Residuals

Suppose we have a set of data pointsrelating one quantity to another. We can plot the points on a scattergraph and find the equation of the regression line ofonso thatis expressed linearly in terms ofIf we take one of the points from which the equation of the regression line was calculated,he regression line predicts, for a valuea valueThe residual is then

Residual

65.0 57.8 77.8 89.0 93.4 73.1 83.1 86.8 70  83

74.4 97.7 74.4 83.3 78.2 87.7 81.0 83.3 65.6 78.9

-9.4 -39.9 3.4 5.7 15.2 -14.6 2.1 3.5 4.4 4.1

The residuals add to zero, since

This might make it seem that they do not have much use, but in fact the sum of the squares of the residuals is an important statistical measure, enabling us to derive the equation of the regression line and to derive the normal distribution.