Question

What are some of the violations of the linearity assumption in the multiple linear regression model and how can we correct those violations? Mainly focus on how to correct them by stating the violations.

Answer 1

Assumptions of multiple linear regression model--and the way to correct violations-----

relationship-------

There must be a linear relationship between the outcome variable and the independent variables. Scatterplots can show whether there is a linear or curvilinear relationship.

Independent variables and the dependent variables could be transformed so that the relationship between them is linear.

Multivariate normality-----

Multipleregression assumes that the residuals are normally distributed

In the case where errors are not normally distributed, one could verify that the other assumptions are respected (i.e. homoscedasticity, linearity), as it may often be a tell-tale sign of such a violation, and fine-tune the model accordingly.

No multicolinearity---

Multipleregression assumes that the independent variables are not highly correlated with each other. This assumption is tested using Variance Inflation Factor (VIF) values....

Multicollinearity can be fixed by performing feature selection: deleting one or more independent variables.

Homoscedasticity---

Thisassumption states that the variance of error terms are similar across the values of the independent variables. A plot of standardized residuals versus predicted values can show whether points are equally distributed across all values of the independent variables

To verify homoscedasticity. one may look at the residual plot and verify that the variance of the error terms is constant across the values of the dependent variable...

As heteroscedasticity generally reflects the absence of confounding variables, it can be tackled by reviewing the predictors and providing additional independent variables

Note-if there is any understanding problem regarding this please feel free to ask via comment box..thank you