Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2019 / Paper 1 / 18 / b / i

Each prediction is a linear combination of the constant parameter and the coefficient of $x_i$. Thus the design matrix isIts $i$th row multiplied by the parameter vector $(\alpha ,\beta {)}^{\mathsf{T}}$ gives the required prediction $\alpha +\beta x_i$.