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.

Production Volume $($units$)$

$400$

Total Cost $($$$)$

$4,100$

$450$

$4,900$

$550$

$5,300$

$600$

$5,900$

$700$

$6,400$

$750$

$7,100$

Use these data to develop an estimated regression equation that could be used to predict the total cost for a given production volume. $($Round your numerical values to two decimal places.$)$

$=$