Explore BrainMass
Share

Explore BrainMass

    Introduction to Econometrics problem

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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.

    © BrainMass Inc. brainmass.com October 10, 2019, 3:11 am ad1c9bdddf
    https://brainmass.com/economics/econometric-models/introduction-econometrics-problem-410318

    Attachments

    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.

    $2.19