# Dealing with diverse groups in regression

What happens if a certain dataset contains different "groups" that follow different linear models?

For example, let's imagine that examining the scatterplot of a certain feature $$x_i$$ against $$y$$ we can see that some points follow a linear relationship with a coefficient $$\beta_A<0$$ while other points clearly have $$\beta_B>0$$. We can infer that these points belong to two different populations, population $$A$$ responds negatively to high values of feature $$x_i$$ while population $$B$$ responds positively. We then create a categorical feature (or one hot encoding) to show which population each row belongs to.

Is splitting the dataset required or are commonly used algorithms able to recognize the different relations between features from different categorical variables?

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