{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Correlation and Dependency" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finding links between variables is a very important task. The main purpose of data science is to find relationships between variables, and to understand how these relationships can help us make better decisions. \n", "\n", "Machine learning models are also sensitive to the number of variables and how they relate and affect each other, so finding correlations and dependencies can help us make better use of our machine learning algorithms.\n", "\n", "Let's use the Telco Churn dataset to understand how we can find links between different variables in VerticaPy." ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
Abc
customerID
Varchar(20)
Abc
gender
Varchar(20)
123
SeniorCitizen
Integer
010
Partner
Boolean
010
Dependents
Boolean
123
tenure
Integer
010
PhoneService
Boolean
Abc
MultipleLines
Varchar(100)
Abc
InternetService
Varchar(22)
Abc
OnlineSecurity
Varchar(38)
Abc
OnlineBackup
Varchar(38)
Abc
DeviceProtection
Varchar(38)
Abc
TechSupport
Varchar(38)
Abc
StreamingTV
Varchar(38)
Abc
StreamingMovies
Varchar(38)
Abc
Contract
Varchar(28)
010
PaperlessBilling
Boolean
Abc
PaymentMethod
Varchar(50)
123
MonthlyCharges
Numeric(10)
123
TotalCharges
Numeric(11)
010
Churn
Boolean
10002-ORFBOFemale0
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9
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Mailed check65.6593.3
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20003-MKNFEMale0
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9
✅
YesDSLNoNoNoNoNoYesMonth-to-month
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Mailed check59.9542.4
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❌
❌
4
✅
NoFiber opticNoNoYesNoNoNoMonth-to-month
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Electronic check73.9280.85
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40011-IGKFFMale1
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13
✅
NoFiber opticNoYesYesNoYesYesMonth-to-month
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Electronic check98.01237.85
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50013-EXCHZFemale1
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3
✅
NoFiber opticNoNoNoYesYesNoMonth-to-month
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9
✅
NoDSLNoNoNoYesYesYesMonth-to-month
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Credit card (automatic)69.4571.45
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70013-SMEOEFemale1
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❌
71
✅
NoFiber opticYesYesYesYesYesYesTwo year
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Bank transfer (automatic)109.77904.25
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80014-BMAQUMale0
✅
❌
63
✅
YesFiber opticYesNoNoYesNoNoTwo year
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Credit card (automatic)84.655377.8
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90015-UOCOJFemale1
❌
❌
7
✅
NoDSLYesNoNoNoNoNoMonth-to-month
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Electronic check48.2340.35
❌
100016-QLJISFemale0
✅
✅
65
✅
YesDSLYesYesYesYesYesYesTwo year
✅
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110017-DINOCMale0
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❌
54
❌
No phone serviceDSLYesNoNoYesYesNoTwo year
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120017-IUDMWFemale0
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72
✅
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❌
5
✅
NoFiber opticNoNoNoNoNoNoMonth-to-month
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140019-EFAEPFemale0
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✅
YesFiber opticYesYesYesNoYesNoTwo year
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150019-GFNTWFemale0
❌
❌
56
❌
No phone serviceDSLYesYesYesYesNoNoTwo year
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160020-INWCKFemale0
✅
✅
71
✅
YesFiber opticNoYesYesNoNoYesTwo year
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170020-JDNXPFemale0
✅
✅
34
❌
No phone serviceDSLYesNoYesYesYesYesOne year
❌
Mailed check61.251993.2
❌
180021-IKXGCFemale1
❌
❌
1
✅
YesFiber opticNoNoNoNoNoNoMonth-to-month
✅
Electronic check72.172.1
❌
190022-TCJCIMale1
❌
❌
45
✅
NoDSLYesNoYesNoNoYesOne year
❌
Credit card (automatic)62.72791.5
✅
200023-HGHWLMale1
❌
❌
1
❌
No phone serviceDSLNoNoNoNoNoNoMonth-to-month
✅
Electronic check25.125.1
✅
210023-UYUPNFemale1
✅
❌
50
✅
YesNoNo internet serviceNo internet serviceNo internet serviceNo internet serviceNo internet serviceNo internet serviceOne year
❌
Electronic check25.21306.3
❌
220023-XUOPTFemale0
✅
❌
13
✅
YesFiber opticNoYesYesNoYesNoMonth-to-month
❌
Electronic check94.11215.6
✅
230027-KWYKWFemale0
✅
✅
23
✅
YesFiber opticNoNoNoNoYesNoMonth-to-month
✅
Electronic check83.751849.95
❌
240030-FNXPPFemale0
❌
❌
3
✅
NoNoNo internet serviceNo internet serviceNo internet serviceNo internet serviceNo internet serviceNo internet serviceMonth-to-month
❌
Mailed check19.8557.2
❌
250031-PVLZIFemale0
✅
✅
4
✅
NoNoNo internet serviceNo internet serviceNo internet serviceNo internet serviceNo internet serviceNo internet serviceMonth-to-month
❌
Mailed check20.3576.35
✅
260032-PGELSFemale0
✅
✅
1
❌
No phone serviceDSLYesNoNoNoNoNoMonth-to-month
❌
Bank transfer (automatic)30.530.5
✅
270036-IHMOTFemale0
✅
✅
55
✅
NoFiber opticNoYesYesYesYesYesOne year
✅
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❌
280040-HALCWMale0
✅
✅
54
✅
NoNoNo internet serviceNo internet serviceNo internet serviceNo internet serviceNo internet serviceNo internet serviceTwo year
❌
Credit card (automatic)20.41090.6
❌
290042-JVWOJMale0
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❌
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✅
NoNoNo internet serviceNo internet serviceNo internet serviceNo internet serviceNo internet serviceNo internet serviceOne year
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300042-RLHYPFemale0
✅
✅
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✅
NoNoNo internet serviceNo internet serviceNo internet serviceNo internet serviceNo internet serviceNo internet serviceTwo year
❌
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310048-LUMLSMale0
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✅
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✅
NoFiber opticNoNoNoNoYesYesOne year
❌
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❌
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✅
❌
49
✅
NoNoNo internet serviceNo internet serviceNo internet serviceNo internet serviceNo internet serviceNo internet serviceOne year
❌
Bank transfer (automatic)20.45900.9
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❌
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✅
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❌
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❌
340052-YNYOTFemale0
❌
❌
67
✅
NoNoNo internet serviceNo internet serviceNo internet serviceNo internet serviceNo internet serviceNo internet serviceOne year
❌
Electronic check20.551343.4
❌
350056-EPFBGMale0
✅
✅
20
❌
No phone serviceDSLYesNoYesYesNoNoTwo year
✅
Credit card (automatic)39.4825.4
❌
360057-QBUQHFemale0
❌
✅
43
✅
