Building the Normal Equations - Linear Regression (Least Squares)

The system entries are sums of the shown data. This lesson assembles those sums before any solving happens.

highlighted = computed this step

The entries are sums

The exact sums are n=4, sum x=6, sum y=11, sum x times x=14, and sum x times y=22.

n,\sum x,\sum y,\sum x\cdot x,\sum xy

Placing those sums into X-transpose X and X-transpose y gives the displayed system.

\begin{bmatrix}n&\sum x&\sum y\\\sum x&\sum x\cdot x&\sum xy\end{bmatrix}

The assembly step is exact integer arithmetic from the shown data. Every displayed arithmetic value is recomputed exactly from the data.

\begin{bmatrix}4&6&11\\6&14&22\end{bmatrix}