Data Science for Business and Decision Making

13.3.3 The Problem of Heteroskedasticity

Besides the presuppositions previously discussed, the distribution of probability for each random term of Y_i = a + b₁ ⋅ X_1i + b₂ ⋅ X_2i + ⋯ + b_k ⋅ X_ki + u_i (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, ...