YesNoNo internet serviceNo internet serviceNo internet serviceNo internet serviceNo internet serviceNo internet serviceTwo year
✅
Electronic check25.11070.15
❌
370058-EVZWMFemale0
✅
❌
55
✅
YesFiber opticYesNoNoNoYesNoMonth-to-month
✅
Bank transfer (automatic)89.84959.6
❌
380060-FUALYFemale0
✅
❌
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✅
YesFiber opticYesYesNoNoYesNoMonth-to-month
✅
Electronic check94.755597.65
❌
390064-SUDOGFemale0
✅
✅
12
✅
NoNoNo internet serviceNo internet serviceNo internet serviceNo internet serviceNo internet serviceNo internet serviceTwo year
❌
Bank transfer (automatic)20.3224.5
❌
400064-YIJGFMale0
✅
✅
27
✅
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Bank transfer (automatic)75.751929.0
❌
410067-DKWBLMale1
❌
❌
2
✅
NoDSLYesNoNoNoNoNoMonth-to-month
✅
Electronic check49.2591.1
✅
420068-FIGTFFemale0
❌
❌
27
✅
NoDSLNoYesYesYesYesYesOne year
❌
Mailed check78.22078.95
❌
430071-NDAFPMale0
✅
✅
25
✅
YesNoNo internet serviceNo internet serviceNo internet serviceNo internet serviceNo internet serviceNo internet serviceTwo year
❌
Credit card (automatic)25.5630.6
❌
440074-HDKDGMale0
✅
✅
25
✅
NoDSLYesYesYesNoNoNoOne year
✅
Bank transfer (automatic)61.61611.0
❌
450076-LVEPSMale0
❌
✅
29
❌
No phone serviceDSLYesYesYesYesNoNoMonth-to-month
✅
Mailed check45.01242.45
❌
460078-XZMHTMale0
✅
❌
72
✅
YesDSLNoYesYesYesYesYesTwo year
✅
Bank transfer (automatic)85.156316.2
❌
470080-EMYVYFemale0
❌
❌
14
✅
NoDSLNoYesNoNoNoNoOne year
❌
Credit card (automatic)51.45727.85
❌
480080-OROZOFemale0
❌
❌
35
✅
NoFiber opticNoNoYesYesYesYesOne year
✅
Electronic check99.253532.0
❌
490082-LDZUEMale0
❌
❌
1
✅
NoDSLNoNoNoNoNoNoMonth-to-month
✅
Mailed check44.344.3
❌
500082-OQIQYMale0
❌
❌
29
✅
NoFiber opticNoNoNoYesYesYesMonth-to-month
✅
Electronic check94.22607.6
❌
510083-PIVIKMale0
❌
❌
64
✅
YesDSLYesYesYesYesYesNoOne year
❌
Electronic check81.255567.55
❌
520089-IIQKOFemale0
✅
✅
39
✅
YesFiber opticNoNoNoYesYesYesMonth-to-month
✅
Credit card (automatic)99.953767.4
❌
530093-EXYQLFemale1
❌
❌
40
✅
NoFiber opticNoNoNoNoYesYesMonth-to-month
✅
Electronic check91.553673.6
❌
540093-XWZFYMale0
❌
❌
40
✅
YesFiber opticNoYesYesNoYesYesMonth-to-month
✅
Credit card (automatic)104.54036.85
✅
550094-OIFMOFemale1
❌
❌
11
✅
NoFiber opticNoYesNoNoYesYesMonth-to-month
✅
Electronic check95.01120.3
✅
560096-BXERSFemale0
✅
❌
6
✅
YesDSLNoNoNoNoNoNoMonth-to-month
❌
Electronic check50.35314.55
❌
570096-FCPUFMale0
❌
❌
30
✅
YesDSLYesNoNoNoNoYesMonth-to-month
✅
Mailed check64.51888.45
❌
580098-BOWSOMale0
❌
❌
27
✅
NoNoNo internet serviceNo internet serviceNo internet serviceNo internet serviceNo internet serviceNo internet serviceMonth-to-month
✅
Electronic check19.4529.8
❌
590100-DUVFCMale1
✅
❌
70
✅
YesFiber opticNoYesYesNoYesYesOne year
✅
Electronic check104.87308.95
❌
600103-CSITQFemale0
✅
❌
57
✅
YesFiber opticNoYesYesYesYesYesOne year
✅
Bank transfer (automatic)109.46252.7
❌
610104-PPXDVMale0
✅
❌
58
✅
NoDSLNoNoYesNoNoNoOne year
❌
Credit card (automatic)50.32878.55
❌
620106-GHRQRMale0
❌
❌
16
✅
YesDSLNoYesYesNoNoYesMonth-to-month
✅
Bank transfer (automatic)71.41212.1
❌
630106-UGRDOFemale0
✅
❌
69
✅
YesFiber opticYesYesYesYesYesYesTwo year
✅
Electronic check116.08182.85
❌
640107-WESLMMale0
❌
❌
1
✅
NoNoNo internet serviceNo internet serviceNo internet serviceNo internet serviceNo internet serviceNo internet serviceMonth-to-month
✅
Electronic check19.8519.85
✅
650107-YHINAMale0
❌
✅
1
✅
YesFiber opticNoNoYesNoYesYesMonth-to-month
✅
Electronic check99.7599.75
✅
660111-KLBQGMale1
✅
✅
32
✅
NoFiber opticNoYesNoNoYesYesMonth-to-month
✅
Mailed check93.952861.45
❌
670112-QAWRZMale0
✅
✅
16
✅
YesFiber opticNoNoYesNoYesNoMonth-to-month
✅
Bank transfer (automatic)90.81442.2
❌
680112-QWPNCMale0
✅
❌
49
✅
YesDSLYesNoYesYesYesYesOne year
❌
Electronic check84.354059.35
✅
690114-IGABWFemale0
✅
❌
71
❌
No phone serviceDSLNoYesYesYesYesYesTwo year
❌
Bank transfer (automatic)58.254145.9
❌
700114-PEGZZFemale0
❌
❌
33
✅
YesFiber opticNoYesYesNoYesYesMonth-to-month
❌
Electronic check107.553645.5
❌
710114-RSRRWFemale0
✅
❌
10
✅
NoNoNo internet serviceNo internet serviceNo internet serviceNo internet serviceNo internet serviceNo internet serviceMonth-to-month
✅
Bank transfer (automatic)19.95187.75
❌
720115-TFERTMale0
✅
❌
21
✅
YesFiber opticNoYesYesYesYesYesMonth-to-month
✅
Electronic check111.22317.1
✅
730117-LFRMWMale0
✅
✅
37
❌
No phone serviceDSLYesYesYesNoNoNoMonth-to-month
❌
Bank transfer (automatic)40.21448.8
✅
740118-JPNOYFemale1
❌
❌
26
✅
NoFiber opticYesNoNoNoYesNoMonth-to-month
✅
Credit card (automatic)85.82193.65
❌
750121-SNYRKMale0
❌
❌
50
❌
No phone serviceDSLYesNoNoYesNoNoOne year
✅
Mailed check35.41748.9
❌
760122-OAHPZFemale0
❌
❌
7
✅
YesFiber opticNoNoNoNoNoNoMonth-to-month
✅
Electronic check73.85511.25
✅
770123-CRBRTFemale0
✅
✅
61
✅
YesDSLYesYesYesYesYesYesTwo year
❌
Mailed check88.15526.75
❌
780125-LZQXKMale0
❌
❌
15
✅
NoFiber opticNoNoYesYesYesYesMonth-to-month
✅
Electronic check101.351553.95
✅
790128-MKWSGFemale0
❌
✅
26
❌
No phone serviceDSLYesNoNoYesNoYesMonth-to-month
❌
Mailed check45.81147.0
❌
800129-KPTWJMale0
✅
❌
72
✅
NoFiber opticNoNoYesNoYesYesMonth-to-month
✅
Electronic check94.656747.35
❌
810129-QMPDRMale0
✅
✅
44
✅
NoNoNo internet serviceNo internet serviceNo internet serviceNo internet serviceNo internet serviceNo internet serviceOne year
✅
Bank transfer (automatic)20.5865.05
❌
820130-SXOUNMale0
❌
❌
66
✅
YesFiber opticNoYesNoNoNoYesMonth-to-month
❌
Credit card (automatic)89.45976.9
❌
830133-BMFZOFemale0
❌
❌
2
✅
NoFiber opticYesYesNoYesNoNoMonth-to-month
✅
Electronic check86.25181.65
✅
840134-XWXCEFemale1
❌
❌
44
✅
NoDSLNoNoYesYesYesYesOne year
❌
Bank transfer (automatic)74.853268.05
❌
850135-NMXAPFemale0
❌
❌
12
✅
YesFiber opticNoYesNoNoYesNoMonth-to-month
✅
Bank transfer (automatic)89.751052.4
✅
860136-IFMYDMale1
✅
❌
69
✅
YesFiber opticNoYesYesYesYesYesTwo year
✅
Electronic check109.957634.25
❌
870137-OCGABFemale0
❌
❌
1
✅
YesFiber opticNoYesNoNoNoNoMonth-to-month
✅
Mailed check80.280.2
✅
880137-UDEUOFemale0
❌
❌
3
✅
NoNoNo internet serviceNo internet serviceNo internet serviceNo internet serviceNo internet serviceNo internet serviceMonth-to-month
❌
Mailed check19.8563.75
✅
890139-IVFJGFemale0
✅
❌
2
✅
NoFiber opticYesYesNoNoYesNoMonth-to-month
❌
Electronic check90.35190.5
❌
900141-YEAYSFemale1
❌
❌
27
✅
YesFiber opticNoYesYesNoNoNoMonth-to-month
✅
Bank transfer (automatic)86.452401.05
❌
910142-GVYSNMale0
❌
❌
26
✅
NoNoNo internet serviceNo internet serviceNo internet serviceNo internet serviceNo internet serviceNo internet serviceMonth-to-month
✅
Electronic check20.3511.25
❌
920147-ESWWRFemale1
✅
❌
39
✅
YesFiber opticNoNoNoYesYesYesMonth-to-month
✅
Electronic check101.253949.15
❌
930148-DCDOSMale0
❌
❌
25
✅
YesFiber opticNoNoNoNoYesYesMonth-to-month
✅
Bank transfer (automatic)94.72362.1
✅
940151-ONTOVFemale0
❌
❌
1
✅
NoFiber opticNoNoNoNoNoNoMonth-to-month
❌
Mailed check70.970.9
✅
950156-FVPTAMale0
✅
❌
22
✅
NoDSLYesNoNoYesNoNoMonth-to-month
✅
Electronic check54.21152.7
✅
960164-APGRBFemale0
❌
❌
72
✅
YesFiber opticYesYesYesYesYesYesTwo year
✅
Electronic check114.98496.7
❌
970164-XAIRPFemale0
❌
❌
24
✅
NoNoNo internet serviceNo internet serviceNo internet serviceNo internet serviceNo internet serviceNo internet serviceTwo year
✅
Bank transfer (automatic)19.55470.2
❌
980168-XZKBBFemale0
✅
❌
19
✅
