Correlation

The correlation of two variables is a measure of how the variables conform to a linear relationship. r is often used as the symbol for correlation.

The measure ranges from -1 to 1.

Possible values

• A positive correlation indicates that a high value for one variable predicts a high value for the other variable and a low value predicts a low value for the other variable. Here the pattern in the scatter plot shows an increasing line (positive slope).
• A negative correlation indicates that a high value for one variable predicts a low value for the other variable and a low value predicts a high value for the other variable. Here the pattern in the scatter plot shows a decreasing line (negative slope).
• A correlation of 0 shows no pattern in the form of a line.

Textbook process for calculating correlation

1. Calculate the standard scores for the values of both variables.
2. For each observation, calculate the product of the standard scores.
3. Sum the products and divide by n - 1.
4. The result of the division is the correlation.

Here's an Excel spreadsheet that demonstrates this process of calculating correlation.

Note: r² indicates the fraction that the regression equation accounts for the variance of y. It can be calculated as the ratio of the variance the predicted y values over the variance of the actual y values (see section 2.3 in text).