Understanding Multicollinearity in Regression Analysis

Multicollinearity in regression analysis can be assessed using various tests such as Variable Inflation Factors (VIF) and R^2 value. VIF measures the strength of correlation between independent variables, while an R^2 value close to 1 indicates high multicollinearity. The Farrar Glauber test and construction of a correlation matrix are also methods to detect multicollinearity in regression models.

• Multicollinearity
• Regression Analysis
• VIF
• R^2 Value
• Correlation Matrix

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1. TESTS TO CHECK MULTICOLLINEARITY Anindita Chakravarty

2. VIF (Variable Inflation Factors). VIF determines the strength of the correlation between the independent variables. It is predicted by taking a variable and regressing it against every other variable. VIF score of an independent variable represents how well the variable is explained by other independent variables.

3. R^2 value is determined to find out how well an independent variable is described by the other independent variables. A high value of R^2 means that the variable is highly correlated with the other variables. This is captured by the VIF which is denoted below: VIF= 1 1- R2

4. So, the closer the R^2 value to 1, the higher the value of VIF and the higher the multicollinearity with the particular independent variable. NOTE: VIF starts at 1 and has no upper limit VIF = 1, no correlation between the independent variable and the other variables VIF exceeding 5 or multicollinearity between this independent variable and the others 10 indicates high

5. FarrarGlauber test: If the variables are found to be orthogonal, there is no multicollinearity; if orthogonal, then at multicollinearity is present. the variables are not least some degree of The Farrar Glauber test has also been criticized by other researchers

6. Construction of a correlation matrix Construction of a correlation matrix among the explanatory variables will yield indications as to the likelihood that any given couplet of right-hand- side variables are problems. creating multicollinearity Correlation values (off-diagonal elements) of at least 0.4 are sometimes interpreted as indicating a multicollinearity problem.