# 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.