In fact, our model is quite bad, as we can see that by visualizing the data, no linear regression is observed. Why is it so important to first see the data and not blindly rely on calculations and metrics?

In 1973, the English mathematician Francis Anscombe, to illustrate the importance of using graphs for statistical analysis, and the impact of outliers on the properties of the entire data set, composed 4 datasets (it also called Anscombe's quartet). The simple statistical properties of these sets are identical. They have the same mean for each variable, variance, the correlation between x and y, linear regression line, and even R-squared. However, their graphs differ significantly. Each set consists of 11 pairs of numbers.

In the first case, we see a situation that is quite familiar to us, where this model can be applied. On the rest of the graphs, we see that the outliers greatly spoil the more probable and obvious location of the straight line, or the linear regression model is completely inapplicable to the dataset since the points go along a parabola.