Assumptions of Linear Regression

The very first assumption that we make is that linear regression shows linear relationships between the independent variables x and dependent variables y. It needs the Linear Regression to be independent and dependent variables to be linear. It is also important to check for outliers since linear regression is sensitive to outlier effects. To test the linearity assumption can be through the examination of scatter plots.

Assumption Of Multivariate Normality

In the analysis process of Linear Regression, it required all the variables to be multivariate normal. Its residuals are normally distributed. This type of assumption can be best checked with the help of a histogram or a Q-Q-Plot and normality can be best checked with the goodness of fit test. When the data is not normally distributed in a non-linear transformation it might fix the issue.

Assumption Of The Absence Of Autocorrelation

The process of Linear Regression analysis requires little autocorrelation in the data or no autocorrelation. Autocorrelation generally occurs when the residuals are not independent of each other. We can check for autocorrelation with the help of a scatter plot and we can also test the linear regression model for autocorrelation with the Durbin-Watson test. Durbin-Watson’s d tests the null hypothesis that the residuals are not linearly auto-correlated.

Assumption Of Homoscedasticity

Another Assumption in linear regression is that the residuals have constant variance at every level of x. This is process is also known as homoscedasticity. And in some cases, this does not happen then it is said to suffer from heteroscedasticity. Its analysis assumes the presence of homoscedasticity. 

We can check homoscedasticity by examining the scatter plot because it is a good way. The Goldfeld-Quandt Test can also be used to test for heteroscedasticity. This test splits the data into two groups and then test to see if the variances of the residuals are similar across the groups. If homoscedasticity is present, a non-linear correction might fix the problem. If homoscedasticity is present, a non-linear correction might fix the problem.