Hello everyone, could you please help me with the following problem? In the data

Question

Hello everyone, could you please help me with the following problem?

In the data above, assume this data represents total variable costs of production across 39 different weeks producing different levels of output.

Use TVC and Q to calculate AVC.

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. 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”?

Thank you!

K-1 APof LMP ofL 25 25.0 5 17.5 43 14.3 50 12.9 11.2 61 10.2 66 9.4 71 8.9 K-2 AP of L MP of L 35 35.0 50 25. 61 20.3 79 15.8 87 14.S 94 13.4 00 12.5 K-3 AP of L MP of L 3 43.0 61 30.5 75 25.0 87 21.8 9719.4 14 106 17.7 7 115 16.4 122 15.3 K-4 APof L MP of L 50.0 71 35.5 87 29.0 100 25.0 112 22.4 122 20.3 713218.9 141 17.6 21

Explanation / Answer

a) To calculate AVC using TVC and Q we can divide AVC by Q therefore it will be AVC = TVC/Q as given in problem as AP of L

b) To find AVC=a+bQ+cQ^2 we need Q and Q^2 as they are indepdent variables and AVC is dependent variable. In the given data in question we can use K=1 column values as Y and APL values as Q and square of it as Q^2 and run the regression which will give us the following equation

AVC = -9.18822X1 + 0.19085*Q + 135.7711*Q^2

c) The regression coefficient t-value for both the variables is greater than 2 therefore using the 2t thumb rule we can say both are variables are statistically significant.

d) THe estimated regession equation as mentioned above will be ? = -9.18822X1 + 0.19085X2 + 135.7711 that is AVC = -9.18822X1 + 0.19085*Q + 135.7711*Q^2

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