# Multi-collinearity test - MATLAB

I'm a complete beginner with regression analysis, so this question will probably seem really silly to you.

But, I simply need to check multi-collinearity among dependent variables before I start modelling.

I know, that when variables are multi-collinear, then $|x| > 0.8$.

So, if I have following table with data (first four columns are independent variables and the last one is dependent):

1,24,288,375,0.1647815
2,12,288,375,0.06300775
3,8,288,375,0.05769325
4,6,288,375,0.04803725
6,4,288,375,0.04290825
8,3,288,375,0.0405065
12,2,288,375,0.03807525
24,1,288,375,0.03487725
1,24,288,1029,0.284112
2,12,288,1029,0.13495675
3,8,288,1029,0.12740075
4,6,288,1029,0.11109725
6,4,288,1029,0.105036
8,3,288,1029,0.11022575
12,2,288,1029,0.100587
24,1,288,1029,0.09803775
1,24,288,2187,0.48695475
2,12,288,2187,0.30563525
3,8,288,2187,0.30084925
4,6,288,2187,0.283312
6,4,288,2187,0.2745085
8,3,288,2187,0.271998
12,2,288,2187,0.27472625
24,1,288,2187,0.27103925
1,24,288,3993,0.89953925
2,12,288,3993,0.68234025
3,8,288,3993,0.6783635
4,6,288,3993,0.65540225
6,4,288,3993,0.64421475
8,3,288,3993,0.64214725
12,2,288,3993,0.63949875
24,1,288,3993,0.623119
1,24,288,6591,1.588605
2,12,288,6591,1.37335275
3,8,288,6591,1.36082075
4,6,288,6591,1.35097375
6,4,288,6591,1.34813125
8,3,288,6591,1.34932025
12,2,288,6591,1.3519095
24,1,288,6591,1.34521625
1,24,288,10125,2.820884
2,12,288,10125,2.63251325
3,8,288,10125,2.640659
4,6,288,10125,2.6338805
6,4,288,10125,2.636361
8,3,288,10125,2.62748
12,2,288,10125,2.6233345
24,1,288,10125,2.63821
1,24,288,14739,4.81472975
2,12,288,14739,4.65116425
3,8,288,14739,4.664892
4,6,288,14739,4.64225625
6,4,288,14739,4.6734825
8,3,288,14739,4.63981675
12,2,288,14739,4.635483
24,1,288,14739,4.6280245
1,24,384,375,0.23542825
2,12,384,375,0.0846985
3,8,384,375,0.07688475
4,6,384,375,0.06345925
6,4,384,375,0.056576
8,3,384,375,0.053811
12,2,384,375,0.0507895
24,1,384,375,0.04879525
1,24,384,1029,0.392991
2,12,384,1029,0.17615175
3,8,384,1029,0.16448675
4,6,384,1029,0.14737925
6,4,384,1029,0.13978
8,3,384,1029,0.13718475
12,2,384,1029,0.13415075
24,1,384,1029,0.13456225
1,24,384,2187,0.62601575
2,12,384,2187,0.4082805
3,8,384,2187,0.39490075
4,6,384,2187,0.371756
6,4,384,2187,0.3702825
8,3,384,2187,0.3597025
12,2,384,2187,0.37200225
24,1,384,2187,0.3535595
1,24,384,3993,1.15287125
2,12,384,3993,0.895903
3,8,384,3993,0.87552425
4,6,384,3993,0.867359
6,4,384,3993,0.8583945
8,3,384,3993,0.84443875
12,2,384,3993,0.84789075
24,1,384,3993,0.82982625
1,24,384,6591,2.13270225
2,12,384,6591,1.829307
3,8,384,6591,1.81909125
4,6,384,6591,1.82385475
6,4,384,6591,1.80537075
8,3,384,6591,1.8317485
12,2,384,6591,1.79930075
24,1,384,6591,1.79099875
1,24,384,10125,3.7804935
2,12,384,10125,3.536092
3,8,384,10125,3.5323925
4,6,384,10125,3.547385
6,4,384,10125,3.51202675
8,3,384,10125,3.50338675
12,2,384,10125,3.51060175
24,1,384,10125,3.54526575
1,24,384,14739,6.42843375
2,12,384,14739,6.1926005
3,8,384,14739,6.19580925
4,6,384,14739,6.23405025
6,4,384,14739,6.177645
8,3,384,14739,6.175222
12,2,384,14739,6.255368
24,1,384,14739,6.17023175
1,24,576,375,0.3541645
2,12,576,375,0.127843
3,8,576,375,0.1166405
