Assumptions Of Linear Regression | What To Do If The Assumptions Do Not Hold? | Part 1

Key Takeaways

linear regression has four assumptions the assumptions are important because they ensure the model provides reliable and accurate results violation of at least one of the assumptions compromises the model's reliability however you can still use the linear regression in the case of a violation if you follow our instructions the first assumption says there should be a linear relationship between the independent variable X and the dependent variable y if the relationship isn't straight the model's predict will be off because it's trying to fit a straight line to a potentially curved Trend secondly each observation should be independent of the others the independence of observations ensures that each data point contributes new and unique information to the estimation of the regression coefficients the violation would lead to a biased estimate of the coefficients of the model thirdly the residuals have constant variance at every level of X it matters because if the spread of the error changes the model predictions might be less reliable for certain values having more errors than others lastly the residuals of the model are normally distributed this ensures that the statistical tests used to determine the significance of the predictors are valid leading to correct inferences now what if the assumptions do not hold firstly you need to understand your objective of using linear regression if you want to approach the problem statistically meaning you want necessarily to interpret with the statistical properties of the model then you can apply transformations to the variables consider alternative models use a smaller number of predictors or Implement other remedies to mitigate the potential violations however if you target a good performing model and you care less about the interpretability then in machine learning there is a powerful technique to check the reliability and the performance of the model called train test split if you run a linear regression model and see that it performs well on both train and test sets then you can probably use that model despite the violations however note that even with a good performing model you still can't interpret its statistical properties if there are violations we will refer to the train test split and how to check the assumptions of the linear regression model in the upcoming videos so stay tuned if you want to learn more about artificial intelligence subscribe to our channel to be aware of the new videos press the like button and let's discuss AI in the comment section [Music]