YesFiber opticNoNoNoNoYesNoMonth-to-month
✅
Electronic check86.851564.4
❌
990174-QRVVYMale0
✅
✅
71
✅
YesNoNo internet serviceNo internet serviceNo internet serviceNo internet serviceNo internet serviceNo internet serviceTwo year
❌
Credit card (automatic)25.351847.55
❌
1000177-PXBATMale1
✅
❌
33
✅
YesFiber opticYesNoYesYesYesYesMonth-to-month
✅
Bank transfer (automatic)109.93694.7
❌
Rows: 1-100 | Columns: 21
" ], "text/plain": [ "None customerID gender SeniorCitizen Partner Dependents \\\\\n", "1 0002-ORFBO Female 0 True True \\\\\n", "2 0003-MKNFE Male 0 False False \\\\\n", "3 0004-TLHLJ Male 0 False False \\\\\n", "4 0011-IGKFF Male 1 True False \\\\\n", "5 0013-EXCHZ Female 1 True False \\\\\n", "6 0013-MHZWF Female 0 False True \\\\\n", "7 0013-SMEOE Female 1 True False \\\\\n", "8 0014-BMAQU Male 0 True False \\\\\n", "9 0015-UOCOJ Female 1 False False \\\\\n", "10 0016-QLJIS Female 0 True True \\\\\n", "11 0017-DINOC Male 0 False False \\\\\n", "12 0017-IUDMW Female 0 True True \\\\\n", "13 0018-NYROU Female 0 True False \\\\\n", "14 0019-EFAEP Female 0 False False \\\\\n", "15 0019-GFNTW Female 0 False False \\\\\n", "16 0020-INWCK Female 0 True True \\\\\n", "17 0020-JDNXP Female 0 True True \\\\\n", "18 0021-IKXGC Female 1 False False \\\\\n", "19 0022-TCJCI Male 1 False False \\\\\n", "20 0023-HGHWL Male 1 False False \\\\\n", "21 0023-UYUPN Female 1 True False \\\\\n", "22 0023-XUOPT Female 0 True False \\\\\n", "23 0027-KWYKW Female 0 True True \\\\\n", "24 0030-FNXPP Female 0 False False \\\\\n", "25 0031-PVLZI Female 0 True True \\\\\n", "26 0032-PGELS Female 0 True True \\\\\n", "27 0036-IHMOT Female 0 True True \\\\\n", "28 0040-HALCW Male 0 True True \\\\\n", "29 0042-JVWOJ Male 0 False False \\\\\n", "30 0042-RLHYP Female 0 True True \\\\\n", "31 0048-LUMLS Male 0 True True \\\\\n", "32 0048-PIHNL Female 0 True False \\\\\n", "33 0052-DCKON Male 0 True False \\\\\n", "34 0052-YNYOT Female 0 False False \\\\\n", "35 0056-EPFBG Male 0 True True \\\\\n", "36 0057-QBUQH Female 0 False True \\\\\n", "37 0058-EVZWM Female 0 True False \\\\\n", "38 0060-FUALY Female 0 True False \\\\\n", "39 0064-SUDOG Female 0 True True \\\\\n", "40 0064-YIJGF Male 0 True True \\\\\n", "41 0067-DKWBL Male 1 False False \\\\\n", "42 0068-FIGTF Female 0 False False \\\\\n", "43 0071-NDAFP Male 0 True True \\\\\n", "44 0074-HDKDG Male 0 True True \\\\\n", "45 0076-LVEPS Male 0 False True \\\\\n", "46 0078-XZMHT Male 0 True False \\\\\n", "47 0080-EMYVY Female 0 False False \\\\\n", "48 0080-OROZO Female 0 False False \\\\\n", "49 0082-LDZUE Male 0 False False \\\\\n", "50 0082-OQIQY Male 0 False False \\\\\n", "51 0083-PIVIK Male 0 False False \\\\\n", "52 0089-IIQKO Female 0 True True \\\\\n", "53 0093-EXYQL Female 1 False False \\\\\n", "54 0093-XWZFY Male 0 False False \\\\\n", "55 0094-OIFMO Female 1 False False \\\\\n", "56 0096-BXERS Female 0 True False \\\\\n", "57 0096-FCPUF Male 0 False False \\\\\n", "58 0098-BOWSO Male 0 False False \\\\\n", "59 0100-DUVFC Male 1 True False \\\\\n", "60 0103-CSITQ Female 0 True False \\\\\n", "61 0104-PPXDV Male 0 True False \\\\\n", "62 0106-GHRQR Male 0 False False \\\\\n", "63 0106-UGRDO Female 0 True False \\\\\n", "64 0107-WESLM Male 0 False False \\\\\n", "65 0107-YHINA Male 0 False True \\\\\n", "66 0111-KLBQG Male 1 True True \\\\\n", "67 0112-QAWRZ Male 0 True True \\\\\n", "68 0112-QWPNC Male 0 True False \\\\\n", "69 0114-IGABW Female 0 True False \\\\\n", "70 0114-PEGZZ Female 0 False False \\\\\n", "71 0114-RSRRW Female 0 True False \\\\\n", "72 0115-TFERT Male 0 True False \\\\\n", "73 0117-LFRMW Male 0 True True \\\\\n", "74 0118-JPNOY Female 1 False False \\\\\n", "75 0121-SNYRK Male 0 False False \\\\\n", "76 0122-OAHPZ Female 0 False False \\\\\n", "77 0123-CRBRT Female 0 True True \\\\\n", "78 0125-LZQXK Male 0 False False \\\\\n", "79 0128-MKWSG Female 0 False True \\\\\n", "80 0129-KPTWJ Male 0 True False \\\\\n", "81 0129-QMPDR Male 0 True True \\\\\n", "82 0130-SXOUN Male 0 False False \\\\\n", "83 0133-BMFZO Female 0 False False \\\\\n", "84 0134-XWXCE Female 1 False False \\\\\n", "85 0135-NMXAP Female 0 False False \\\\\n", "86 0136-IFMYD Male 1 True False \\\\\n", "87 0137-OCGAB Female 0 False False \\\\\n", "88 0137-UDEUO Female 0 False False \\\\\n", "89 0139-IVFJG Female 0 True False \\\\\n", "90 0141-YEAYS Female 1 False False \\\\\n", "91 0142-GVYSN Male 0 False False \\\\\n", "92 0147-ESWWR Female 1 True False \\\\\n", "93 0148-DCDOS Male 0 False False \\\\\n", "94 0151-ONTOV Female 0 False False \\\\\n", "95 0156-FVPTA Male 0 True False \\\\\n", "96 0164-APGRB Female 0 False False \\\\\n", "97 0164-XAIRP Female 0 False False \\\\\n", "98 0168-XZKBB Female 0 True False \\\\\n", "99 0174-QRVVY Male 0 True True \\\\\n", "100 0177-PXBAT Male 1 True False \\\\\n", "None tenure PhoneService MultipleLines InternetService \\\\\n", "1 9 True No DSL \\\\\n", "2 9 True Yes DSL \\\\\n", "3 4 True No Fiber optic \\\\\n", "4 13 True No Fiber optic \\\\\n", "5 3 True No Fiber optic \\\\\n", "6 9 True No DSL \\\\\n", "7 71 True No Fiber optic \\\\\n", "8 63 True Yes Fiber optic \\\\\n", "9 7 True No DSL \\\\\n", "10 65 True Yes DSL \\\\\n", "11 54 False No phone service DSL \\\\\n", "12 72 True Yes Fiber optic \\\\\n", "13 5 True No Fiber optic \\\\\n", "14 72 True Yes Fiber optic \\\\\n", "15 56 False No phone service DSL \\\\\n", "16 71 True Yes Fiber optic \\\\\n", "17 34 False No phone service DSL \\\\\n", "18 1 True Yes Fiber optic \\\\\n", "19 45 True No DSL \\\\\n", "20 1 False No phone service DSL \\\\\n", "21 50 True Yes No \\\\\n", "22 13 True Yes Fiber optic \\\\\n", "23 23 True Yes Fiber optic \\\\\n", "24 3 True No No \\\\\n", "25 4 True No No \\\\\n", "26 1 False No phone service DSL \\\\\n", "27 55 True No Fiber optic \\\\\n", "28 54 True No No \\\\\n", "29 26 True No No \\\\\n", "30 69 True No No \\\\\n", "31 37 True No Fiber optic \\\\\n", "32 49 True No No \\\\\n", "33 66 True Yes Fiber optic \\\\\n", "34 67 True No No \\\\\n", "35 20 False No phone service DSL \\\\\n", "36 43 True Yes No \\\\\n", "37 55 True Yes Fiber optic \\\\\n", "38 59 True Yes Fiber optic \\\\\n", "39 12 True No No \\\\\n", "40 27 True Yes Fiber optic \\\\\n", "41 2 True No DSL \\\\\n", "42 27 True No DSL \\\\\n", "43 25 True Yes No \\\\\n", "44 25 True No DSL \\\\\n", "45 29 False No phone service DSL \\\\\n", "46 72 True Yes DSL \\\\\n", "47 14 True No DSL \\\\\n", "48 35 True No Fiber optic \\\\\n", "49 1 True No DSL \\\\\n", "50 29 True No Fiber optic \\\\\n", "51 64 True Yes DSL \\\\\n", "52 39 True Yes Fiber optic \\\\\n", "53 40 True No Fiber optic \\\\\n", "54 40 True Yes Fiber optic \\\\\n", "55 11 True No Fiber optic \\\\\n", "56 6 True Yes DSL \\\\\n", "57 30 True Yes DSL \\\\\n", "58 27 True No No \\\\\n", "59 70 True Yes Fiber optic \\\\\n", "60 57 True Yes Fiber optic \\\\\n", "61 58 True No DSL \\\\\n", "62 16 True Yes DSL \\\\\n", "63 69 True Yes Fiber optic \\\\\n", "64 1 True No No \\\\\n", "65 1 True Yes Fiber optic \\\\\n", "66 32 True No Fiber optic \\\\\n", "67 16 True Yes Fiber optic \\\\\n", "68 49 True Yes DSL \\\\\n", "69 71 False No phone service DSL \\\\\n", "70 33 True Yes Fiber optic \\\\\n", "71 10 True No No \\\\\n", "72 21 True Yes Fiber optic \\\\\n", "73 37 False No