Correlation and Prediction Error

• The amount of prediction error is associated with the strength of the correlation between X and Y

Distribution of Prediction Error

• Prediction error is the extent that an actual score deviates from the predicted score– Prediction error is normally distributed and has a

standard deviation– The standard error of prediction (or standard error

of the estimate) is the standard deviation for prediction error

Formula for Standard Error of Prediction

• Standard Error of Prediction is calculated with the following formula

• The standard error of prediction is influenced by – The strength of the relationship between X and Y – The variability in Y

Visual Depiction of Standard Error

• Influence of correlation coefficient on standard error of prediction

• Standard deviation of Y

Confidence Intervals

• The standard error of prediction can be used to calculate a confidence interval for Y’