CHOOSING THE BEST LINE

Thinking back to the last chapter, you will remember that the correlation coefficient was based on how closely points cluster about "a line." We did not say anything about how we selected the line shown on the plots. We will consider that now. When the correlation coefficient is +1 or -1, all the data points fall on a single line. All you have to do is connect the points and you have a line. You do not have to worry about choosing a line. When the observations are not perfectly correlated, many different lines may be drawn through the data. How do we choose among them? Since we want a line that describes the data, it should be as close as possible to the points. "As close as possible" can be defined in different ways. The most commonly used method for determining the line is called the method of least squares. The least squares line is the line that has the smallest sum of squared vertical distances from the observed points to the line.