The tolerance value and Variance Inflation Factor (VIF) are important metrics that you can use to detect multicollinearity among independent variables. If we recall the basic theory, multicollinearity testing is an assumption test in the Ordinary Least Squares (OLS) regression method, which aims to ensure that there is no strong correlation between independent variables.
You probably know that in the OLS regression method, it is assumed that there is no strong correlation between independent variables. Therefore, to obtain the Best Linear Unbiased Estimator (BLUE), you need to detect multicollinearity, one of which can be done using the tolerance value and VIF.
You can calculate the tolerance and VIF values yourself. Since this is an important aspect, I have written this article to explain how to calculate the tolerance and VIF values along with the interpretation of the results.
Tolerance and VIF Formulas
To calculate the tolerance and VIF values, you need to understand the formulas used. Essentially, we can detect multicollinearity among independent variables by choosing either the tolerance value or VIF. The results of both calculations will lead to the same conclusion. Therefore, we must understand these two formulas properly.
The formula you can use to calculate the tolerance value is shown below:
Based on the formula above, the tolerance value is obtained by subtracting the coefficient of determination from 1. However, you need to understand that the coefficient of determination used to calculate the tolerance value is the coefficient of determination from the influence of one independent variable on another independent variable.
To clarify, the coefficient of determination used here is not from the influence of independent variables on the dependent variable but rather from the influence of independent variables on other independent variables.
The formula used to calculate the VIF value is shown below:
Based on the formula above, we can see that the VIF value will always be greater than the tolerance value. This is because the VIF value is obtained by dividing 1 by the tolerance value.
Case Study Example
In this article, I will provide a case study example to help you understand the steps for calculating the tolerance and VIF values. The case study I use applies multiple linear regression with two independent variables.
In this case study, the researcher’s goal in collecting data is to determine the impact of the inflation rate and unemployment rate on economic growth. Based on this case study, we will detect whether there is multicollinearity between the inflation rate and the unemployment rate variables.
The detailed data collected by the researcher can be seen in the table below:
Based on the table above, the first step in calculating multicollinearity is to find the coefficient of determination of one independent variable’s influence on another independent variable. In this case study, I will determine the coefficient of determination for the effect of the unemployment rate on the inflation rate.
To obtain this coefficient of determination, you can use various statistical software tools. However, in this article, I will provide a tutorial on how to obtain the coefficient of determination using the “Data Analysis” menu in Excel.
The first step is to click the “Data” ribbon, then go to the upper right section where you will find the “Data Analysis” menu—click on it. If you do not see this menu, it means you have not activated it yet. Please refer to my previous article, which provides a tutorial on how to activate the “Data Analysis” menu in Excel.
Next, after clicking the “Data Analysis” menu in Excel, several analysis tools will appear. Look for “Regression” and click OK.
After clicking OK, input all the data along with their labels. Enter the inflation rate as the Y variable and the unemployment rate as the X variable. Also, remember to enable or check the label option and set the confidence level to 95%. Then, choose to save the analysis results in the same Excel sheet. The detailed steps are illustrated in the image below:
Based on the image above, once you have confirmed that there are no errors in the steps, click OK, and the analysis results will appear. Look at the coefficient of determination or R Square value shown in the image below:
From the image above, we can see that the coefficient of determination for the effect of one independent variable on another independent variable is 0.36808. The next step is to calculate the tolerance and VIF values.
Steps to Calculate Tolerance and VIF
After successfully obtaining the coefficient of determination, the next step is to use the first formula, which is the calculation formula for the tolerance value. Based on this formula, we can calculate the tolerance value as follows:
Based on the calculation above, the tolerance value for this equation is 0.63192. Next, we can calculate the VIF value using the formula mentioned earlier, as follows:
Based on the calculation above, we find that the VIF value is 1.582478795. The next step is to interpret the tolerance and VIF values to determine whether there is a strong correlation between the independent variables in the regression equation we are analyzing.
Interpretation of Tolerance and VIF Values
After successfully calculating the tolerance and VIF values, the next step is to interpret them. A regression equation with a tolerance value of less than 0.1 indicates the presence of multicollinearity. Meanwhile, based on the VIF criteria, if the VIF value is greater than 10, there is a strong indication of multicollinearity.
From the results, a VIF value of less than 5 indicates no multicollinearity. Similarly, since the tolerance value is greater than 0.1, we can conclude that there is no multicollinearity. Based on these findings, it can be concluded that there is no strong correlation between the independent variables.
Thus, the analyzed regression equation meets the assumptions required in the OLS linear regression method. That concludes this article for now. Hopefully, it is useful and provides new insights for you. Stay tuned for updates from Kanda Data in the next article. Thank you.
