# 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)

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

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
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 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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