phone service DSL \\\\\n", "74 26 True No Fiber optic \\\\\n", "75 50 False No phone service DSL \\\\\n", "76 7 True Yes Fiber optic \\\\\n", "77 61 True Yes DSL \\\\\n", "78 15 True No Fiber optic \\\\\n", "79 26 False No phone service DSL \\\\\n", "80 72 True No Fiber optic \\\\\n", "81 44 True No No \\\\\n", "82 66 True Yes Fiber optic \\\\\n", "83 2 True No Fiber optic \\\\\n", "84 44 True No DSL \\\\\n", "85 12 True Yes Fiber optic \\\\\n", "86 69 True Yes Fiber optic \\\\\n", "87 1 True Yes Fiber optic \\\\\n", "88 3 True No No \\\\\n", "89 2 True No Fiber optic \\\\\n", "90 27 True Yes Fiber optic \\\\\n", "91 26 True No No \\\\\n", "92 39 True Yes Fiber optic \\\\\n", "93 25 True Yes Fiber optic \\\\\n", "94 1 True No Fiber optic \\\\\n", "95 22 True No DSL \\\\\n", "96 72 True Yes Fiber optic \\\\\n", "97 24 True No No \\\\\n", "98 19 True Yes Fiber optic \\\\\n", "99 71 True Yes No \\\\\n", "100 33 True Yes Fiber optic \\\\\n", "None OnlineSecurity OnlineBackup DeviceProtection \\\\\n", "1 No Yes No \\\\\n", "2 No No No \\\\\n", "3 No No Yes \\\\\n", "4 No Yes Yes \\\\\n", "5 No No No \\\\\n", "6 No No No \\\\\n", "7 Yes Yes Yes \\\\\n", "8 Yes No No \\\\\n", "9 Yes No No \\\\\n", "10 Yes Yes Yes \\\\\n", "11 Yes No No \\\\\n", "12 Yes Yes Yes \\\\\n", "13 No No No \\\\\n", "14 Yes Yes Yes \\\\\n", "15 Yes Yes Yes \\\\\n", "16 No Yes Yes \\\\\n", "17 Yes No Yes \\\\\n", "18 No No No \\\\\n", "19 Yes No Yes \\\\\n", "20 No No No \\\\\n", "21 No internet service No internet service No internet service \\\\\n", "22 No Yes Yes \\\\\n", "23 No No No \\\\\n", "24 No internet service No internet service No internet service \\\\\n", "25 No internet service No internet service No internet service \\\\\n", "26 Yes No No \\\\\n", "27 No Yes Yes \\\\\n", "28 No internet service No internet service No internet service \\\\\n", "29 No internet service No internet service No internet service \\\\\n", "30 No internet service No internet service No internet service \\\\\n", "31 No No No \\\\\n", "32 No internet service No internet service No internet service \\\\\n", "33 Yes Yes Yes \\\\\n", "34 No internet service No internet service No internet service \\\\\n", "35 Yes No Yes \\\\\n", "36 No internet service No internet service No internet service \\\\\n", "37 Yes No No \\\\\n", "38 Yes Yes No \\\\\n", "39 No internet service No internet service No internet service \\\\\n", "40 No No No \\\\\n", "41 Yes No No \\\\\n", "42 No Yes Yes \\\\\n", "43 No internet service No internet service No internet service \\\\\n", "44 Yes Yes Yes \\\\\n", "45 Yes Yes Yes \\\\\n", "46 No Yes Yes \\\\\n", "47 No Yes No \\\\\n", "48 No No Yes \\\\\n", "49 No No No \\\\\n", "50 No No No \\\\\n", "51 Yes Yes Yes \\\\\n", "52 No No No \\\\\n", "53 No No No \\\\\n", "54 No Yes Yes \\\\\n", "55 No Yes No \\\\\n", "56 No No No \\\\\n", "57 Yes No No \\\\\n", "58 No internet service No internet service No internet service \\\\\n", "59 No Yes Yes \\\\\n", "60 No Yes Yes \\\\\n", "61 No No Yes \\\\\n", "62 No Yes Yes \\\\\n", "63 Yes Yes Yes \\\\\n", "64 No internet service No internet service No internet service \\\\\n", "65 No No Yes \\\\\n", "66 No Yes No \\\\\n", "67 No No Yes \\\\\n", "68 Yes No Yes \\\\\n", "69 No Yes Yes \\\\\n", "70 No Yes Yes \\\\\n", "71 No internet service No internet service No internet service \\\\\n", "72 No Yes Yes \\\\\n", "73 Yes Yes Yes \\\\\n", "74 Yes No No \\\\\n", "75 Yes No No \\\\\n", "76 No No No \\\\\n", "77 Yes Yes Yes \\\\\n", "78 No No Yes \\\\\n", "79 Yes No No \\\\\n", "80 No No Yes \\\\\n", "81 No internet service No internet service No internet service \\\\\n", "82 No Yes No \\\\\n", "83 Yes Yes No \\\\\n", "84 No No Yes \\\\\n", "85 No Yes No \\\\\n", "86 No Yes Yes \\\\\n", "87 No Yes No \\\\\n", "88 No internet service No internet service No internet service \\\\\n", "89 Yes Yes No \\\\\n", "90 No Yes Yes \\\\\n", "91 No internet service No internet service No internet service \\\\\n", "92 No No No \\\\\n", "93 No No No \\\\\n", "94 No No No \\\\\n", "95 Yes No No \\\\\n", "96 Yes Yes Yes \\\\\n", "97 No internet service No internet service No internet service \\\\\n", "98 No No No \\\\\n", "99 No internet service No internet service No internet service \\\\\n", "100 Yes No Yes \\\\\n", "None TechSupport StreamingTV StreamingMovies \\\\\n", "1 Yes Yes No \\\\\n", "2 No No Yes \\\\\n", "3 No No No \\\\\n", "4 No Yes Yes \\\\\n", "5 Yes Yes No \\\\\n", "6 Yes Yes Yes \\\\\n", "7 Yes Yes Yes \\\\\n", "8 Yes No No \\\\\n", "9 No No No \\\\\n", "10 Yes Yes Yes \\\\\n", "11 Yes Yes No \\\\\n", "12 Yes Yes Yes \\\\\n", "13 No No No \\\\\n", "14 No Yes No \\\\\n", "15 Yes No No \\\\\n", "16 No No Yes \\\\\n", "17 Yes Yes Yes \\\\\n", "18 No No No \\\\\n", "19 No No Yes \\\\\n", "20 No No No \\\\\n", "21 No internet service No internet service No internet service \\\\\n", "22 No Yes No \\\\\n", "23 No Yes No \\\\\n", "24 No internet service No internet service No internet service \\\\\n", "25 No internet service No internet service No internet service \\\\\n", "26 No No No \\\\\n", "27 Yes Yes Yes \\\\\n", "28 No internet service No internet service No internet service \\\\\n", "29 No internet service No internet service No internet service \\\\\n", "30 No internet service No internet service No internet service \\\\\n", "31 No Yes Yes \\\\\n", "32 No internet service No internet service No internet service \\\\\n", "33 Yes Yes Yes \\\\\n", "34 No internet service No internet service No internet service \\\\\n", "35 Yes No No \\\\\n", "36 No internet service No internet service No internet service \\\\\n", "37 No Yes No \\\\\n", "38 No Yes No \\\\\n", "39 No internet service No internet service No internet service \\\\\n", "40 No No No \\\\\n", "41 No No No \\\\\n", "42 Yes Yes Yes \\\\\n", "43 No internet service No internet service No internet service \\\\\n", "44 No No No \\\\\n", "45 Yes No No \\\\\n", "46 Yes Yes Yes \\\\\n", "47 No No No \\\\\n", "48 Yes Yes Yes \\\\\n", "49 No No No \\\\\n", "50 Yes Yes Yes \\\\\n", "51 Yes Yes No \\\\\n", "52 Yes Yes Yes \\\\\n", "53 No Yes Yes \\\\\n", "54 No Yes Yes \\\\\n", "55 No Yes Yes \\\\\n", "56 No No No \\\\\n", "57 No No Yes \\\\\n", "58 No internet service No internet service No internet service \\\\\n", "59 No Yes Yes \\\\\n", "60 Yes Yes Yes \\\\\n", "61 No No No \\\\\n", "62 No No Yes \\\\\n", "63 Yes Yes Yes \\\\\n", "64 No internet service No internet service No internet service \\\\\n", "65 No Yes Yes \\\\\n", "66 No Yes Yes \\\\\n", "67 No Yes No \\\\\n", "68 Yes Yes Yes \\\\\n", "69 Yes Yes Yes \\\\\n", "70 No Yes Yes \\\\\n", "71 No internet service No internet service No internet service \\\\\n", "72 Yes Yes Yes \\\\\n", "73 No No No \\\\\n", "74 No Yes No \\\\\n", "75 Yes No No \\\\\n", "76 No No No \\\\\n", "77 Yes Yes Yes \\\\\n", "78 Yes Yes Yes \\\\\n", "79 Yes No Yes \\\\\n", "80 No Yes Yes \\\\\n", "81 No internet service No internet service No internet service \\\\\n", "82 No No Yes \\\\\n", "83 Yes No No \\\\\n", "84 Yes Yes Yes \\\\\n", "85 No Yes No \\\\\n", "86 Yes Yes Yes \\\\\n", "87 No No No \\\\\n", "88 No internet service No internet service No internet service \\\\\n", "89 No Yes No \\\\\n", "90 No No No \\\\\n", "91 No internet service No