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
• 𝑠𝑦𝑥 = 𝑠𝑦 1 − 𝑟 2 𝑥𝑦
• 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’