The Coefficient Ridge Pulls Back

A model is fit on four training examples with two features and no intercept term:

$x_1$	$x_2$	$y$
$1$	$2$	$4$
$2$	$1$	$3$
$3$	$5$	$11$
$4$	$2$	$7$

The rows of the table are the rows of the design matrix $X$ (a $4\times 2$ matrix) and the entries of the target vector $y$ .

Ordinary least squares would use $\hat{\beta} = (X^{\top}X)^{-1}X^{\top}y$ . Because the two feature columns are strongly correlated, ridge regression is used instead:

$\hat{\beta} = \left(X^{\top}X + \lambda I\right)^{-1} X^{\top} y$

with regularization strength $\lambda = 3$ , where $I$ is the $2\times 2$ identity matrix.

What is $\hat{\beta}_2$ , the coefficient on the second feature? Round your answer to 2 decimal places.

The Coefficient Ridge Pulls Back

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