# Tech Note 495 Detail

## Correlation Coefficient

Affected Products:
Problem/Symptom:
What are the linear fit parameters?

PASCO Solution:

r is defined as the linear correlation coefficient. It may have any value between -1 and 1. r represents the degree to which the change in one value effects the change in the other.

For unweighted data the relationship between r and the goodness of fit measure chi2 is

chi2 = (1-r2) * SUM((yi-y)2)

, where

The significance of r can be hard to interpret; a small data set can have a relatively high linear correlation coefficient, but we should have no confidence that the two are correlated because of the small sample size.

A quantity that is easier to interpret is the probability that a set of data with N points and a given correlation coefficient r is correlated. The probability of correlation is called the p value or significance. We can determine the p value from a correlation table, where the number of degrees of freedom f = N-2.

• yi is the value of the ith measurement
• y is the mean value of the yi
• r is the linear correlation coefficient.

The errors of the intercept and slope are the standard errors SE(a) and SE(b). See Wolfram.

Creation Date: 06/9/2004