Introduction to Prediction (1 of 3)

When two variables are related, it is possible to predict a person's score on one variable from their score on the second variable with better than chance accuracy. This section describes how these predictions are made and what can be learned about the relationship between the variables by developing a prediction equation. It will be assumed that the relationship between the two variables is linear. Although there are methods for making predictions when the relationship is nonlinear, these methods are beyond the scope of this text.

Given that the relationship is linear, the prediction problem becomes one of finding the straight line that best fits the data. Since the terms "regression" and "prediction" are synonymous, this line is called the regression line.

The mathematical form of the regression line predicting Y from X is:

Y' = bX + A

where X is the variable represented on the abscissa (X-axis), b is the slope of the line, A is the Y intercept, and Y' consists of the predicted values of Y for the various values of X.