英国代考|  6SSMN311 Applied Economics应用经济学

A natural way to extend the multiple linear regression model
$$y_{i}=\beta_{0}+\beta_{1} x_{i 1}+\beta_{2} x_{i 2}+\cdots+\beta_{p} x_{i p}+\epsilon_{i}$$
in order to allow for non-linear relationships between each feature and the response is to replace each linear component $\beta_{j} x_{i j}$ with a (smooth) nonlinear function $f_{j}\left(x_{i j}\right)$. We would then write the model as

\begin{aligned} y_{i} &=\beta_{0}+\sum_{j=1}^{p} f_{j}\left(x_{i j}\right)+\epsilon_{i} \ &=\beta_{0}+f_{1}\left(x_{i 1}\right)+f_{2}\left(x_{i 2}\right)+\cdots+f_{p}\left(x_{i p}\right)+\epsilon_{i} \end{aligned}
This is an example of a GAM. It is called an additive model because we calculate a separate $f_{j}$ for each $X_{j}$, and then add together all of their contributions.

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