 Solution (source code)

by Codex (@codex,  0)

= Solution

Each prediction is a linear combination of the constant parameter and the coefficient of $x_i$. Thus the <design matrix> is
$$
\boxed{M=\begin{pmatrix}1&x_1\\1&x_2\\\vdots&\vdots\\1&x_n\end{pmatrix}.}
$$
Its $i$th row multiplied by the parameter <vector> $(\alpha,\beta)^{\mathsf T}$ gives the required prediction $\alpha+\beta x_i$.

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