One way to calculate the regression line is to use the
five summary statistics
,
,
,
,
and *r* (i.e. the mean and
SD of *X*, the mean and SD of *Y*, and the Pearson
correlation between *X* and *Y*.) The least squares regression line
is represented by the equation

where the slope

Consider the Saturn Price data. We let

Car Miles Price (X) (Y) 1 9300 7100 2 10565 15500 3 15000 4400 4 15000 4400 5 17764 5900 6 57000 4600 7 65940 8800 8 73676 2000 9 77006 2750 10 93739 2550 11 146088 960 12 153260 1025

Using the formulas for slope and intercept of the LS line, we get

so that the regression line is

In terms of the original variable names, we may write the regression line as

PREDICTED PRICE = 8136 -.05127 (MILES)