Furthermore, a correlation coefficient near -1 or 1 does not, by itself, imply that a linear relationship by itself is most appropriate. A nonlinear curve could be a better description of the relationship. It may be interpreted as the proportion of the variability in y that is explained the regression. In other words, there is no variability around the regression line. For any line drawn through the points, the vertical distance from a point to the line is called a residual .
Residuals are positve for points above the line and negative for points below the line.
This line is called the least squares line . Notice that because residuals are measured vertically, it matters quite a bit which variable is designated x and which is y. The slope and intercept are determined by the mean and standard deviation of x and y and the correlation coefficient. You may think of the line as representing the average y value for all individuals in a population with a given x value. Note that the method of least squares will always provide a line, even when a nonlinear curve would be more appropriate.