The following summary statistics, which I took from Study Suggestion 1 in Chapter 5, are presented in the format I used in Table 5.2. That is, diagonal elements are sums of squares, elements above the diagonal are sums of cross products, and elements below the diagonal are correlations. The last line contains standard deviations.
Use matrix algebra to do the calculations indicated, and compare your results with those I obtained in Chapter 5. Calculate the following:
(a) The inverse of the matrix of the sums of squares and cross products of the X's: (X’dXd)-I.
(b) (XdXd)-1XdYd, where XdYd
is a column of the cross products of the X's with Y. What is the meaning of the resulting values?
(c) The standardized regression coefficients (ß’s), using the b's obtained in the preceding and the standard deviations of the variables.
(d) b'Xdyd, where b' is a row vector of the b's obtained previously. What is the meaning of the ob-
tained result?
(e) The residual sum of squares, and
12.
(f)
12
(X’dXd)-1
What is the resulting matrix?
(g) The t ratios for the b's, using relevant values from the matrix obtained under (0.
(h) (1) the increment in the regression sum of squares due to X1, over and above X2, and (2) the increment in the regression sum of squares due to X2, over and above X1. For the preceding, use the b's and relevant values from (XdXd)-1.
(i)
12
and the F ratio for the test of R2. (N = 20.) If you have access to a matrix procedure, replicate the previous analyses and compare the results with those you got through hand calculations.