POLS 6482 ADVANCED MULTIVARIATE STATISTICS
Fourth Assignment
Due 1 October 2001

This Homework assumes that you have read Chapters I and II of the Epple Notes!

  1. This problem is a continuation of the party identification problem that was part 1 of the 2nd Homework Assignment.

    1. Compute the correlation matrix for the variables education, income, and age for both the 1968 and 1996 datasets. Interpret the changes in the correlations between 1968 and 1996. Do the changes make sense to you? Why? Why not?

    2. Find the eigenvalues and eigenvectors of the correlation matrix for both 1968 and 1996. Use the method shown in 3.b. of the 2nd homework.

  2. This problem is a continuation of 1.c of the 3rd homework. Bring up the EVIEWS version of HDMG105X.DTA from the 3rd homework. Run the regression:

    LS clint96 C black south hisp income rep

    and save the residuals by copying them to another vector; namely:

    genr clintresid=resid

    1. Compute the correlation matrix between clintresid, black, south, hisp, income, and rep. What should the values of the correlations between clintresid and the other variables be? Why?

    2. In EVIEWS you can generate the fitted values of the dependent variable (the y-hats) with the forecast command. For the regression above:

      forecast clintyhat

      and EVIEWS puts the y-hats into the vector clintyhat. (In Stata the corresponding command is predict clintyhat.) Calculate the correlation between clintyhat, clintresid, black, south, hisp, income, and rep. What should the values of the correlations between clintyhat and the other variables be? Why?

    3. In EVIEWS use the HIST command on clintresid. What famous probability distribution does the histogram look like?

    4. In EVIEWS use the SCAT command to get scatterplots of clintresid versus black, hisp, and income. The syntax of the command is:

      scat black clintresid

      which makes black the "x" axis and clintresid the "y" axis of the scatterplot. Do these scatterplots look random to you?

    5. In EVIEWS run the regression:

      LS clint96 C clintresid

      Compare the coefficients and r-square to the original regression. Explain the values of the coefficients. Explain the value of the r-square.