Checking for multicollinearity is a routine task while solving a data problem.

Most people rely on pairwise correlations for detecting multicollinearity which is a faulty approach in many scenarios

So what to do? Check this ↓

1/11

Multicollinearity creates a problem in the interpretation of the model when some predictors explain predictors.

Because then we are unable to understand the effect of each predictor in isolation towards the target variable and our coefficients become less useful.

2/11
Variance Inflation Factor or VIF is an efficient method to check for multicollinearity.

Variance Inflation refers to the inflation in the variance of the estimated coefficient of the independent variable because of the presence of multicollinearity.

3/11
We could have low pairwise correlations, but still have high VIF and vice-versa.

A strong relationship is possible between a predictor and other variables together combined, even though there's no high correlation individually.

4/11
Hence we prefer VIF

VIF performs a set of multivariate regression analyses to check the dependence among the independent variables by fitting multiple regression models on the dependent variables.

5/11
In each fit, one of the variables is treated as a target while the rest of them act as regressors.

If we have regressors A,B,C,D, then VIF would fit models like,

A <- B,C,D
B <- A,C,D
C <- A,B,D
D <- A,B,C

and since we are looking for explained variance, we would use...

6/11
...R2 as a metric for each model.

We will calculate the VIF for each predictor by using the R2 given by the model where the predictor has been used as the target.

Putting the values in the following formula we will get our VIF values:

7/11
The high R2 would show that other predictors explain most of the variance in the current predictor (current model target).

And in the formula, high R2 would yield high VIF values as well, suggesting multicollinearity.

8/11
Now that we got the calculated VIF values what to do with them?

VIF values start from 1 and do not have an upper limit.

1 suggests that there's no multicollinearity among the variables,
as a rule-of-thumb, values > 5 or > 10 indicate high multicollinearity but not always.

9/11
Once we know the correlated variables, for removing the multi-collinearity we can,

• either remove all but one of the variables with high VIF or
• combine those variables into a single variable.

and we are good to go!

10/11
That's one good way to check for multicollinearity!

11/11

If you do find a mistake or have any questions, drop them below ↓

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॥ॐ॥
अस्य श्री गायत्री ध्यान श्लोक:
(gAyatri dhyAna shlOka)
• This shloka to meditate personified form of वेदमाता गायत्री was given by Bhagwaan Brahma to Sage yAgnavalkya (याज्ञवल्क्य).

• 14th shloka of गायत्री कवचम् which is taken from वशिष्ठ संहिता, goes as follows..


• मुक्ता-विद्रुम-हेम-नील धवलच्छायैर्मुखस्त्रीक्षणै:।
muktA vidruma hEma nIla dhavalachhAyaiH mukhaistrlkShaNaiH.

• युक्तामिन्दुकला-निबद्धमुकुटां तत्वार्थवर्णात्मिकाम्॥
yuktAmindukalA nibaddha makutAm tatvArtha varNAtmikam.

• गायत्रीं वरदाभयाङ्कुश कशां शुभ्रं कपालं गदाम्।
gAyatrIm vardAbhayANkusha kashAm shubhram kapAlam gadAm.

• शंखं चक्रमथारविन्दयुगलं हस्तैर्वहन्ती भजै॥
shankham chakramathArvinda yugalam hastairvahantIm bhajE.

This shloka describes the form of वेदमाता गायत्री.

• It says, "She has five faces which shine with the colours of a Pearl 'मुक्ता', Coral 'विद्रुम', Gold 'हेम्', Sapphire 'नील्', & a Diamond 'धवलम्'.

• These five faces are symbolic of the five primordial elements called पञ्चमहाभूत:' which makes up the entire existence.

• These are the elements of SPACE, FIRE, WIND, EARTH & WATER.

• All these five faces shine with three eyes 'त्रिक्षणै:'.

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