U_linear model assumptions.py

Linear regression assumptions are:

(1) Linearity: The mean values of the outcome variable for each increment of the predictor(s) lie along a straight line. 
  In other words, there is a linear relationship between predictors and target.

(2) No perfect multicollinearity: There should be no perfect linear relationship between two or more of the predictors. 

(3) Normally distributed errors: the residuals are random and normally distributed with a mean of 0.

(4) Homoscedasticity: At each level of the predictor variable(s), the variance of the residual terms should be constant.
  

To determine if a linear model fits the data well:
  (1) The residuals should have a normal distribution with the mean centered at zero, and should be homoscedastic. 
  If this is true, we can be fairly confident that the model is doing a good job.

  (2) The normal distribution can be assessed by Q-Q plots. Homoscedasticity can be assessed by residual plots.

  (3) We can also examine if there is a linear relationship between the predictors and the target with scatter-plots and residuals plots, 
  and assess multi-colinearity with correlation matrices.