Centred Features, Clean Fit

A feature has already been centred during preprocessing, so its column sums to zero. The training set is:

example	$x$ (centred)	$y$
1	$-3$	3
2	$-1$	5
3	$1$	9
4	$3$	15

Run the full pipeline: build $X$ with a leading column of ones, form $X^\top X$ and $X^\top y$ , solve $w = (X^\top X)^{-1}X^\top y$ , then use the fitted model to predict for a new example whose centred feature value is $x = 5$ .

What are $w = (w_0,\ w_1)^\top$ and the prediction $\hat{y}$ at $x = 5$ ?

Centred Features, Clean Fit

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