如何解释数据的线性回归假设

Question

I have a data set with 3719 observation with 9 features. In that I have performed multiple linear regression with selected features. I got the diagnostic plots like this:

I have understood by plots that there is no linearity between dependent and independent variables.Residual plots giving non linear trend. But from Normal QQ plot it follows the normal distribution. I did not get the what is mean by residual vs leverage plots?

Am I understanding correctly? How to interpret those plots.

Answer 1

Your residuals are exhibiting heteroscedasticity (top-left), meaning that the variability in your outcome increases with the values of the outcome. For example, income vs expenditure: wealthier people have more variability in the price of food that they buy (they sometimes buy cheap food and sometimes buy expensive food) while poorer people tend to buy only cheap food.

The QQ-plot (bottom-left) assesses the normality of residuals assumption and I see nothing to suggest a serious violation. The slight departure at the top right is not as serious as your heteroscedasticity problem though.

The residuals vs leverage plot (bottom-right) indicates points that may have a large influence on your results based on Cook's distance. This can help identify outliers in your data, and you could consider omitting these before running another model (a rather subjective assessment).