Tech Note 495 Detail
What are the linear fit parameters?
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)
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.
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