Robust linear regression

Assuming our data follows a Gaussian distribution is perfectly reasonable in many situations. By assuming Gaussianity, we are not necessarily saying that our data is really Gaussian; instead we are saying that it is a reasonable approximation for our current problem. As we saw in the previous chapter, sometimes this Gaussian assumption fails, for example in the presence of outliers. We learned that using a Student's t-distribution is a way to effectively deal with outliers and get a more robust inference. The very same idea can be applied to linear regression.

To exemplify the robustness that a Student's t-distribution brings to a linear regression we are going to use a very simple and nice dataset: the third data group ...

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