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Home / Old / Examples / Telco Churn / Index
Telco Churn¶
This example uses the Telco Churn dataset to predict which Telco user is likely to churn; that is, customers that will likely stop using Telco. You can download the Jupyter Notebook of the study here.
- Churn - customers that left within the last month
- Services - services of each customer (phone, multiple lines, internet, online security, online backup, device protection, tech support, and streaming TV and movies)
- Customer account information - how long they’ve been a customer, contract, payment method, paperless billing, monthly charges, and total charges
- Customer demographics - gender, age range, and if they have partners and dependents
We will follow the data science cycle (Data Exploration - Data Preparation - Data Modeling - Model Evaluation - Model Deployment) to solve this problem.
Initialization¶
This example uses the following version of VerticaPy:
import verticapy as vp
vp.__version__
'0.9.0'
Connect to Vertica. This example uses an existing connection called "VerticaDSN." For details on how to create a connection, use see the connection tutorial.
vp.connect("VerticaDSN")
Let's create a Virtual DataFrame of the dataset. The dataset is available here.
churn = vp.read_csv('data/churn.csv')
display(churn)
Abc customerIDVarchar(20) | Abc genderVarchar(20) | 123 SeniorCitizenInt | 010 PartnerBoolean | 010 DependentsBoolean | 123 tenureInt | 010 PhoneServiceBoolean | Abc MultipleLinesVarchar(100) | Abc InternetServiceVarchar(22) | Abc OnlineSecurityVarchar(38) | Abc OnlineBackupVarchar(38) | Abc DeviceProtectionVarchar(38) | Abc TechSupportVarchar(38) | Abc StreamingTVVarchar(38) | Abc StreamingMoviesVarchar(38) | Abc ContractVarchar(28) | 010 PaperlessBillingBoolean | Abc PaymentMethodVarchar(50) | 123 MonthlyChargesNumeric(8,3) | 123 TotalChargesNumeric(9,3) | 010 ChurnBoolean | |
| 1 | 0002-ORFBO | Female | 0 | 9 | No | DSL | No | Yes | No | Yes | Yes | No | One year | Mailed check | 65.6 | 593.3 | |||||
| 2 | 0003-MKNFE | Male | 0 | 9 | Yes | DSL | No | No | No | No | No | Yes | Month-to-month | Mailed check | 59.9 | 542.4 | |||||
| 3 | 0004-TLHLJ | Male | 0 | 4 | No | Fiber optic | No | No | Yes | No | No | No | Month-to-month | Electronic check | 73.9 | 280.85 | |||||
| 4 | 0011-IGKFF | Male | 1 | 13 | No | Fiber optic | No | Yes | Yes | No | Yes | Yes | Month-to-month | Electronic check | 98.0 | 1237.85 | |||||
| 5 | 0013-EXCHZ | Female | 1 | 3 | No | Fiber optic | No | No | No | Yes | Yes | No | Month-to-month | Mailed check | 83.9 | 267.4 | |||||
| 6 | 0013-MHZWF | Female | 0 | 9 | No | DSL | No | No | No | Yes | Yes | Yes | Month-to-month | Credit card (automatic) | 69.4 | 571.45 | |||||
| 7 | 0013-SMEOE | Female | 1 | 71 | No | Fiber optic | Yes | Yes | Yes | Yes | Yes | Yes | Two year | Bank transfer (automatic) | 109.7 | 7904.25 | |||||
| 8 | 0014-BMAQU | Male | 0 | 63 | Yes | Fiber optic | Yes | No | No | Yes | No | No | Two year | Credit card (automatic) | 84.65 | 5377.8 | |||||
| 9 | 0015-UOCOJ | Female | 1 | 7 | No | DSL | Yes | No | No | No | No | No | Month-to-month | Electronic check | 48.2 | 340.35 | |||||
| 10 | 0016-QLJIS | Female | 0 | 65 | Yes | DSL | Yes | Yes | Yes | Yes | Yes | Yes | Two year | Mailed check | 90.45 | 5957.9 | |||||
| 11 | 0017-DINOC | Male | 0 | 54 | No phone service | DSL | Yes | No | No | Yes | Yes | No | Two year | Credit card (automatic) | 45.2 | 2460.55 | |||||
| 12 | 0017-IUDMW | Female | 0 | 72 | Yes | Fiber optic | Yes | Yes | Yes | Yes | Yes | Yes | Two year | Credit card (automatic) | 116.8 | 8456.75 | |||||
| 13 | 0018-NYROU | Female | 0 | 5 | No | Fiber optic | No | No | No | No | No | No | Month-to-month | Electronic check | 68.95 | 351.5 | |||||
| 14 | 0019-EFAEP | Female | 0 | 72 | Yes | Fiber optic | Yes | Yes | Yes | No | Yes | No | Two year | Bank transfer (automatic) | 101.3 | 7261.25 | |||||
| 15 | 0019-GFNTW | Female | 0 | 56 | No phone service | DSL | Yes | Yes | Yes | Yes | No | No | Two year | Bank transfer (automatic) | 45.05 | 2560.1 | |||||
| 16 | 0020-INWCK | Female | 0 | 71 | Yes | Fiber optic | No | Yes | Yes | No | No | Yes | Two year | Credit card (automatic) | 95.75 | 6849.4 | |||||
| 17 | 0020-JDNXP | Female | 0 | 34 | No phone service | DSL | Yes | No | Yes | Yes | Yes | Yes | One year | Mailed check | 61.25 | 1993.2 | |||||
