Question

In: Statistics and Probability

Customer # Order Size (Quantity) Total Cost of Order 10211 28 1631 10212 31 1923 10213...

*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

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:

What is the dependent variable in this analysis? What is the independent variable in this analysis?
Use excel to estimate the regression model. State the estimated total cost function.
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.)
What is the estimated average unit variable cost for the Company? (Look at the regression output produced by Excel for part b.)
Develop a 95% confidence interval for the true average unit variable cost. (Look at the regression output produced by Excel for part b.)
What percent of the variation in monthly total costs is “explained” by the regression model with monthly production output as the explanatory variable? (Look at the regression output produced by Excel for part b.)
Suppose the plant manager is interested in estimating the mean total costs for several months where output is 30,000 units (i.e., Xp = 30) each month. Develop a 95% confidence interval for the mean total costs for months that average 30,000 units of output.

Expert Solution

(a) Total Cost is the dependent variable and the order size is the independent variable.

(b) Steps: Enter the data correctly into the excel sheet from A1. Now go to Data, select Data Analysis and then select Regression. In the new dialogue box which appears, enter the Y range as $C$1:$C$29 and the X range as $B$1:$B$29, check the check boxes of Labels, Confidence interval and give it as 95%. Click on OK.

The estimated regression equation is :

(c) Hence, the estimated fixed cost is obtained as 725.6413209

(d) The estimated average unit variable cost for the company is 34.89119826.

(e) The upper 95% of the confidence interval for the true average unit variable cost for the company is

39.85841299

The lower 95% of the confidence interval for the true average unit variable cost for the company is

29.92398354

Thus the 95% confidence interval for the true average unit variable cost for the company is (29.92398354,39.85841299)

(f) The SS due to regression is

1683962.625

and the total SS is

1893978.679

Hence the required percentage is

(g) Enter the revised output as 30 for the entire dataset. Carry out the regression in the same way as instructed in (a) with the revised output as the independent variable. Hence the 95% confidence interval for the intercept, equivalent to the mean total is then given by:

Lower 95%	Upper 95%
1903.065665	2112.72005

Hopefully this will help you. In case of any query, do comment. If ou are satisfied with the answer, give it a like. Thanks.

orchestra answered 1 year ago

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