Q TVC From the data aboce, assume it represents represents total variable costs

Question

Q

TVC

From the data aboce, assume it represents represents total variable costs of production across 39 different weeks producing different levels of output.

Use TVC and Q to calculate AVC.

Use Regression tool to estimate an average variable cost function of the form AVC=a+bQ+cQ2. Be sure to note which variable is the dependent variable. If only Q is provided, make sure you create an additional column and calculate Q2. REMINDER: the independent variables should be located in adjacent columns so you can easily highlight the data as you enter it in the Regression dialog box. Based on the results:

a. Is the regression model statistically significant?

b. Write the estimated regression equation.

c. Are the coefficients statistically significant?

d. How large is the coefficient of determination (r2)?

e. How large is s?

f. How can the estimated AVC equation be converted to an estimated TVC equation?

g. If the current fixed cost of capital is $5,000, what is the TC equation?

Now consider an average variable cost function of the form AVC=a+bQ. Use Microsoft Excel’s Regression tool to estimate the equation. Based on the results:

h. Write the estimated regression equation.

i. Is the estimated slope coefficient statistically significant?

j. How large is the coefficient of determination (r2)?

k. How large is s?

l. Based on the results, which model provides a better “fit”?

Q

TVC

150 1905 150 1865 150 1835 150 1895 150 1875 150 1885 150 1805 150 1885 150 1815 150 1925 200 2200 200 2260 200 2220 200 2130 200 2240 200 2150 200 2180 200 2230 200 2180 200 2160 225 2385 225 2325 225 2335 225 2325 225 2275 225 2365 225 2285 225 2345 225 2265 225 2335 175 1970 175 1990 175 2070 175 2020 175 1980 175 2050 175 1990 175 2010 175 1990

Explanation / Answer

When we regress the average variable cost in which AVC is dependent variable and Q and Q^2 are independent variables. we got the following result.s

lm(formula = Cost$AVC ~ Cost$Q + Cost$Q.2)

Coefficients:

              Estimate Std. Error t value Pr(>|t|)   

(Intercept) 21.0307302 1.9635338 10.711 9.62e-13 ***

Cost$Q      -0.0771862 0.0213238 -3.620 0.000899 ***

Cost$Q.2     0.0001323 0.0000568   2.328 0.025627 *

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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.2216 on 36 degrees of freedom

Multiple R-squared: 0.9314, Adjusted R-squared: 0.9275

F-statistic: 244.2 on 2 and 36 DF, p-value: < 2.2e-16

a) model is statistically significant because the overall p-value is very low ( p-value: < 2.2e-16) it shows that model is significant.

b) estimated regression model : AVC= 21.0307 -0.0771Q + 0.0001323Q^2

c) coefficient are statistically significant. T value is 10.711. that is at 0.0001% level of significance it is significant. Or p-value is very low . see it in above result.

d) R-squared is 0.9314. it means 93.14% of AVC explained by the model

Q TVC AVC (TVC/Q) Q^2 150 1905 12.70 22500 150 1865 12.43 22500 150 1835 12.23 22500 150 1895 12.63 22500 150 1875 12.50 22500 150 1885 12.57 22500 150 1805 12.03 22500 150 1885 12.57 22500 150 1815 12.10 22500 150 1925 12.83 22500 200 2200 11.00 40000 200 2260 11.30 40000 200 2220 11.10 40000 200 2130 10.65 40000 200 2240 11.20 40000 200 2150 10.75 40000 200 2180 10.90 40000 200 2230 11.15 40000 200 2180 10.90 40000 200 2160 10.80 40000 225 2385 10.60 50625 225 2325 10.33 50625 225 2335 10.38 50625 225 2325 10.33 50625 225 2275 10.11 50625 225 2365 10.51 50625 225 2285 10.16 50625 225 2345 10.42 50625 225 2265 10.07 50625 225 2335 10.38 50625 175 1970 11.26 30625 175 1990 11.37 30625 175 2070 11.83 30625 175 2020 11.54 30625 175 1980 11.31 30625 175 2050 11.71 30625 175 1990 11.37 30625 175 2010 11.49 30625 175 1990 11.37 30625

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