Least Squares in Matrices

We can also express the problem this way: Let A be a matrix with the n_i column as its first column and a column of all 1s for its second column. Let x be the column vector containing x₁ and x₂ and b be a column vector of the y_i values.

We want to find the x that minimizes (Ax-b)².

In this general form, we can also consider fitting other functions. For example, $x_1 n_i^2 + x_2 n_i + x_3 \approx t_i$ can be expressed by putting n_i² values in the first column of A, n_i in the second column of A, and 1s in the third column.