Adding a quadratic term

An alternative solution to the problem of curvature is to extend the simple linear model with the addition of a quadratic term,

y  =  b0  +  b1 x  +  b2 x2

Fitted values and residuals are defined (and interpreted) in a similar way to those for a linear model,

  =  b0  +  b1 xi  +  b1 xi2
ei  =  yi

As in a linear model, the quadratic model's residuals are the vertical distances between the crosses in a scatterplot and the curve. We again use least squares to estimate the unknown parameters — choose values of the three parameters to minimise the residual sum of squares,