Multicollinearity is a term used in statistics referring to the correlation of two or more independent variables in a regression model. The word is spelled /mʌlti kəˌlaɪni ˈærəti/ in the International Phonetic Alphabet. The first syllable "mul" is pronounced with the short "ʌ" sound, followed by "ti" with a long "i" sound. The second part "colli" has a short "ə" sound and "ne" is pronounced as a long "i". Finally, "arity" is pronounced with the short "ær" sound and "ti" with a long "i" sound.
Multicollinearity refers to the occurrence of a high degree of correlation among independent variables in a statistical model or analysis. It is a phenomenon where two or more predictor variables within a regression analysis are strongly related to each other, making it difficult to determine the individual effect of each variable on the dependent variable.
In statistical terms, multicollinearity distorts the results of regression analysis, leading to difficulties in interpreting the coefficients and undermining the statistical significance of the variables. When multicollinearity is present, it becomes challenging to isolate the effect of one variable while holding others constant, as the variables end up influencing each other.
Multicollinearity can arise due to various reasons, such as including redundant variables that measure similar aspects, highly correlated variables, or the inclusion of derived explanatory variables. It can also occur naturally in datasets with interrelated variables, leading to higher standard errors, unstable coefficients, and less accurate predictions.
Detecting multicollinearity typically involves examining pairwise correlations or variance inflation factors (VIF) among the predictor variables. Remedies for multicollinearity include removing one or more of the highly correlated variables, transforming the variables, or collecting additional data.
Understanding and addressing multicollinearity is crucial for reliable and valid statistical analysis, as it ensures that the relationship between the independent and dependent variables remains accurate and interpretable.
The word "multicollinearity" is derived from combining the prefix "multi-" meaning multiple or many, and "collinear" which refers to a mathematical relationship between variables lying on the same straight line. Therefore, "multicollinearity" implies the presence of multiple variables that are highly linearly related to each other in a statistical context.