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GO Classes DPP | ML |LINEAR REGRESSION

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1 1 vote
Let a set of data points with five samples and two features per sample be $X=\left[\begin{array}{cc}1 & 2 \\ 2 & 3 \\ 4 & 2.5 \\ 6 & 4 \\ 7.5 & 5\end{array}\right]$ and the corresponding labels be $y=\left[\begin{array}{c}1.5 \\ 2 \\ 2.5 \\ 3 \\ 4\end{array}\right]$. Perform linear regression on this data set and choose the optimal solution for $w^*$ to minimize the sum of squares error.

A. $\left[\begin{array}{l}0.2763 \\ 1.2039\end{array}\right]$

B. $\left[\begin{array}{l}0.0691 \\ 0.3010\end{array}\right]$

C. $\left[\begin{array}{l}0.1382 \\ 0.6019\end{array}\right]$

D. $\left[\begin{array}{l}0.0276 \\ 0.1204\end{array}\right]$

1 Answer

2 2 votes
$$
\begin{aligned}
&\text { optimal } w^*=\left(X^T X\right)^{-1}\left(X^T y\right)\\
&\begin{aligned}
& X^T X=\left[\begin{array}{cc}
113.25 & 79.5 \\
79.5 & 60.25
\end{array}\right] \\
& X^T y=\left[\begin{array}{c}
63.5 \\
47.25
\end{array}\right] \\
& w^*=\left[\begin{array}{l}
0.1382 \\
0.6019
\end{array}\right]
\end{aligned}
\end{aligned}
$$
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