Scoring a Guessed Weight Vector — easy Linear Algebra for ML problem | Incognition

Scoring a Guessed Weight Vector

Linear Algebra for MLEasy+10 XP+10

Scoring a Guessed Weight Vector

The model $\hat{y} = w_0 + w_1 x$ is written in matrix form as $\hat{y} = Xw$ , where $X$ carries a leading column of ones and $w = (w_0,\ w_1)^\top$ . The training set is:

example	$x$	$y$
1	1	1
2	2	6
3	3	9
4	4	9

A colleague proposes the weights $w = (1,\ 2)^\top$ — not necessarily the best fit, just a guess worth scoring. How much squared error does this $w$ make? That is, what is

$\lVert y - Xw \rVert_2^2 \;=\; \sum_{i=1}^{4}\bigl(y_i - \hat{y}_i\bigr)^2 \ ?$

Hints

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Scoring a Guessed Weight Vector

Scoring a Guessed Weight Vector

Hints

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Fitting the Least-Squares Line

Regression Line & Residuals (SSE = 3.250)

Fitting Verdict