Least Squares

Data as an Exact Table

The book starts with data as rows, not with a fitted curve. The target column is shown beside the input column so every later computation has a visible source.

highlighted = computed this step

Rows and labels

Each row stores a leading 1, then x, then y. The shown points are (0, 1), (1, 3), (2, 2), and (3, 5).

row=[1,x,y]\text{row}=[1,x,y]
Design matrix with targetExact rows split into a leading column, x, and target y.Design matrix with target101113122135

Why this table matters

The leading 1 is the intercept column. It lets the same matrix store both the vertical shift and the slope.

β=[ab]\beta=\begin{bmatrix}a\\b\end{bmatrix}
Design matrix with targetExact rows split into a leading column, x, and target y.Design matrix with target101113122135

Summary

The table is exact data, not sampled noise. The displayed data are exact integers; no noise model is added.

exact rows, exact target\text{exact rows, exact target}
Design matrix with targetExact rows split into a leading column, x, and target y.Design matrix with target101113122135