Question

A company would like to estimate its total cost equation. It has collected 48 months of monthly production output and corresponding total production costs. The collected data is in the file Production Cost Data Only.xlsx. Recall that

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

Use the data to estimate a function that describes total cost for this company. (Round answers to 2 decimal places)

1. State the estimated total cost function.
2. 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”.
3. What is the estimated average unit variable cost for the Company?
4. Develop a 95% confidence interval for the true average unit variable cost.
5. What percent of the variation in monthly total costs is “explained” by the regression model with monthly production output as the explanatory variable?
6. 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.

Monthly Output (in thousands of units)	Monthly Total Production Cost (in thousand $)
47	926
45	888
42	841
43	888
42	863
42	898
41	885
48	911
41	812
40	837
39	845
39	856
40	858
38	852
39	877
39	926
37	915
37	841
37	812
37	833
36	822
38	809
37	769
38	783
41	745
38	716
39	656
39	620
37	616
35	771
34	754
34	703
32	667
31	643
28	540
25	502
20	436
17	380
14	314
13	294
10	290
10	190
9	203
8	176
8	192
6	149
5	114
4	126

Answer 1

Sol:

in excel install analysis tool pak and then go to

data >data analysis>regression

you willl get

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.970684
R Square	0.942227
Adjusted R Square	0.940971
Standard Error	64.2522
Observations	48
ANOVA
	df	SS	MS	F	Significance F
Regression	1	3097160	3097160	750.2182	3.98E-30
Residual	46	189903.9	4128.346
Total	47	3287064
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	38.24585	24.28492	1.574881	0.122137	-10.6372	87.12887	-10.6372	87.12887
nthly Output (in thousands of units)	19.68526	0.718699	27.39011	3.98E-30	18.23859	21.13192	18.23859	21.13192

1. State the estimated total cost function.

Monthly Total Production Cost=38.25+19.69*monthly Output

Solution2:

What is the estimated Fixed Cost for the Company

=y intercept=38.25

38.25

Solution3:

the estimated average unit variable cost for the Company=slope=

=19.69

Solution4:

a 95% confidence interval for the true average unit variable cost.

lies in between 18.23859 and 21.13192