$1$ Review Assignment $11$

$6.6$

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 $($$$)],[400,4100],[500,4700],[600,5400],[650,6300],[750,6800],[800,7200]]$

equation hat$(y)=798\mathrm{.}53+8\mathrm{.}03x.$

a$.$ The company's production schedule shows that $550$ units must be produced next month. Predict the total cost for next month.

hat$(y{)}^{**}=$

$($to $2$ decimals$)$

b$.$ Develop a $95\%$ prediction interval for the total cost for next month.

$($to $2$ decimals$)$

$($to $3$ decimals$)$

$($to $2$ decimals$)$

Prediction Interval for an individual Value next month

$$

$$

$($to whole number$)$

c$.$ If an accounting cost report at the end of next month shows that the actual production cost during the month was $$6,000,$ should managers be concerned about incurring such a high total cost for the month? Discuss.