OpenStax - Ch. 12 Linear Regression and Correlation

Question 1

Coefficient of Correlation

Answer 1

a measure developed by Karl Pearson (early 1900s) that gives the strength of association between the independent variable and the dependent variable; the formula is:

r=nΣ(xy)−(Σx)(Σy)[nΣx2−(Σx)2][nΣy2−(Σy)2]−−−−−−−−−−−−−−−−−−−−−−−−−−√r=nΣ(xy)−(Σx)(Σy)[nΣx2−(Σx)2][nΣy2−(Σy)2]

where n is the number of data points. The coefficient cannot be more than 1 or less than –1. The closer the coefficient is to ±1, the stronger the evidence of a significant linear relationship between x and y.