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 r XY 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 r XY CaseXYzXzX zYzY zXzYzXzY 1303000 2104-1.414.707–1 3401.707-1.414–1 4502 1.414 -.707–1 5205 –.707 1.414–1 Mean30300.80

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 XY 303 104 401 502 205

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, r XY =.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.