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)

Develop a scatterplot of the two variables: monthly output and monthly total costs. Describe the relationship.

Estimate a total cost curve for this company.  State the estimated total cost function.

Based on your estimated total cost curve what is the estimated Fixed Cost for the Company?

Based on your estimated total cost curve what is the estimated average unit variable cost for the Company?

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

What percent of the variation in monthly production costs is “explained” by the monthly production output?

Suppose the plant manager is interested in mean costs for several monthswhere output averages 30,000 units (i.e., Xp = 30). What is the predicted monthly total costs when output averages 30?  Construct a 95% confidence interval for the mean production 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

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.970683724
R Square	0.942226892
Adjusted R Square	0.940970955
Standard Error	64.25220388
Observations	48
ANOVA
	df	SS	MS	F	Significance F
Regression	1	3097160.098	3097160.098	750.2182035	3.98347E-30
Residual	46	189903.9024	4128.345704
Total	47	3287064
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	38.24585352	24.28492378	1.574880526	0.122137456	-10.63716267	87.12886971
Monthly Output	19.68525619	0.718699384	27.39011142	3.98347E-30	18.23858937	21.13192302

Develop a scatterplot of the two variables: monthly output and monthly total costs. Describe the relationship.

Estimate a total cost curve for this company. State the estimated total cost function.

Total cost = 38.2459 + 19.6853 * monthly output

Based on your estimated total cost curve what is the estimated Fixed Cost for the Company?

Fixed cost = intercept = 38.2459

Based on your estimated total cost curve what is the estimated average unit variable cost for the Company?

= average unit variable cost = slope = 19.6853

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

95% confidence interval for slope =(18.2386,21.1319)

What percent of the variation in monthly production costs is “explained” by the monthly production output?

R^2   = 0.942226892