5. Regression and linear fitting

5.1 Introduction: regression and least squares

As we mentioned earlier, regression curves do not allow us to extrapolate from observed data. And yet, one of the missions of statistics is precisely prediction. We therefore need to introduce tools to explain the behavior of one variable in relation to another. In general, we can only obtain an explanation of the average behavior: this is known as regression.

The idea is as follows: to try to explain Y by means of X, we'll look for a "reasonable" function f such that for all i : ${\overline{y}}_{\mathrm{/}X=x_i}=f\left(x_i\right)$

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