So far, we are assuming this is a perfect formula. But it doesn't have to be this perfect. Linear Regression models always have the residuals, which is the difference between the estimated values by the model and the actual values. And one way to measure how small the error of this model is to calculate the R-Squared. The R-Squared is a measure of how good a given model can explain the variance of the target variable. It ranges between 0 and 1. As it gets closer to 1 the correlation between the target and predictor variables is considered to be higher.
As it gets closer to 0 there is not much correlation between the two variables. So, we can build a model with the Job Level as the target variable and the Working Years as the predictor variable and measure the R-Squared to see how much they are correlated. And this means that having both of them as predictor variables could cause the multicollinearity problem.
On the other hand, if the R-Squared is low, then these two variables are not well correlated. And this is the basic logic of how we can detect the multicollinearity problem at a high level.
In order to detect the multicollinearity problem in our model, we can simply create a model for each predictor variable to predict the variable based on the other predictor variables. And we want to find out if we have the multicollinearity problem among the predictor variables of Job Level, Working Years, and Age.
Then, we can build a model for each predictor variable to predict the values based on other predictor variables like below. And we can measure the R-Squared for each model. If the R-Squared for a particular variable is closer to 1 it indicates the variable can be explained by other predictor variables and having the variable as one of the predictor variables can cause the multicollinearity problem.
This indicates that having the Job Level most likely to cause the multicollinearity problem. But if the Job Level and the Working Years are highly correlated then the R-Squared for this model should be high regardless of whether the Job Level is correlated with the Age or not.
This indicates that the Working Years might cause the problem, but the evidence is not as strong as the first one. This indicates that the Age is not going to cause the problem. So, by building the models for every single predictor variable and measuring the R-Squared for each we can detect the multicollinearity problem.
As we have seen so far, the R-Squared can be our guide for detecting the multicollinearity problem. But there is another measure called VIF Variance Inflation Factor that is often used as a measure of detecting the multicollinearity problem. What is VIF? VIF is nothing but the inflated version of the R-Squared. Anyway, we can calculate the VIF for the above models as below. Now, what are we going to do when we have the multicollinearity in our model?
Just remove one of the variables with high VIF, rebuild the model, and see if it still has such a problem. How are we going to decide which variables to remove? In the above example, you want to remove either the Job Level or the Working Years. If you are interested in understanding the relationship between the Job Level and the Salary then keep the Job Level but remove the Working Years. Here is a quick example. I had an employee salary data and wanted to build a linear regression model to explain how the salary changes based on a given set of employee attributes such as Age, Gender, Working Years, etc.
So I built one, and here is the Coefficient tab showing the coefficients of all the predictor variables. By looking at the relationship between the Job Role and the Department by using the Bar chart, we can see that they are super associated with one another. My goal in this blog post is to bring the effects of multicollinearity to life with real data! Moderate multicollinearity may not be problematic.
However, severe multicollinearity is a problem because it can increase the variance of the coefficient estimates and make the estimates very sensitive to minor changes in the model. The result is that the coefficient estimates are unstable and difficult to interpret. Multicollinearity saps the statistical power of the analysis, can cause the coefficients to switch signs, and makes it more difficult to specify the correct model.
The symptoms sound serious, but the answer is both yes and no—depending on your goals. In short, multicollinearity:. You can read about the actual experiment here and the worksheet is here. If you're not already using it, please download the free day trial of Minitab and play along!
A VIF of 5 or greater indicates a reason to be concerned about multicollinearity. However, three of the VIFs are very high because they are well over 5. These values suggest that the coefficients are poorly estimated and we should be wary of their p-values.
In this model, the VIFs are high because of the interaction term. Interaction terms and higher-order terms e. To reduce high VIFs produced by interaction and higher-order terms, you can standardize the continuous predictor variables. This method removes the multicollinearity produced by interaction and higher-order terms as effectively as the other standardization methods, but it has the added benefit of not changing the interpretation of the coefficients.
If you subtract the mean, each coefficient continues to estimate the change in the mean response per unit increase in X when all other predictors are held constant.
Because standardizing the predictors effectively removed the multicollinearity, we could run the same model twice, once with severe multicollinearity and once with moderate multicollinearity. This provides a great head-to-head comparison and it reveals the classic effects of multicollinearity.
The standard error of the coefficient SE Coef indicates the precision of the coefficient estimates. Smaller values represent more reliable estimates.
In fact, if you want to use the model to make predictions , both models produce identical results for fitted values and prediction intervals! Multicollinearity can cause a number of problems. We saw how it sapped the significance of one of our predictors and changed its sign. Imagine trying to specify a model with many more potential predictors.
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