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 chi^{2} is chi^{2} = (1r^{2}) * SUM((y_{i}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 = N2.
The errors of the intercept and slope are the standard errors SE(a) and SE(b). See Wolfram. 
Creation Date: 06/9/2004
Last Modified: 11/5/2009
Mod Summary: