# RSS, OLS Residuals

From a cross-section sample on average costs (C) and output (O) for 30 firms (10 small, 10 medium and 10 large) the following OLS estimates were obtained...

a) How do I Interpret the estimated equations and use an F Test to test the hypothesis that there is no difference in the cost functions for small, medium and large firms. What assumptions does this test require? Is there any evidence given above that these assumptions are violated and how would I explain this?

(b) How can I plot the estimated functions for small, medium and large firms with Output varying between 0 and 25. What conclusions can I draw from this?

(c) Would it make sense to estimate the model connecting average costs and output for all firms by including dummy variables? Explain.

(Please see attachment for full question)

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#### Solution Summary

OLS estimates are obtained.

Bivariate data

Please see the attached file for full problem description.

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Bivariate data obtained for the paired variables and are shown below, in the table labelled "Sample data." These data are plotted in the scatter plot in Figure 1, which also displays the least-squares regression line for the data. The equation for this line is .

In the "Calculations" table are calculations involving the observed values, the mean of these values, and the values predicted from the regression equation.

Sample data

X Y

56.3 58.2

60.6 60.1

66.1 65.7

68.6 64.7

75.7 77.0

Calculations

- 2 ^ - 2 - 2

(y - y) (y - y) (y - y)

2.0678 70.1909 48.1636

0.4956 18.8009 25.4016

0.0751 0.6956 0.3136

13.1334 10.1379 0.1936

4.0080 97.1802 140.6596

19.7799 197.0054 214.7320

Answer the following:

1. The variation in the sample y values that is explained by the estimated linear relationship between x and y is given by the ____

a. Regression sum of squares

b. error sum of squares

c. total sum of squares

which for these data is ___

a. 197.0054

b. 214.7320

c. 19.7799

2. The proportion of the total variation in the sample y values can be explained by the estimated linear relationship between x and y is___ (Round your answer to at least two decimal places.)

3. The least-squares regression line given above is said to be a line which "best fits" the sample data. The term "best fits" is used because the line has an equation that minimizes the ___

a. regression sum of squares

b. error sum of squares

c. total sum of squares

which for these data is ___

a. 197.0054

b. 214.7320

c. 19.7799

4. For the data point (56.3, 58.2), the value of the residual is ___ (Round your answer to at least two decimal places.)

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