Question

A company would like to estimate its total cost equation using customer records.  The company has randomly sampled 28 customer records. Each customer record contains a Customer #, the Order Size, and the Total Cost of the Order.  The analyst remembers from accounting and economics classes taken in college that

TOTAL COST = Fixed Costs + Variable Cost per Unit *Order Size.

The analysis sees that this is a linear relationship where the TOTAL COST depends on the Fixed Costs, which do not depend on order size, and a variable cost per unit, which is multiplied by the Order Size.  The analysis decides to use simple linear regression to estimate the firm’s Total Cost function.  Use the data file, Estimating a Total Cost Regression Model.xlsx to answer the following questions:

1. What is the dependent variable in this analysis? What is the independent variable in this analysis?
2. Use excel to estimate the regression model.  State the estimated total cost function.
3. What is the estimated Fixed Cost for the Company? Remember the fixed costs is independent of output. You can estimate it as the Total Cost when output is “0”. (Look at the regression output produced by Excel for part b.)
4. What is the estimated average unit variable cost for the Company? (Look at the regression output produced by Excel for part b.)

Customer #	Order Size (Quantity)	Total Cost of Order
10211	28	1631
10212	31	1923
10213	43	2070
10214	47	2392
10215	32	1886
10216	43	2307
10217	25	1486
10218	46	2448
10219	41	2210
10220	48	2401
10221	29	1860
10222	32	1786
10223	49	2485
10224	44	2203
10225	33	1855
10226	46	2380
10227	42	2102
10228	31	1683
10229	30	1706
10230	35	1955
10231	34	1992
10232	33	1926
10233	27	1852
10234	32	1807
10235	31	1880
10236	42	2134
10237	39	1979
10238	36	1882

Answer 1

a.) Looking at the equation

Total Cost = Fixed Costs + Variable Cost per unit*Order Size.

We can infer that Total Cost is the dependent variable and Order Size is the independent variable, As order size changes, the total cost also changes.

b.) Using Excel, we get the cost function as follows:

y = 34.891x + 725.64

where y stands for Total Cost function and x stands for the size of the order.

Refer below image for clarification:

Procedure for getting the equation:

1.) Put the data in excel

2.) Select two columns order size and total cost

3.) Insert Scatter Plot

4.) Then click on format and choose more trendline options under the trendline tab

5.) Choose the linear regression type and select the display equation on the chart and you will be able to see the equation on the chart as in the above figure

c.) Estimated Fixed Cost for the company as per below equation

y = 34.891x + 725.64

Fixed Cost = $ 725.64

d.) Estimated Variable Cost for the Company is $34.891 / unit.