In regression analysis, occurs when two or more predictor variables are highly correlated with each other, such that they do not provide unique or independent information in the regression model.

If the degree of correlation is high enough between predictor variables, it can cause problems when fitting and interpreting the regression model. 

The most straightforward way to detect multicollinearity in a regression model is by calculating a metric known as the variance inflation factor, often abbreviated VIF.

VIF measures the strength of correlation between predictor variables in a model. It takes on a value between 1 and positive infinity.

We use the following rules of thumb for interpreting VIF values:

• VIF = 1: There is no correlation between a given predictor variable and any other predictor variables in the model.
• VIF between 1 and 5: There is moderate correlation between a given predictor variable and other predictor variables in the model.
• VIF > 5: There is severe correlation between a given predictor variable and other predictor variables in the model.

The following example shows how to detect multicollinearity in a regression model in Python by calculating VIF values for each predictor variable in the model.

Example: Testing for Multicollinearity in Python

Suppose we have the following pandas DataFrame that contains information about various basketball players:

import pandas as pd

#create DataFrame
df = pd.DataFrame({'rating': [90, 85, 82, 88, 94, 90, 76, 75, 87, 86],
                   'points': [25, 20, 14, 16, 27, 20, 12, 15, 14, 19],
                   'assists': [5, 7, 7, 8, 5, 7, 6, 9, 9, 5],
                   'rebounds': [11, 8, 10, 6, 6, 9, 6, 10, 10, 7]})

#view DataFrame
print(df)

	rating	points	assists	rebounds
0	90	25	5	11
1	85	20	7	8
2	82	14	7	10
3	88	16	8	6
4	94	27	5	6
5	90	20	7	9
6	76	12	6	6
7	75	15	9	10
8	87	14	9	10
9	86	19	5	7

Suppose we would like to fit a using rating as the response variable and points, assists, and rebounds as the predictor variables.

To calculate the VIF for each predictor variable in the model, we can use the function from the statsmodels library:

from patsy import dmatrices
from statsmodels.stats.outliers_influenceimport variance_inflation_factor

#find design matrix for regression model using 'rating' as response variable 
y, X = dmatrices('rating ~ points+assists+rebounds', data=df, return_type='dataframe')

#create DataFrame to hold VIF values
vif_df = pd.DataFrame()
vif_df['variable'] = X.columns#calculate VIF for each predictor variable 
vif_df['VIF'] = [variance_inflation_factor(X.values, i) for i in range(X.shape[1])]

#view VIF for each predictor variableprint(vif_df)

	       VIF	 variable
0	101.258171	Intercept
1	  1.763977	   points
2	  1.959104	  assists
3	  1.175030	 rebounds

We can see the VIF values for each of the predictor variables:

• points: 1.76
• assists: 1.96
• rebounds: 1.18

Note: Ignore the VIF for the “Intercept” in the model since this value is irrelevant.

Since each of the VIF values for the predictor variables in the model are close to 1, multicollinearity is not a problem in the model.

The following tutorials explain how to perform other common tasks in Python: