Testing the assumptions of a linear regression model

Question

I am building a model for predicting airline prices. I have 19 relevant predictors and and 114000 observations. I am getting an $R^2$ predicted of 95.87 (Minitab displays $R^2$ predicted after applying the PRESS Statistic for cross- validation).

Do I need to test for the five assumptions of a linear regression model before running Multiple Linear regression in Minitab ?

The five assumptions are the following i.e

1. Linear relationship
2. Multivariate normality
3. No or little multicollinearity
4. No auto-correlation
5. Homoscedasticity

Answer 1

The text book answer is that you should always check the assumptions before fitting in model. In practice, most people just apply the model, usually not even aware of the assumptions.

The reason to applying the model directly is thinking that in the worse case the model won't fit. It is true that your test set/cross validation functions a a safety belt that will alert if the model won't fit. In many cases validating the assumptions is hard so "giving it a try" looks like a good method.

Yet, one should note that giving it a try might be misleading. Let's say that you tried your model and it didn't fit. It might be since your data represent a relation that is not linear but quadratic. If you validated the assumptions, you could have find it add a quadratic term and get a good model. Without validating you will not go in a fruitful direction.

Even when your model works. you might get into problems. It is way to common to assume (without any validation) that parameter weight indicates importance and causality. If you have collinearity than a parameter with a positive influence might get a negative weight. Here the path of wrong assumptions might send you in the opposite direction.

On top of all that, you cannot "give a try" to all the options. If you check the assumptions you can learn which directions a more promising and invest your time there.