A company would like to estima
A company would like to estimate its total cost equation. It hascollected 48 months of monthly production output and correspondingtotal production costs. The collected data is in the fileProduction Cost Data Only.xlsx. Recallthat
TOTAL COST = Fixed Costs + Variable Cost per Unit *Output.
Use the data to estimate a function that describes total costfor this company. (Round answers to 2 decimal places)
- State the estimated total cost function.
- What is the estimated Fixed Cost for the Company? Remember thefixed costs is independent of output. You can estimate it as theTotal Cost when output is “0”.
- What is the estimated average unit variable cost for theCompany?
- Develop a 95% confidence interval for the true average unitvariable cost.
- What percent of the variation in monthly total costs is“explained” by the regression model with monthly production outputas the explanatory variable?
- Suppose the plant manager is interested in estimating themean total costs for several months whereoutput is 30,000 units (i.e., Xp = 30) each month. Develop a 95%confidence interval for the mean total costs for months thataverage 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:
Sol:
in excel install analysis tool pak and then go to
data >data analysis>regression
you willl get
| SUMMARY OUTPUT | ||||||||
| Regression Statistics | ||||||||
| MultipleR | 0.970684 | |||||||
| RSquare | 0.942227 | |||||||
| AdjustedR Square | 0.940971 | |||||||
| StandardError | 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 |
- 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 theCompany=slope=
=19.69
Solution4:
a 95% confidence interval for the true average unit variablecost.
lies in between 18.23859 and 21.13192
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