An important application of regression analysis in accounting is in the estimation of cost$.$ By collecting data on volume and cost and using the least squares method to develop an estimated regression equation relating volume and cost, an accountant can estimate the cost associated with a particular manufacturing volume. Consider the following sample of production volumes and total cost data for a manufacturing operation.

$\backslash$table$[[$Production Volume $($units$),$Total Cost $($$$)],[400,3,500],[450,4,500],[550,4,900],[600,5,400],[700,5,900],[750,6,500]]$

a$.$ Use these data to develop an estimated regression equation that could be used to predict the total cost for a given production volume. Do not round intermediate calculations.

Compute $b_1$ and $b_0($to $1$ decimal$).$ Do not round intermediate calculations.

$b_1$

$b_0$

Complete the estimated regression equation $($to $1$ decimal$).$ Do not round intermediate calculations.

hat$(y)=+x$

b$.$ What is the variable cost per unit produced $($to $2$ decimal$)?$ Do not round intermediate calculations.

$