# What does residual mean in the context of minimizing a function?

equation 1.2 in PRML: pattern recognition and machine learning

denotes the sum of the squares of the errors between the predictions $$y(x_n,w)$$ and the corresponding target values $$t_n$$.

$$w^*$$ denotes a unique solution for the error function above.

page 6 of that book says

For each choice of M, we can then evaluate the residual value of E($$w^*$$) given by (1.2) for the training data

is residual a math term or machine learning term? what does residual here mean?

I've searched differentiate residual, the result is more confusing.

could someone please give some explanation about residual in this case (equation 1.2)

please provide a solid reference, such as a textbook, for the definition of residual.