### 13.3.3 The Problem of Heteroskedasticity

Besides the presuppositions previously discussed, the distribution of probability for each random term of Yi = a + b1 ⋅ X1i + b2 ⋅ X2i + ⋯ + bk ⋅ Xki + ui (i = 1, 2, …, n) is such that all distributions should present the same variance, or rather, the distributions should be homoskedastic. Therefore:

$\mathit{Var}\left({u}_{i}\right)=E{\left({u}_{i}\right)}^{2}={\sigma }_{u}^{2}$

(13.39)

Fig. 13.39 provides, for a simple linear regression models, a view of the heteroskedasticity problem, or rather, the nonconstancy of variance of the residuals along the explanatory variable. In other words, there should be a correlation between the terms of error and the X variable, ...

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