internet service No internet service \\\\\n", "92 Yes Yes Yes \\\\\n", "93 No Yes Yes \\\\\n", "94 No No No \\\\\n", "95 Yes No No \\\\\n", "96 Yes Yes Yes \\\\\n", "97 No internet service No internet service No internet service \\\\\n", "98 No Yes No \\\\\n", "99 No internet service No internet service No internet service \\\\\n", "100 Yes Yes Yes \\\\\n", "None Contract PaperlessBilling PaymentMethod \\\\\n", "1 One year True Mailed check \\\\\n", "2 Month-to-month False Mailed check \\\\\n", "3 Month-to-month True Electronic check \\\\\n", "4 Month-to-month True Electronic check \\\\\n", "5 Month-to-month True Mailed check \\\\\n", "6 Month-to-month True Credit card (automatic) \\\\\n", "7 Two year True Bank transfer (automatic) \\\\\n", "8 Two year True Credit card (automatic) \\\\\n", "9 Month-to-month True Electronic check \\\\\n", "10 Two year True Mailed check \\\\\n", "11 Two year False Credit card (automatic) \\\\\n", "12 Two year True Credit card (automatic) \\\\\n", "13 Month-to-month True Electronic check \\\\\n", "14 Two year True Bank transfer (automatic) \\\\\n", "15 Two year False Bank transfer (automatic) \\\\\n", "16 Two year True Credit card (automatic) \\\\\n", "17 One year False Mailed check \\\\\n", "18 Month-to-month True Electronic check \\\\\n", "19 One year False Credit card (automatic) \\\\\n", "20 Month-to-month True Electronic check \\\\\n", "21 One year False Electronic check \\\\\n", "22 Month-to-month False Electronic check \\\\\n", "23 Month-to-month True Electronic check \\\\\n", "24 Month-to-month False Mailed check \\\\\n", "25 Month-to-month False Mailed check \\\\\n", "26 Month-to-month False Bank transfer (automatic) \\\\\n", "27 One year True Bank transfer (automatic) \\\\\n", "28 Two year False Credit card (automatic) \\\\\n", "29 One year True Bank transfer (automatic) \\\\\n", "30 Two year False Bank transfer (automatic) \\\\\n", "31 One year False Credit card (automatic) \\\\\n", "32 One year False Bank transfer (automatic) \\\\\n", "33 One year False Bank transfer (automatic) \\\\\n", "34 One year False Electronic check \\\\\n", "35 Two year True Credit card (automatic) \\\\\n", "36 Two year True Electronic check \\\\\n", "37 Month-to-month True Bank transfer (automatic) \\\\\n", "38 Month-to-month True Electronic check \\\\\n", "39 Two year False Bank transfer (automatic) \\\\\n", "40 Month-to-month True Bank transfer (automatic) \\\\\n", "41 Month-to-month True Electronic check \\\\\n", "42 One year False Mailed check \\\\\n", "43 Two year False Credit card (automatic) \\\\\n", "44 One year True Bank transfer (automatic) \\\\\n", "45 Month-to-month True Mailed check \\\\\n", "46 Two year True Bank transfer (automatic) \\\\\n", "47 One year False Credit card (automatic) \\\\\n", "48 One year True Electronic check \\\\\n", "49 Month-to-month True Mailed check \\\\\n", "50 Month-to-month True Electronic check \\\\\n", "51 One year False Electronic check \\\\\n", "52 Month-to-month True Credit card (automatic) \\\\\n", "53 Month-to-month True Electronic check \\\\\n", "54 Month-to-month True Credit card (automatic) \\\\\n", "55 Month-to-month True Electronic check \\\\\n", "56 Month-to-month False Electronic check \\\\\n", "57 Month-to-month True Mailed check \\\\\n", "58 Month-to-month True Electronic check \\\\\n", "59 One year True Electronic check \\\\\n", "60 One year True Bank transfer (automatic) \\\\\n", "61 One year False Credit card (automatic) \\\\\n", "62 Month-to-month True Bank transfer (automatic) \\\\\n", "63 Two year True Electronic check \\\\\n", "64 Month-to-month True Electronic check \\\\\n", "65 Month-to-month True Electronic check \\\\\n", "66 Month-to-month True Mailed check \\\\\n", "67 Month-to-month True Bank transfer (automatic) \\\\\n", "68 One year False Electronic check \\\\\n", "69 Two year False Bank transfer (automatic) \\\\\n", "70 Month-to-month False Electronic check \\\\\n", "71 Month-to-month True Bank transfer (automatic) \\\\\n", "72 Month-to-month True Electronic check \\\\\n", "73 Month-to-month False Bank transfer (automatic) \\\\\n", "74 Month-to-month True Credit card (automatic) \\\\\n", "75 One year True Mailed check \\\\\n", "76 Month-to-month True Electronic check \\\\\n", "77 Two year False Mailed check \\\\\n", "78 Month-to-month True Electronic check \\\\\n", "79 Month-to-month False Mailed check \\\\\n", "80 Month-to-month True Electronic check \\\\\n", "81 One year True Bank transfer (automatic) \\\\\n", "82 Month-to-month False Credit card (automatic) \\\\\n", "83 Month-to-month True Electronic check \\\\\n", "84 One year False Bank transfer (automatic) \\\\\n", "85 Month-to-month True Bank transfer (automatic) \\\\\n", "86 Two year True Electronic check \\\\\n", "87 Month-to-month True Mailed check \\\\\n", "88 Month-to-month False Mailed check \\\\\n", "89 Month-to-month False Electronic check \\\\\n", "90 Month-to-month True Bank transfer (automatic) \\\\\n", "91 Month-to-month True Electronic check \\\\\n", "92 Month-to-month True Electronic check \\\\\n", "93 Month-to-month True Bank transfer (automatic) \\\\\n", "94 Month-to-month False Mailed check \\\\\n", "95 Month-to-month True Electronic check \\\\\n", "96 Two year True Electronic check \\\\\n", "97 Two year True Bank transfer (automatic) \\\\\n", "98 Month-to-month True Electronic check \\\\\n", "99 Two year False Credit card (automatic) \\\\\n", "100 Month-to-month True Bank transfer (automatic) \\\\\n", "None MonthlyCharges TotalCharges Churn \n", "1 65.6 593.3 False \n", "2 59.9 542.4 False \n", "3 73.9 280.85 True \n", "4 98.0 1237.85 True \n", "5 83.9 267.4 True \n", "6 69.4 571.45 False \n", "7 109.7 7904.25 False \n", "8 84.65 5377.8 False \n", "9 48.2 340.35 False \n", "10 90.45 5957.9 False \n", "11 45.2 2460.55 False \n", "12 116.8 8456.75 False \n", "13 68.95 351.5 False \n", "14 101.3 7261.25 False \n", "15 45.05 2560.1 False \n", "16 95.75 6849.4 False \n", "17 61.25 1993.2 False \n", "18 72.1 72.1 False \n", "19 62.7 2791.5 True \n", "20 25.1 25.1 True \n", "21 25.2 1306.3 False \n", "22 94.1 1215.6 True \n", "23 83.75 1849.95 False \n", "24 19.85 57.2 False \n", "25 20.35 76.35 True \n", "26 30.5 30.5 True \n", "27 103.7 5656.75 False \n", "28 20.4 1090.6 False \n", "29 19.6 471.85 False \n", "30 19.7 1396.9 False \n", "31 91.2 3247.55 False \n", "32 20.45 900.9 False \n", "33 115.8 7942.15 False \n", "34 20.55 1343.4 False \n", "35 39.4 825.4 False \n", "36 25.1 1070.15 False \n", "37 89.8 4959.6 False \n", "38 94.75 5597.65 False \n", "39 20.3 224.5 False \n", "40 75.75 1929.0 False \n", "41 49.25 91.1 True \n", "42 78.2 2078.95 False \n", "43 25.5 630.6 False \n", "44 61.6 1611.0 False \n", "45 45.0 1242.45 False \n", "46 85.15 6316.2 False \n", "47 51.45 727.85 False \n", "48 99.25 3532.0 False \n", "49 44.3 44.3 False \n", "50 94.2 2607.6 False \n", "51 81.25 5567.55 False \n", "52 99.95 3767.4 False \n", "53 91.55 3673.6 False \n", "54 104.5 4036.85 True \n", "55 95.0 1120.3 True \n", "56 50.35 314.55 False \n", "57 64.5 1888.45 False \n", "58 19.4 529.8 False \n", "59 104.8 7308.95 False \n", "60 109.4 6252.7 False \n", "61 50.3 2878.55 False \n", "62 71.4 1212.1 False \n", "63 116.0 8182.85 False \n", "64 19.85 19.85 True \n", "65 99.75 99.75 True \n", "66 93.95 2861.45 False \n", "67 90.8 1442.2 False \n", "68 84.35 4059.35 True \n", "69 58.25 4145.9 False \n", "70 107.55 3645.5 False \n", "71 19.95 187.75 False \n", "72 111.2 2317.1 True \n", "73 40.2 1448.8 True \n", "74 85.8 2193.65 False \n", "75 35.4 1748.9 False \n", "76 73.85 511.25 True \n", "77 88.1 5526.75 False \n", "78 101.35 1553.95 True \n", "79 45.8 1147.0 False \n", "80 94.65 6747.35 False \n", "81 20.5 865.05 False \n", "82 89.4 5976.9 False \n", "83 86.25 181.65 True \n", "84 74.85 3268.05 False \n", "85 89.75 1052.4 True \n", "86 109.95 7634.25 False \n", "87 80.2 80.2 True \n", "88 19.85 63.75 True \n", "89 90.35 190.5 False \n", "90 86.45 2401.05 False \n", "91 20.3 511.25 False \n", "92 101.25 3949.15 False \n", "93 94.7 2362.1 True \n", "94 70.9 70.9 True \n", "95 54.2 1152.7 True \n", "96 114.9 8496.7 False \n", "97 19.55 470.2 False \n", "98 86.85 1564.4 False \n", "99 25.35 1847.55 False \n", "100 109.9 3694.7 False \n", "Rows: 1-100 | Columns: 21" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import verticapy as vp\n", "\n", "vdf = vp.read_csv(\"data/churn.csv\")\n", "display(vdf)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Pearson correlation coefficient is a very common correlation function. In this case, it helped us to find linear links between the variables. Having a strong Pearson relationship means that the two input variables are linearly correlated." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vdf.corr(method = \"pearson\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see that 'tenure' is well-correlated to the 'TotalCharges', which makes sense." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vdf.scatter([\"tenure\", \"TotalCharges\"])" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.825880460933202" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vdf.corr([\"tenure\", \"TotalCharges\"], method = \"pearson\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note, however, that having a low Pearson relationship imply that the variables aren't correlated. For example, let's compute the Pearson correlation coefficient between 'tenure' and 'TotalCharges' to the power of 20." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vdf[\"TotalCharges^20\"] = vdf[\"TotalCharges\"] ** 20\n", "vdf.scatter([\"tenure\", \"TotalCharges^20\"])" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.224994408804537" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vdf.corr([\"tenure\", \"TotalCharges^20\"], method = \"pearson\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We know that the 'tenure' and 'TotalCharges' are strongly linearly correlated. However we can notice that the correlation between the 'tenure' and 'TotalCharges' to the power of 20 is not very high. Indeed, the Pearson correlation coefficient is not robust for monotonic relationships, but rank-based correlations are. Knowing this, we'll calculate the Spearman's rank correlation coefficient instead." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
"SeniorCitizen"
"Partner"
"Dependents"
"tenure"
"PhoneService"
"PaperlessBilling"
"MonthlyCharges"
"TotalCharges"
"Churn"
"TotalCharges^20"
"SeniorCitizen"1.00.0164786575974139-0.2111850884939580.01907678987011520.008576401079279440.1565295593111730.2210925291021620.1057953423037250.1508893281764730.105795342303725
"Partner"0.01647865759741391.00.4526762829294640.3846657102841190.017705663223972-0.0148766222878910.1084109458959810.343930553215626-0.1504475449591770.343930553215626
"Dependents"-0.2111850884939580.4526762829294641.00.164485741353804-0.00176167854468371-0.111377229193644-0.1070827255867110.0866797760484616-0.1642214015797250.0866797760484616
"tenure"0.01907678987011520.3846657102841190.1644857413538041.00.008150819869071840.007928762394763210.2763422452237080.883103368818293-0.3696207787634350.883103368818293
"PhoneService"0.008576401079279440.017705663223972-0.001761678544683710.008150819869071841.00.01650480573256970.2388264102300160.08380485478560370.01194198002900310.0838048547856037
"PaperlessBilling"0.156529559311173-0.014876622287891-0.1113772291936440.007928762394763210.01650480573256971.00.3461588793813230.1516697127990970.1918253316664680.151669712799097
"MonthlyCharges"0.2210925291021620.108410945895981-0.1070827255867110.2763422452237080.2388264102300160.3461588793813231.00.6339584053012060.1848392857837580.633958405301206
"TotalCharges"0.1057953423037250.3439305532156260.08667977604846160.8831033688182930.08380485478560370.1516697127990970.6339584053012061.0-0.2332110185851041.0
"Churn"0.150889328176473-0.150447544959177-0.164221401579725-0.3696207787634350.01194198002900310.1918253316664680.184839285783758-0.2332110185851041.0-0.233211018585104
"TotalCharges^20"0.1057953423037250.3439305532156260.08667977604846160.8831033688182930.08380485478560370.1516697127990970.6339584053012061.0-0.2332110185851041.0
Rows: 1-10 | Columns: 11
" ], "text/plain": [ "None \"SeniorCitizen\" \"Partner\" \"Dependents\" \\\\\n", "\"SeniorCitizen\" 1.0 0.0164786575974139 -0.211185088493958 \\\\\n", "\"Partner\" 0.0164786575974139 1.0 0.452676282929464 \\\\\n", "\"Dependents\" -0.211185088493958 0.452676282929464 1.0 \\\\\n", "\"tenure\" 0.0190767898701152 0.384665710284119 0.164485741353804 \\\\\n", "\"PhoneService\" 0.00857640107927944 0.017705663223972 -0.00176167854468371 \\\\\n", "\"PaperlessBilling\" 0.156529559311173 -0.014876622287891 -0.111377229193644 \\\\\n", "\"MonthlyCharges\" 0.221092529102162 0.108410945895981 -0.107082725586711 \\\\\n", "\"TotalCharges\" 0.105795342303725 0.343930553215626 0.0866797760484616 \\\\\n", "\"Churn\" 0.150889328176473 -0.150447544959177 -0.164221401579725 \\\\\n", "\"TotalCharges^20\" 0.105795342303725 0.343930553215626 0.0866797760484616 \\\\\n", "None \"tenure\" \"PhoneService\" \"PaperlessBilling\" \\\\\n", "\"SeniorCitizen\" 0.0190767898701152 0.00857640107927944 0.156529559311173 \\\\\n", "\"Partner\" 0.384665710284119 0.017705663223972 -0.014876622287891 \\\\\n", "\"Dependents\" 0.164485741353804 -0.00176167854468371 -0.111377229193644 \\\\\n", "\"tenure\" 1.0 0.00815081986907184 0.00792876239476321 \\\\\n", "\"PhoneService\" 0.00815081986907184 1.0 0.0165048057325697 \\\\\n", "\"PaperlessBilling\" 0.00792876239476321 0.0165048057325697 1.0 \\\\\n", "\"MonthlyCharges\" 0.276342245223708 0.238826410230016 0.346158879381323 \\\\\n", "\"TotalCharges\" 0.883103368818293 0.0838048547856037 0.151669712799097 \\\\\n", "\"Churn\" -0.369620778763435 0.0119419800290031 0.191825331666468 \\\\\n", "\"TotalCharges^20\" 0.883103368818293 0.0838048547856037 0.151669712799097 \\\\\n", "None \"MonthlyCharges\" \"TotalCharges\" \"Churn\" \\\\\n", "\"SeniorCitizen\" 0.221092529102162 0.105795342303725 0.150889328176473 \\\\\n", "\"Partner\" 0.108410945895981 0.343930553215626 -0.150447544959177 \\\\\n", "\"Dependents\" -0.107082725586711 0.0866797760484616 -0.164221401579725 \\\\\n", "\"tenure\" 0.276342245223708 0.883103368818293 -0.369620778763435 \\\\\n", "\"PhoneService\" 0.238826410230016 0.0838048547856037 0.0119419800290031 \\\\\n", "\"PaperlessBilling\" 0.346158879381323 0.151669712799097 0.191825331666468 \\\\\n", "\"MonthlyCharges\" 1.0 0.633958405301206 0.184839285783758 \\\\\n", "\"TotalCharges\" 