# Detect Non-Linear and Non- Monotonic Relationship between Variables

In linear regression analysis, it's an important assumption that there should be a linear relationship between independent variable and dependent variable. Whereas, logistic regression assumes there should be a linear relationship between independent variable and logit function.

How to check non-linearity

Pearson correlation is a measure of linear relationship. The variables must be measured at interval scales. It is sensitive to outliers. If pearson correlation coefficient of a variable is close to 0, it means there is no linear relationship between variables.

Spearman's correlation is a measure of monotonic relationship. It can be used for ordinal variables. It is less sensitive to outliers. If spearman correlation coefficient of a variable is close to 0, it means there is no monotonic relationship between variables.

Hoeffding’s D correlation is a measure of linear, monotonic and non-monotonic relationship. It has values between –0.5 to 1. The signs of Hoeffding coefficient has no interpretation.
If a variable has a very low rank for Spearman (coefficient - close to 0) and a very high rank for Hoeffding indicates a non-monotonic relationship.
If a variable has a very low rank for Pearson (coefficient - close to 0) and a very high rank for Hoeffding indicates a non-linear relationship.

Criterion to eliminate irrelevant variables
If a variable has poor rank on both the spearman and hoeffding correlation metrics, it means the relationship between the variables is random.

SAS Macro to detect non-monotonic relationship

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Deepanshu founded ListenData with a simple objective - Make analytics easy to understand and follow. He has over 7 years of experience in data science and predictive modeling. During his tenure, he has worked with global clients in various domains like banking, Telecom, HR and Health Insurance.

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