Correlation-Regression

1. Correlation-Regression The correlation coefficient measures how well one can predict X from Y or Y from X

2. Correlation Coefficient • Formula for correlation coefficient:

3. Computing rXY • Convert each raw score, X, to a standard score • Convert each raw score Y, to a standard score • Find the product of z-scores for each case. • Find the average product, by summing these products and dividing by n.

4. Example Computing rXY

5. Summary: Computing correlations • If means and standard deviations are not given, compute them for X and Y. • Find the z-score for each value of X • Find the z-score for each value of Y • Compute the product of z-scores for each case. • Find the average of these products.

6. Drawing a Scatterplot

7. Correlation from Scatterplots • By examining the scatterplot, one can estimate the correlation coefficient. • In this case, small values of X go with large values of Y and vice versa. • Thus, we see from the graph that the correlation is negative. • The graph shows a relation that is not perfect, but is highly predictable.

8. Percentage of Variance Reduced • How “high” is a correlation? • To answer this, square the correlation coefficient. The squared coefficient measures the percentage of variance that would be reduced by knowing X and using it to predict Y from the best linear formula. • In our example, rXY = .8; the squared value is .64. Would you go shopping if everything is 64% off today?

9. Next Topic: Prediction (Regression) Equation • Once one knows the value of the correlation coefficient, one can then compute a prediction from X to Y, or one can use Y to predict X. • The next lesson will show how to calculate a prediction from one variable to another.