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What is the aim of regression estimation?
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In regression estimation, we are usually given an i.i.d. sample $\left(\mathbf{X}_1, Y_1\right), \ldots$. $\left(\mathbf{X}_n, Y_n\right)$ from a joint distribution $P_{\mathbf{X}, Y}$. Our aim is to predict the target $Y$ from the covariates or predictors $\mathbf{X}$. In least squares regression, for example, we are looking for a function $\hat{f}$ such that
$\hat{f}=\underset{f \in \mathcal{F}}{\operatorname{argmin}} \sum_{i=1}^n\left(Y_i-f\left(\mathbf{X}_i\right)\right)^2 .$
by Platinum (141,884 points)

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