4,6,576,375,0.10090825
6,4,576,375,0.08759975
8,3,576,375,0.0793245
12,2,576,375,0.08268425
24,1,576,375,0.07081675
1,24,576,1029,0.60797725
2,12,576,1029,0.264799
3,8,576,1029,0.2422255
4,6,576,1029,0.22252375
6,4,576,1029,0.20797275
8,3,576,1029,0.2028935
12,2,576,1029,0.20118775
24,1,576,1029,0.1964075
1,24,576,2187,0.982394
2,12,576,2187,0.6063885
3,8,576,2187,0.5888065
4,6,576,2187,0.5603745
6,4,576,2187,0.553637
8,3,576,2187,0.547993
12,2,576,2187,0.54669525
24,1,576,2187,0.52710575
1,24,576,3993,1.78898225
2,12,576,3993,1.3315755
3,8,576,3993,1.32300125
4,6,576,3993,1.29368275
6,4,576,3993,1.31523675
8,3,576,3993,1.27007825
12,2,576,3993,1.27818725
24,1,576,3993,1.25695125
1,24,576,6591,3.14688025
2,12,576,6591,2.7529635
3,8,576,6591,2.73636325
4,6,576,6591,2.715318
6,4,576,6591,2.703695
8,3,576,6591,2.69762575
12,2,576,6591,2.6950675
24,1,576,6591,2.681704
1,24,576,10125,5.66736275
2,12,576,10125,5.31472525
3,8,576,10125,5.3054185
4,6,576,10125,5.27888475
6,4,576,10125,5.2624
8,3,576,10125,5.29987075
12,2,576,10125,5.306244
24,1,576,10125,5.2835815
1,24,576,14739,9.629366
2,12,576,14739,9.36943975
3,8,576,14739,9.3500265
4,6,576,14739,9.288043
6,4,576,14739,9.31372775
8,3,576,14739,9.261891
12,2,576,14739,9.369188
24,1,576,14739,9.23232975
1,24,1152,375,0.69257475
2,12,1152,375,0.24958025
3,8,1152,375,0.21671725
4,6,1152,375,0.18378975
6,4,1152,375,0.1662175
8,3,1152,375,0.156526
12,2,1152,375,0.1528385
24,1,1152,375,0.1399855
1,24,1152,1029,1.236831
2,12,1152,1029,0.51960825
3,8,1152,1029,0.47870075
4,6,1152,1029,0.43505925
6,4,1152,1029,0.41830025
8,3,1152,1029,0.41236975
12,2,1152,1029,0.40695825
24,1,1152,1029,0.39565
1,24,1152,2187,1.96045075
2,12,1152,2187,1.2135685
3,8,1152,2187,1.1680795
4,6,1152,2187,1.12618325
6,4,1152,2187,1.09753275
8,3,1152,2187,1.08580325
12,2,1152,2187,1.08405325
24,1,1152,2187,1.05973925
1,24,1152,3993,3.52500925
2,12,1152,3993,2.6662955
3,8,1152,3993,2.6484135
4,6,1152,3993,2.633274
6,4,1152,3993,2.5742025
8,3,1152,3993,2.5481415
12,2,1152,3993,2.54718125
24,1,1152,3993,2.52191075
1,24,1152,6591,6.26374
2,12,1152,6591,5.53025875
3,8,1152,6591,5.5939635
4,6,1152,6591,5.45795025
6,4,1152,6591,5.451115
8,3,1152,6591,5.45319025
12,2,1152,6591,5.41498075
24,1,1152,6591,5.38471875
1,24,1152,10125,11.24069125
2,12,1152,10125,10.652649
3,8,1152,10125,10.68708575
4,6,1152,10125,10.71821975
6,4,1152,10125,10.5743805
8,3,1152,10125,10.58216475
12,2,1152,10125,10.5548025
24,1,1152,10125,10.470183
1,24,1152,14739,19.4673695
2,12,1152,14739,18.6765145
3,8,1152,14739,18.81014475
4,6,1152,14739,18.67571725
6,4,1152,14739,18.6215645
8,3,1152,14739,18.54405925
12,2,1152,14739,18.64567375
24,1,1152,14739,18.4975185


Let's call the first four columns $A,B,C,D$.

Is it enough to simply check correlation coef. for every pair of independent variables like this?

corr(A,B)
corr(A,C)
corr(A,D)
corr(B,C)


etc.?

## 1 Answer

I am not a specialist of this topic but I know the Variance Inflation Factor (VIF) allows to check for multicollinearity.

As far as I know, it is not enough to check for correlations when looking for multicollinearity, as it is neither a necessary nor a sufficient condition for collinearity.