Here are X and Y scores (the second, third, and fourth pairs of columns are continuations of the first pair of columns):
Calculate the following:
(a) Means, sums of squares and cross products, standard deviations, and the correlation between X and Y.
(b) Regression equation of Y on X.
(c) Regression and residual sum of squares.
(d) F ratio for the test of significance of the regression of Y on X, using the sums of squares (i.e., SSreg
and SSres
) and using
.
(e) Variance of estimate and the standard error of estimate.
(f) Standard error of the regression coefficient.
(g) t ratio for the test of the regression coefficient. What should the square of the t equal? (That is, what statistic calculated above should it equal?) Using the regression equation, calculate the following:
(h) Each person's predicted score, Y', on the basis of the X's.
(i) The sum of the predicted scores and their mean. 0) The residuals, (Y - Y'); their sum, Σ(Y - Y'), and the sum of the squared residuals, Σ(Y - y')2
.
(k) Plot the data, the regression line, and the standardized residuals against the predicted scores.