Centering
- Subtract the mean from each variable so each centered variable has a mean of zero.
- Reduces correlation among variables, making relationships easier to interpret.
- Helps stabilize regression coefficients and produce more reliable results when multicollinearity is present.
Definition
Section titled “Definition”Centering refers to the practice of subtracting the mean from each variable in a data set before conducting statistical analysis. It is used to address multicollinearity, a statistical issue that arises when two or more variables in a data set are highly correlated.
Explanation
Section titled “Explanation”Multicollinearity can make statistical results unstable and unreliable because it becomes difficult to determine which correlated variable is driving a relationship between dependent and independent variables. By subtracting the mean from each variable, the resulting centered variables have a mean of zero. This reduction in correlation between variables can make it easier to interpret relationships and lead to more stable and reliable coefficient estimates in analyses such as regression.
Examples
Section titled “Examples”Income and education
Section titled “Income and education”A data set that includes income and education level may show high correlation because individuals with higher education tend to earn more. Centering each variable by subtracting its mean reduces the correlation between income and education level, making it easier to interpret the relationship and draw more reliable conclusions about the effect of education on income.
Regression analysis
Section titled “Regression analysis”In regression analysis, multicollinearity can cause coefficients of independent variables to be unstable and unreliable, which may lead to incorrect interpretations. Centering independent variables by subtracting their means can reduce correlations among them, helping to produce more stable and reliable coefficient estimates and more accurate interpretations.
Use cases
Section titled “Use cases”- Addressing multicollinearity in datasets.
- Stabilizing coefficient estimates in regression analysis.
Notes or pitfalls
Section titled “Notes or pitfalls”- Multicollinearity can make it difficult to determine which variable drives relationships and can produce unstable, unreliable results; centering reduces this correlation but does not remove the underlying association between variables.
Related terms
Section titled “Related terms”- Multicollinearity
- Regression analysis