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 assodiated 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 $($$$)],[400,4,700],[450,5,700],[550,6,100],[600,6,600],[700,7,100],[750,7,700]]$

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.

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.

s

c$.$ Compute the coefficient of determination $($to $3$ decimals$).$ Do not round intermediate calculations. Note: report $r^2$ between $0$ and $1.$

$r^2=$

What percentage of the variation in total cost can be explained by the praduction volume $($to $1$ dedimal$)?$ Do not round intermediate calculations.

$\%$

d$.$ The company's production schedule shows $500$ units must be produced next month, What is the estimated total cost for this operation $($to the nearest whole number$)?$ Do not round intermediate calculations.

$8$