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Regression relates an input variable to an output, to either predict new outputs, or understand the effect of the input in the output. A regression dataset consists of a set of pairs $(x_n, y_n)$ of size $N$ with input $x_n$ and output/label $y_n$. For a new input $x_n$, the goal of regression is to find $f$ such that \(y_n \approx f(x_n)\). If we wan’t to fit the dataset to a multidimensional plane, we are solving the (multivariate) linear regression problem, by finding the weights $w$ that app...