0.633958405301206 1.0 -0.233211018585104 \\\\\n", "\"Churn\" 0.184839285783758 -0.233211018585104 1.0 \\\\\n", "\"TotalCharges^20\" 0.633958405301206 1.0 -0.233211018585104 \\\\\n", "None \"TotalCharges^20\" \n", "\"SeniorCitizen\" 0.105795342303725 \n", "\"Partner\" 0.343930553215626 \n", "\"Dependents\" 0.0866797760484616 \n", "\"tenure\" 0.883103368818293 \n", "\"PhoneService\" 0.0838048547856037 \n", "\"PaperlessBilling\" 0.151669712799097 \n", "\"MonthlyCharges\" 0.633958405301206 \n", "\"TotalCharges\" 1.0 \n", "\"Churn\" -0.233211018585104 \n", "\"TotalCharges^20\" 1.0 \n", "Rows: 1-10 | Columns: 11" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vdf.corr(method = \"spearman\", show = False)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "e54a387ea3c943c48837d52ddfb28e9c", "version_major": 2, "version_minor": 0 }, "text/plain": [ " 0%| | 0/9 [00:00" ], "text/plain": [ "" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vdf.corr(method = \"spearman\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Spearman's rank correlation coefficient determines the monotonic relationships between the variables." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.883103368818293" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vdf.corr([\"tenure\", \"TotalCharges^20\"], method = \"spearman\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can notice that Spearman's rank correlation coefficient stays the same if one of the variables can be expressed using a monotonic function on the other. The same applies to Kendall rank correlation coefficient. " ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "e06ab203401b480197f2dc1fb9c0d94e", "version_major": 2, "version_minor": 0 }, "text/plain": [ " 0%| | 0/9 [00:00" ], "text/plain": [ "" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vdf.corr(method = \"kendall\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice that the Kendall rank correlation coefficient will also detect the monotonic relationship." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.731699318287362" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vdf.corr([\"tenure\", \"TotalCharges^20\"], method = \"kendall\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "However, the Kendall rank correlation coefficient is very computationally expensive, so we'll generally use Pearson and Spearman when dealing with correlations between numerical variables. \n", "\n", "Binary features are considered numerical, but this isn't technically accurate. Since binary variables can only take two values, calculating correlations between a binary and numerical variable can lead to misleading results. To account for this, we'll want to use the 'Biserial Point' method to calculate the Point-Biserial correlation coefficient. This powerful method will help us understand the link between a binary variable and a numerical variable." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "c4725d5bf45a43a9b5a6dd13e64739a3", "version_major": 2, "version_minor": 0 }, "text/plain": [ " 0%| | 0/10 [00:00" ], "text/plain": [ "" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vdf.corr(method = \"biserial\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Lastly, we'll look at the relationship between categorical columns. In this case, the 'Cramer's V' method is very efficient. Since there is no position in the Euclidean space for those variables, the 'Cramer's V' coefficients cannot be negative (which is a sign of an opposite relationship) and they will range in the interval [0,1]." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "db56f342d03d407fac47b5ef63f83105", "version_major": 2, "version_minor": 0 }, "text/plain": [ " 0%| | 0/9 [00:00" ], "text/plain": [ "" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vdf.corr(method = \"cramer\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Sometimes, we just need to look at the correlation between a response and other variables. The parameter 'focus' will isolate and show us the specified correlation vector." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vdf.corr(method = \"cramer\", focus = \"Churn\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Sometimes a correlation coefficient can lead to incorrect assumptions, so we should always look at the coefficient p-value." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.7810906445878953, 1.3659871749110484e-36)" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vdf.corr_pvalue(\"Churn\", \"customerID\", method = \"cramer\",)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see that churning correlates to the type of contract (monthly, yearly, etc.) which makes sense: you would expect that different types of contracts differ in flexibility for the customer, and particularly restrictive contracts may make churning more likely.\n", "\n", "The type of internet service also seems to correlate with churning. Let's split the different categories to binaries to understand which services can influence the global churning rate." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vdf[\"InternetService\"].one_hot_encode()\n", "vdf.corr(method = \"spearman\", \n", " focus = \"Churn\", \n", " columns = [\"InternetService_DSL\", \n", " \"InternetService_Fiber_optic\"])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see that the Fiber Optic option in particular seems to be directly linked to a customer's likelihood to churn. Let's compute some aggregations to find a causal relationship." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
123
InternetService_Fiber_optic
Integer
123
tenure
Float(22)
123
totalcharges
Float(22)
123
contract_month-to-month
Float(22)
123
monthlycharges
Float(22)
1031.94223460856351558.065485264230.44261464403344343.7882442361287
2132.91795865633073205.304570413440.6873385012919991.5001291989664
Rows: 1-2 | Columns: 5
" ], "text/plain": [ "None InternetService_Fiber_optic tenure totalcharges \\\\\n", "1 0 31.9422346085635 1558.06548526423 \\\\\n", "2 1 32.9179586563307 3205.30457041344 \\\\\n", "None contract_month-to-month monthlycharges \n", "1 0.442614644033443 43.7882442361287 \n", "2 0.68733850129199 91.5001291989664 \n", "Rows: 1-2 | Columns: 5" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vdf[\"contract\"].one_hot_encode()\n", "vdf.groupby([\"InternetService_Fiber_optic\"], \n", " [\"AVG(tenure) AS tenure\", \n", " \"AVG(totalcharges) AS totalcharges\",\n", " 'AVG(\"contract_month-to-month\") AS \"contract_month-to-month\"',\n", " 'AVG(\"monthlycharges\") AS \"monthlycharges\"'])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It seems that users with the Fiber Optic option tend more to churn not because of the option itself, but probably because of the type of contracts and the monthly charges the users are paying to get it. Be careful when dealing with identifying correlations! Remember: correlation doesn't imply causation!\n", "\n", "Another important type of correlation is the autocorrelation. Let's use the Amazon dataset to understand it." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
📅
date
Date
Abc
state
Varchar(32)
123
number
Integer
11998-01-01ACRE0
21998-01-01ALAGOAS0
31998-01-01AMAPÁ0
41998-01-01AMAZONAS0
51998-01-01BAHIA0
61998-01-01CEARÁ0
