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. The correlation coefficient alone cannot be used as a measure of the appropriateness of a linear fit. Plotting the data to ascertain if a linear fit is appropriate is necessary. 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.
It is often the case that the relationship between two quantitative variables should not be summarized with a straight line. It may be the case that some nonlinear relationship is better. In addition, the methods of statistical inference in a regression framework assume that the variance is constant for different values of the explanatory x variable. Often, a plot of the data itself makes it clear when a nonlinear fit is more appropriate, or when nonconstant variance is a potential problem. Patterns in a residual plot indicate nonlinearity.