Least-squares regression line

The most common method of choosing the line that best summarises the linear relationship (or linear trend) between the two variables in a linear regression analysis is from the bivariate data collected.

Of the many lines that could usefully summarise the linear relationship, the least-squares regression line is the one with the smallest sum of the squares of the residuals.

Two other properties of the least-squares regression line are:

• The sum of the residuals is zero.
• The point with x-coordinate equal to the mean of the x-coordinates of the observations and with y-coordinate equal to the mean of the y-coordinates of the observations is always on the least-squares regression line.

Curriculum achievement objectives reference

Statistical investigation: Level 8

The quality of the images on this page may vary depending on the device you are using.