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$[[\backslash$table$[[$Production Volume$],[($units$)]],\backslash$table$[[$Total Cost$],[($ $$)]]],[400,4,600],[450,5,600],[550,6,000],[600,6,500],[700,7,000],[750,7,600]]$

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.$\text{'}$

$b_{1}q,$

$b_0$

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.

$ $$

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 production volume $($to $1$ decimal$)?$ 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.

$ $$