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$)$ Total Cost $($$$)$

$4004,000$

$4505,000$

$5505,400$

$6005,900$

$7006,400$

$7507,000$

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 and $($to decimal$).$

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

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

c$.$ Compute the coefficient of determination $($to decimals$).$ Do not round intermediate calculations. Note: report between and $.$

What percentage of the variation in total cost can be explained by the production volume $($to decimal$)?$ Do not round intermediate calculations

d$.$ The company's production schedule shows units must be produced next month. Predict the total cost for this operation $($to the nearest whole number$).$ Do not round intermediate calculationsAn 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.

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$).b_1$

$b_0$

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

$

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. Predict the total cost for this operation $($to the nearest whole number$).$ Do not

round intermediate calculations