If the coefficient of determination between two independent variables is .20, what is the VIF?
The variance inflation factor (VIF) is a measure of multicollinearity between independent variables in a regression analysis. It quantifies how much the variance of the estimated coefficient is increased due to multicollinearity.
The VIF is calculated as 1 divided by the coefficient of determination, minus 1.
In this case, the coefficient of determination between two independent variables is 0.20. Thus, the VIF would be 1 / (0.20 - 1) = 1 / (-0.80) = -1.25.
It is important to note that the VIF should always be a positive value, and a negative VIF value is mathematically incorrect. Therefore, it seems there may be an error or misinterpretation in the given information or calculation.
The coefficient of determination (R-squared) is defined as the proportion of the variance in the dependent variable that can be explained by the independent variables. The Variance Inflation Factor (VIF) is used to assess multicollinearity, which measures the extent to which independent variables are related to each other.
To calculate the VIF, you can use the formula:
VIF = 1 / (1 - R-squared)
Substituting the given coefficient of determination (R-squared = 0.20) into the formula, we can find the VIF:
VIF = 1 / (1 - 0.20)
VIF = 1 / 0.80
VIF = 1.25
Therefore, the VIF is 1.25.
To determine the Variance Inflation Factor (VIF) between two independent variables, you need to know the coefficient of determination. However, the coefficient of determination measures the proportion of variance shared by two variables, rather than directly providing the VIF.
The VIF is a measure that provides insights into multicollinearity, which is the extent to which independent variables are related to each other. It quantifies how much the variance of the estimated regression coefficient is increased due to correlation with other independent variables.
To calculate the VIF, you need to perform the following steps:
1. Calculate the coefficient of determination (R-squared or R^2) between the two independent variables. In this case, the coefficient of determination is 0.20.
2. Compute the VIF using the formula: VIF = 1 / (1 - R^2)
3. Substitute the coefficient of determination value into the formula: VIF = 1 / (1 - 0.20) = 1 / 0.80 = 1.25
Therefore, based on a coefficient of determination of 0.20, the VIF between the two independent variables would be approximately 1.25.