Calculating the least-squares line. Like to know the details when you study something? Here is the formula for the least-squares regression line for predicting y from x. Start with the means x and y and the standard deviations sx and sy of the two variables and the correlation r between them. The least-squares line has equation y = a + bx with slope: b = r sy sx intercept: a = y − bx Example 4 in Chapter 14 (page 296) gives the means, standard deviations, and correlation for the fossil bone length data. Use these values in the formulas just given to verify the equation of the least-squares line given on page 315:

humerus length = −3.66 + (1.197 × femur length)

The remaining exercises require a two-variable statistics calculator or software that will calculate the least-squares regression line from data.