Understanding Multicollinearity in Regression Analysis

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TESTS TO CHECK MULTICOLLINEARITY
 
Anindita Chakravarty
 
 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.
 
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- R
2
 
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 10 indicates high
multicollinearity between this independent variable
and the others
 
Farrar–Glauber test
:
 
If the variables are found to be orthogonal, there is
no multicollinearity; if the variables are not
orthogonal, then at least some degree of
multicollinearity is present.
 
 The Farrar–Glauber test has also been criticized
by other researchers
 
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 creating multicollinearity
problems.
Correlation values (off-diagonal elements) of at
least 0.4 are sometimes interpreted as indicating a
multicollinearity problem.
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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.


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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.

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