Page 147 - Quantitative Data Analysis

Quantitative Data Analysis
Simply Explained Using SPSS

Simple Regression Example # 3

Here are X and Y scores (the second, third, and fourth pairs of
columns are continuations of the first pair of columns):
X Y X Y X Y X Y
2 2 4 4 4 3 9 9
2 1 5 7 3 3 10 6
1 1 5 6 6 6 9 6
1 1 7 7 6 6 4 9
3 5 6 8 8 10 4 10

1. Means, sum of squares and cross products, standard
deviations, and the correlation between X and Y.
2. Regression equation of Y on X.
3. Regression and residual sum of squares.
4. F ratio for the test of significance of the regression of Y on X,
2
using the sums of squares (i.e., ss reg and ss res) and using r xy.
5. Variance of estimate and the standard error of estimate.
6. Standard error of the regression coefficient.
7. t ratio for the rest 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:
8. Each person’s predicted score, Y’, on the basis of the X’s.
9. The sum of the predicted scores and their mean.
10. The residuals, (Y - Y’); their sum, ∑( Y - Y’), and the sum of
2
the squared residuals, ∑( Y - Y’) .
11. Plot the data, the regression line, and the standardized
residuals against the predicted scores.
12. Provide SAS code and output to answer above problems
13. Interpret results

The Theory and Applications of Statistical Inferences 131