# Introduction to Econometrics problem

Please see the table attached to use for the two questions below. Thank you.

Q1) Calculate the R-squared in column (2), (3),(4), and (5) and use:

R(squared) = 1 - (SSR/TSS).

R(hat)(squared) = 1 - (n - 1/n - k - 1)(SSR/TSS)

to find out the relationship between the adjusted R-squared (given in the table) and R-squared.

Q2) Explain your results.

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#### Solution Preview

First we calculate the required items, and then we discuss our results.

To begin, we find the relationship between R^2 and R(bar)^2. (note that the adjusted R^2 is usually denoted as R(bar)^2, not R(hat)^2.)

Note that R^2 = 1 - SSR/TSS implies 1 - R^2 = SSR/TSS.

Thus, R(bar)^2 = 1 - (n - 1/n - k - 1)(SSR/TSS) = 1 - (n - 1/n - k - 1)(1 - R^2).

Usually, we don't expand the term (n - 1/n - k - 1)(1 - R^2) for ease of calculation.

Now, we use the relationship R(bar)^2 = 1 - (n - 1/n - k - 1)(1 - R^2) to calculate the R^2's in column 2, 3, 4 and 5. Recall that n is sample size (=420 for all columns) and k is the number of regressors, which are 2, 3, 3, 4 respectively.

(2) R(bar)^2 = 0.424 = 1 - (419/417)(1 - R^2), this implies R^2 = 0.4267.

(3) R(bar)^2 = 0.773 = 1 - (419/416)(1 - R^2), this ...

#### Solution Summary

The introduction to econometric problems are given. The relationship between the adjusted R-squared and R-squared adjusted are determined.

Econometrics, Regression, Tariffs

1) Consider a competitive market where inverse supply and demand are given by:

D: P = 160-2Q

S: P = 50+3Q

A) Solve for the equilibrium price.

B) If a $10 per unit tax is placed on this good, how much of the tax is paid by consumers? How much of the tax is paid by the firm? Show your work and explain in a sentence or two.

2) If you want to estimate the demand for a product, is it OK to regress Quantity on Price (and perhaps a few other variables) and interpret the results as the demand curve? Explain clearly.

3) We know that the minimum efficient scale of production varies widely across industries. How might the minimum efficient scale affect the level of competition in these industries? Explain in a few sentences.

4) The regression results below are for a company's sales. Quantity sold at various stores was regressed on the price charged at that store and average per capita income for the customers of that store. The results are reported below. (Assume the reported results are valid.)

SUMMARY OUTPUT

Regression Statistics

Multiple R 0.83

R Square 0.68

Adjusted R Square 0.68

Standard Error 1.25

Observations 100.00

ANOVA

Df SS MS F Significance F

Regression 2.00 324.81 162.40 104.40 6.52225E-25

Residual 97.00 150.89 1.56

Total 99.00 475.70

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%

Intercept 1.47 13.48 0.11 0.9136 -25.28 28.21

PRICE -0.50 0.05 -9.58 1.08078E-15 -0.60 -0.39

INCOME 2.04 0.22 9.39 2.79372E-15 1.61 2.47

A) Interpret the price and income coefficients. Explain clearly in a couple of sentences. Are the coefficients significant? Explain.

B) The standard error for the income coefficient was .22. If the standard error had been 1.5 would our estimate of 2.04 be significant? Explain.

5) In class we talked about why tariffs on imports usually reduce welfare. We also noted that the reason why tariffs are often used is that the government wants to protect or assist a particular domestic industry.

A) Explain why tariffs on imports reduce welfare and also use a graph to demonstrate your answer.

B) Instead of using a tariff to assist a domestic industry, suppose that the government used a production subsidy to assist firms. For instance the government might pay a per-unit subsidy to domestic firms for every unit produced domestically. (A subsidy is just a negative tax.) Why might the production subsidy result in higher welfare for the country than the tariff policy in part A? Explain clearly. Again, a graph might make your answer more clear.

6) Congress is considering legislation that will provide additional investment tax credits to businesses. Effectively, an investment tax credit reduces the cost to firms of using capital in production. Would you expect labor unions to lobby for or against such a bill? Explain clearly.

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