71998-01-01DISTRITO FEDERAL0
81998-01-01ESPÍRITO SANTO0
91998-01-01GOIÁS0
101998-01-01MARANHÃO0
111998-01-01MATO GROSSO0
121998-01-01MATO GROSSO DO SUL0
131998-01-01MINAS GERAIS0
141998-01-01PARANÁ0
151998-01-01PARAÍBA0
161998-01-01PARÁ0
171998-01-01PERNAMBUCO0
181998-01-01PIAUÍ0
191998-01-01RIO DE JANEIRO0
201998-01-01RIO GRANDE DO NORTE0
211998-01-01RIO GRANDE DO SUL0
221998-01-01RONDÔNIA0
231998-01-01RORAIMA0
241998-01-01SANTA CATARINA0
251998-01-01SERGIPE0
261998-01-01SÃO PAULO0
271998-01-01TOCANTINS0
281998-02-01ACRE0
291998-02-01ALAGOAS0
301998-02-01AMAPÁ0
311998-02-01AMAZONAS0
321998-02-01BAHIA0
331998-02-01CEARÁ0
341998-02-01DISTRITO FEDERAL0
351998-02-01ESPÍRITO SANTO0
361998-02-01GOIÁS0
371998-02-01MARANHÃO0
381998-02-01MATO GROSSO0
391998-02-01MATO GROSSO DO SUL0
401998-02-01MINAS GERAIS0
411998-02-01PARANÁ0
421998-02-01PARAÍBA0
431998-02-01PARÁ0
441998-02-01PERNAMBUCO0
451998-02-01PIAUÍ0
461998-02-01RIO DE JANEIRO0
471998-02-01RIO GRANDE DO NORTE0
481998-02-01RIO GRANDE DO SUL0
491998-02-01RONDÔNIA0
501998-02-01RORAIMA0
511998-02-01SANTA CATARINA0
521998-02-01SERGIPE0
531998-02-01SÃO PAULO0
541998-02-01TOCANTINS0
551998-03-01ACRE0
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571998-03-01AMAPÁ0
581998-03-01AMAZONAS0
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601998-03-01CEARÁ0
611998-03-01DISTRITO FEDERAL0
621998-03-01ESPÍRITO SANTO0
631998-03-01GOIÁS0
641998-03-01MARANHÃO0
651998-03-01MATO GROSSO0
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671998-03-01MINAS GERAIS0
681998-03-01PARANÁ0
691998-03-01PARAÍBA0
701998-03-01PARÁ0
711998-03-01PERNAMBUCO0
721998-03-01PIAUÍ0
731998-03-01RIO DE JANEIRO0
741998-03-01RIO GRANDE DO NORTE0
751998-03-01RIO GRANDE DO SUL0
761998-03-01RONDÔNIA0
771998-03-01RORAIMA0
781998-03-01SANTA CATARINA0
791998-03-01SERGIPE0
801998-03-01SÃO PAULO0
811998-03-01TOCANTINS0
821998-04-01ACRE0
831998-04-01ALAGOAS0
841998-04-01AMAPÁ0
851998-04-01AMAZONAS0
861998-04-01BAHIA0
871998-04-01CEARÁ0
881998-04-01DISTRITO FEDERAL0
891998-04-01ESPÍRITO SANTO0
901998-04-01GOIÁS0
911998-04-01MARANHÃO0
921998-04-01MATO GROSSO0
931998-04-01MATO GROSSO DO SUL0
941998-04-01MINAS GERAIS0
951998-04-01PARANÁ0
961998-04-01PARAÍBA0
971998-04-01PARÁ0
981998-04-01PERNAMBUCO0
991998-04-01PIAUÍ0
1001998-04-01RIO DE JANEIRO0
Rows: 1-100 | Columns: 3
" ], "text/plain": [ "None date state number \n", "1 1998-01-01 ACRE 0 \n", "2 1998-01-01 ALAGOAS 0 \n", "3 1998-01-01 AMAPÁ 0 \n", "4 1998-01-01 AMAZONAS 0 \n", "5 1998-01-01 BAHIA 0 \n", "6 1998-01-01 CEARÁ 0 \n", "7 1998-01-01 DISTRITO FEDERAL 0 \n", "8 1998-01-01 ESPÍRITO SANTO 0 \n", "9 1998-01-01 GOIÁS 0 \n", "10 1998-01-01 MARANHÃO 0 \n", "11 1998-01-01 MATO GROSSO 0 \n", "12 1998-01-01 MATO GROSSO DO SUL 0 \n", "13 1998-01-01 MINAS GERAIS 0 \n", "14 1998-01-01 PARANÁ 0 \n", "15 1998-01-01 PARAÍBA 0 \n", "16 1998-01-01 PARÁ 0 \n", "17 1998-01-01 PERNAMBUCO 0 \n", "18 1998-01-01 PIAUÍ 0 \n", "19 1998-01-01 RIO DE JANEIRO 0 \n", "20 1998-01-01 RIO GRANDE DO NORTE 0 \n", "21 1998-01-01 RIO GRANDE DO SUL 0 \n", "22 1998-01-01 RONDÔNIA 0 \n", "23 1998-01-01 RORAIMA 0 \n", "24 1998-01-01 SANTA CATARINA 0 \n", "25 1998-01-01 SERGIPE 0 \n", "26 1998-01-01 SÃO PAULO 0 \n", "27 1998-01-01 TOCANTINS 0 \n", "28 1998-02-01 ACRE 0 \n", "29 1998-02-01 ALAGOAS 0 \n", "30 1998-02-01 AMAPÁ 0 \n", "31 1998-02-01 AMAZONAS 0 \n", "32 1998-02-01 BAHIA 0 \n", "33 1998-02-01 CEARÁ 0 \n", "34 1998-02-01 DISTRITO FEDERAL 0 \n", "35 1998-02-01 ESPÍRITO SANTO 0 \n", "36 1998-02-01 GOIÁS 0 \n", "37 1998-02-01 MARANHÃO 0 \n", "38 1998-02-01 MATO GROSSO 0 \n", "39 1998-02-01 MATO GROSSO DO SUL 0 \n", "40 1998-02-01 MINAS GERAIS 0 \n", "41 1998-02-01 PARANÁ 0 \n", "42 1998-02-01 PARAÍBA 0 \n", "43 1998-02-01 PARÁ 0 \n", "44 1998-02-01 PERNAMBUCO 0 \n", "45 1998-02-01 PIAUÍ 0 \n", "46 1998-02-01 RIO DE JANEIRO 0 \n", "47 1998-02-01 RIO GRANDE DO NORTE 0 \n", "48 1998-02-01 RIO GRANDE DO SUL 0 \n", "49 1998-02-01 RONDÔNIA 0 \n", "50 1998-02-01 RORAIMA 0 \n", "51 1998-02-01 SANTA CATARINA 0 \n", "52 1998-02-01 SERGIPE 0 \n", "53 1998-02-01 SÃO PAULO 0 \n", "54 1998-02-01 TOCANTINS 0 \n", "55 1998-03-01 ACRE 0 \n", "56 1998-03-01 ALAGOAS 0 \n", "57 1998-03-01 AMAPÁ 0 \n", "58 1998-03-01 AMAZONAS 0 \n", "59 1998-03-01 BAHIA 0 \n", "60 1998-03-01 CEARÁ 0 \n", "61 1998-03-01 DISTRITO FEDERAL 0 \n", "62 1998-03-01 ESPÍRITO SANTO 0 \n", "63 1998-03-01 GOIÁS 0 \n", "64 1998-03-01 MARANHÃO 0 \n", "65 1998-03-01 MATO GROSSO 0 \n", "66 1998-03-01 MATO GROSSO DO SUL 0 \n", "67 1998-03-01 MINAS GERAIS 0 \n", "68 1998-03-01 PARANÁ 0 \n", "69 1998-03-01 PARAÍBA 0 \n", "70 1998-03-01 PARÁ 0 \n", "71 1998-03-01 PERNAMBUCO 0 \n", "72 1998-03-01 PIAUÍ 0 \n", "73 1998-03-01 RIO DE JANEIRO 0 \n", "74 1998-03-01 RIO GRANDE DO NORTE 0 \n", "75 1998-03-01 RIO GRANDE DO SUL 0 \n", "76 1998-03-01 RONDÔNIA 0 \n", "77 1998-03-01 RORAIMA 0 \n", "78 1998-03-01 SANTA CATARINA 0 \n", "79 1998-03-01 SERGIPE 0 \n", "80 1998-03-01 SÃO PAULO 0 \n", "81 1998-03-01 TOCANTINS 0 \n", "82 1998-04-01 ACRE 0 \n", "83 1998-04-01 ALAGOAS 0 \n", "84 1998-04-01 AMAPÁ 0 \n", "85 1998-04-01 AMAZONAS 0 \n", "86 1998-04-01 BAHIA 0 \n", "87 1998-04-01 CEARÁ 0 \n", "88 1998-04-01 DISTRITO FEDERAL 0 \n", "89 1998-04-01 ESPÍRITO SANTO 0 \n", "90 1998-04-01 GOIÁS 0 \n", "91 1998-04-01 MARANHÃO 0 \n", "92 1998-04-01 MATO GROSSO 0 \n", "93 1998-04-01 MATO GROSSO DO SUL 0 \n", "94 1998-04-01 MINAS GERAIS 0 \n", "95 1998-04-01 PARANÁ 0 \n", "96 1998-04-01 PARAÍBA 0 \n", "97 1998-04-01 PARÁ 0 \n", "98 1998-04-01 PERNAMBUCO 0 \n", "99 1998-04-01 PIAUÍ 0 \n", "100 1998-04-01 RIO DE JANEIRO 0 \n", "Rows: 1-100 | Columns: 3" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from verticapy.datasets import load_amazon\n", "vdf = load_amazon()\n", "display(vdf)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Our goal is to predict the number of forest fires in Brazil. To do this, we can draw an autocorrelation plot and a partial autocorrelation plot." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vdf.acf(column = \"number\",\n", " ts = \"date\",\n", " by = [\"state\"],\n", " p = 48,\n", " method = \"pearson\")" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "7dc1f8ae3f5940d08a9f4d4e4ebab587", "version_major": 2, "version_minor": 0 }, "text/plain": [ " 0%| | 0/49 [00:00" ], "text/plain": [ "" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vdf.pacf(column = \"number\",\n", " ts = \"date\",\n", " by = [\"state\"],\n", " p = 48)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see the seasonality forest fires." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It's mathematically impossible to build the perfect correlation function, but we still have several powerful functions at our disposal for finding relationships in all kinds of datasets." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.12" }, "widgets": { "application/vnd.jupyter.widget-state+json": { "state": { "055351763a6e4167aca90f06438eec8d": { "model_module": "@jupyter-widgets/base", "model_module_version": "2.0.0", "model_name": "LayoutModel", "state": { "_model_name": "LayoutModel", "_view_name": "ErrorWidgetView", "align_content": null, "align_items": null, "align_self": null, "border": null, "bottom": null, 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