$($Appendix $3$A$)$ Method of Least Squares

Shafer Company has gathered data on its overhead activities and associated costs for the past $10$ months. Theodore, a member of the controller's department, has convinced management that overhead costs can be better estimated and controlled if the fixed and variable components of each overhead activity are known. One such activity is receiving raw materials $($unloading incoming goods, counting goods, and inspecting goods$),$ which he believes is driven by the number of receiving orders. Ten months of data have been gathered for the receiving activity and are as follows:

Month Receiving Orders Receiving Cost

$11,000$ $$18,000$

$270015,000$

$31,50028,000$

$41,20017,000$

$51,30025,000$

$61,10021,000$

$71,60029,000$

$81,40024,000$

$91,70027,000$

$1090016,000$

Suppose that Theodore has gathered two more months of data:

Month Receiving Orders Receiving Cost

$111,200$ $$28,000$

$1295017,500$

Note:For the following requirements, round the intercept terms to the nearest dollar, round the variable rates to the nearest cent, and R$2$ to two decimal places.

Required:

Download Excel spreadsheet

$1.$ Run two regressions using a computer spreadsheet program such as Excel. First, use the method of least squares on the first $10$ months of data. Then, use the method of least squares on all $12$ months of data. Select the results for the intercept, slope, and R$2$ for each regression. Enter the R$2$ values as decimals to two decimal places rather than as percentages.

Line Item Description $10$ Months' Data $12$ Months' Data

Intercept $fill in the blank $1$

$fill in the blank $2$

Slope fill in the blank $3$

$15\mathrm{.}15$

fill in the blank $4$

$15\mathrm{.}10$

R$2$ fill in the blank $5$

fill in the blank $6$

$2.$ Conceptual Connection: On your own paper, prepare a scattergraph using all $12$ months of data. Which month appears to be an outlier?

fill in the blank $1$ of $1$

$3.$ Conceptual Connection: Rerun the method of least squares, using all the data except for Month $11.($You should now have $11$ months of data.$)$ What is the variable rate $($to the nearest cent$)$ and the fixed cost that would be used in a cost formula for receiving based on these results?

Variable rate fill in the blank $1$ of $1$$

per receiving order

Fixed cost fill in the blank $1$ of $1$$

Calculate the predicted receiving cost for a month with $1,450$ receiving orders. In your calculations, round variable cost per unit to two decimal places. Round your final answer to the nearest dollar.