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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.

The data on the production volume $x$ and total cost $y$ for particular manufacturing operation were used to develop the estimated

regression equation hat$(y)=1200\mathrm{.}00+7\mathrm{.}07x.$

a$.$ The company's production schedule shows that $700$ units must be produced next month. Predict the total cost for next month.

hat$(y{)}^{**}={}_{(to2\text{d}\text{e}\text{c}\text{i}\text{m}\text{a}\text{l}\text{s})}$

b$.$ Develop a $99\%$ prediction interval for the total cost for next month.

$t-$value

$($to $3$ decimals$)$

$s_{\text{p}\text{r}\text{e}\text{d}}$

$($to $2$ decimals$)$

Prediction Interval for an individual Value next month

I

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.

Based on one month, $$6,000$

outside the upper limit of the prediction interval. A sequence of five to

seven months with consistently high costs should cause concern.

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