Edited sentence: For example:.Here the “best” will be understood as in the least-squares approach: such a line that minimizes the sum of squared residuals of the model.Horizontal bar over a variable means the sample average of that variable.If  0 ≤ rxy < 1 ,then we say that the data points exhibit regression toward the mean.In other words, numbers α and β solve the following minimization problem:.Substituting the above expressions for  and  into.Suppose there are n data points {yi, xi}, where i = 1, 2, …, n.This shows the role  plays in the regression line of standardized data points.Using simple calculus it can be shown that the values of α and β that minimize the objective function Q are.We want to find the equation of the straight line.where rxy is the sample correlation coefficient between x and y, sx is the standard deviation of x, and sy is correspondingly the standard deviation of y.which would provide a  “best” fit for the data points