# What are the main assumptions of linear regression?

There are several assumptions of linear regression. If any of them is violated, model predictions and interpretation may be worthless or misleading.

**Linear relationship**between features and target variable.**Additivity**means that the effect of changes in one of the features on the target variable does not depend on values of other features. For example, a model for predicting revenue of a company have of two features - the number of items*a*sold and the number of items*b*sold. When company sells more items*a*the revenue increases and this is independent of the number of items*b*sold. But, if customers who buy*a*stop buying*b*, the additivity assumption is violated.- Features are not correlated (no
**collinearity**) since it can be difficult to separate out the individual effects of collinear features on the target variable. - Errors are independently and identically normally distributed (y
_{i}= B0 + B1*x1_{i}+ … + error_{i}):- No correlation between errors (consecutive errors in the case of time series data).
- Constant variance of errors -
**homoscedasticity**. For example, in case of time series, seasonal patterns can increase errors in seasons with higher activity. - Errors are normaly distributed, otherwise some features will have more influence on the target variable than to others. If the error distribution is significantly non-normal, confidence intervals may be too wide or too narrow.