How does one calculate the coefficient of determination for the least squares approximation? In the book and lectures, the error vector e = b - p is the only measure of fit I can find.

Question

How does one calculate the coefficient of determination for the least squares approximation?  In the book and lectures, the error vector e = b - p is the only measure of fit I can find.

datanewb · Answer

For the best fit linear equation y = C + Dt, the values of constants C & D can be found for a sample of data points by this equation:

$$A ^{T}A \hat x = A^{T}b$$ where $$\hat x\ = \left[\begin{matrix}C \ D\end{matrix}\right]$$
This is discussed on page 222 of the text, and finding the best fit line and the error vector is fairly clear to me.  Linear algebra must give the commonly used coefficient of determination, r-squared, somehow.