Correlation

Abstract

In Chapter 5 we saw that, when a variable y is dependent on a non-random variable x, we can find the equation of the regression line of y on x, using the method of least squares, and, from this equation, estimate the value of y for a given x value. If we have a sample of data giving us the leg and arm lengths of 20 men, we cannot say that leg length is dependent on arm length, nor that arm length is dependent on leg length. In a problem of this kind, all we can consider is the amount of relationship between the two variables, arm length and leg length. This is a problem of correlation; we try to answer the question ‘Is there any relationship between the two variables and, if so, to what degree are they related?’ To do this, we try to determine how well an equation (and we consider only linear equations) represents the relationship between the two variables.