detergents in the sales period

$x_3=$ Enterprise Industries' advertising expenditure $($in hundreds of thousands of dollars$)$ to promote Fresh in the sales period $($Advexp$)$

$x_4=$ the difference between the average industry price $($in dollars$)$ of competitors? similar detergents and the price $($in dollars$)$ of Fresh as offered by Enterprise Industries in the sales period $($PriceD$1$f$).($Note that $x_4=x_2-x_1.$

The JMP Output of a Regression Tree for the Fresh Detergent Demand Data

The JMP Predictions of Demand in Periods $31$ and $32$ Using the Fresh Detergent Regression Tree

Leaf

Number

The above Image and tables show the JMP outputs of a regression tree analysis of the Fresh demand data, where the response varlable is Demand and the predictor varlables are AdvExp and PriceDIf. The default minimum split size of $5$ was used. Find the JMP regression tree prediction of demand for Fresh in Future sales perlods $31$ and $32($Round your answers to $4$ decimal places.$)$

$\backslash$table$[[,$Predicted Demand$],[$Fresh in future sales period $31,,$hundred thousand bottles$],[$Fresh in future sales period $32,,$hundred thousand bottles$]]$