| 18 | 0021-IKXGC | Female | 1 | 1 | Yes | Fiber optic | No | No | No | No | No | No | Month-to-month | Electronic check | 72.1 | 72.1 | |||||
| 19 | 0022-TCJCI | Male | 1 | 45 | No | DSL | Yes | No | Yes | No | No | Yes | One year | Credit card (automatic) | 62.7 | 2791.5 | |||||
| 20 | 0023-HGHWL | Male | 1 | 1 | No phone service | DSL | No | No | No | No | No | No | Month-to-month | Electronic check | 25.1 | 25.1 | |||||
| 21 | 0023-UYUPN | Female | 1 | 50 | Yes | No | No internet service | No internet service | No internet service | No internet service | No internet service | No internet service | One year | Electronic check | 25.2 | 1306.3 | |||||
| 22 | 0023-XUOPT | Female | 0 | 13 | Yes | Fiber optic | No | Yes | Yes | No | Yes | No | Month-to-month | Electronic check | 94.1 | 1215.6 | |||||
| 23 | 0027-KWYKW | Female | 0 | 23 | Yes | Fiber optic | No | No | No | No | Yes | No | Month-to-month | Electronic check | 83.75 | 1849.95 | |||||
| 24 | 0030-FNXPP | Female | 0 | 3 | No | No | No internet service | No internet service | No internet service | No internet service | No internet service | No internet service | Month-to-month | Mailed check | 19.85 | 57.2 | |||||
| 25 | 0031-PVLZI | Female | 0 | 4 | No | No | No internet service | No internet service | No internet service | No internet service | No internet service | No internet service | Month-to-month | Mailed check | 20.35 | 76.35 | |||||
| 26 | 0032-PGELS | Female | 0 | 1 | No phone service | DSL | Yes | No | No | No | No | No | Month-to-month | Bank transfer (automatic) | 30.5 | 30.5 | |||||
| 27 | 0036-IHMOT | Female | 0 | 55 | No | Fiber optic | No | Yes | Yes | Yes | Yes | Yes | One year | Bank transfer (automatic) | 103.7 | 5656.75 | |||||
| 28 | 0040-HALCW | Male | 0 | 54 | No | No | No internet service | No internet service | No internet service | No internet service | No internet service | No internet service | Two year | Credit card (automatic) | 20.4 | 1090.6 | |||||
| 29 | 0042-JVWOJ | Male | 0 | 26 | No | No | No internet service | No internet service | No internet service | No internet service | No internet service | No internet service | One year | Bank transfer (automatic) | 19.6 | 471.85 | |||||
| 30 | 0042-RLHYP | Female | 0 | 69 | No | No | No internet service | No internet service | No internet service | No internet service | No internet service | No internet service | Two year | Bank transfer (automatic) | 19.7 | 1396.9 | |||||
| 31 | 0048-LUMLS | Male | 0 | 37 | No | Fiber optic | No | No | No | No | Yes | Yes | One year | Credit card (automatic) | 91.2 | 3247.55 | |||||
| 32 | 0048-PIHNL | Female | 0 | 49 | No | No | No internet service | No internet service | No internet service | No internet service | No internet service | No internet service | One year | Bank transfer (automatic) | 20.45 | 900.9 | |||||
| 33 | 0052-DCKON | Male | 0 | 66 | Yes | Fiber optic | Yes | Yes | Yes | Yes | Yes | Yes | One year | Bank transfer (automatic) | 115.8 | 7942.15 | |||||
| 34 | 0052-YNYOT | Female | 0 | 67 | No | No | No internet service | No internet service | No internet service | No internet service | No internet service | No internet service | One year | Electronic check | 20.55 | 1343.4 | |||||
| 35 | 0056-EPFBG | Male | 0 | 20 | No phone service | DSL | Yes | No | Yes | Yes | No | No | Two year | Credit card (automatic) | 39.4 | 825.4 | |||||
| 36 | 0057-QBUQH | Female | 0 | 43 | Yes | No | No internet service | No internet service | No internet service | No internet service | No internet service | No internet service | Two year | Electronic check | 25.1 | 1070.15 | |||||
| 37 | 0058-EVZWM | Female | 0 | 55 | Yes | Fiber optic | Yes | No | No | No | Yes | No | Month-to-month | Bank transfer (automatic) | 89.8 | 4959.6 | |||||
| 38 | 0060-FUALY | Female | 0 | 59 | Yes | Fiber optic | Yes | Yes | No | No | Yes | No | Month-to-month | Electronic check | 94.75 | 5597.65 | |||||
| 39 | 0064-SUDOG | Female | 0 | 12 | No | No | No internet service | No internet service | No internet service | No internet service | No internet service | No internet service | Two year | Bank transfer (automatic) | 20.3 | 224.5 | |||||
| 40 | 0064-YIJGF | Male | 0 | 27 | Yes | Fiber optic | No | No | No | No | No | No | Month-to-month | Bank transfer (automatic) | 75.75 | 1929.0 | |||||
| 41 | 0067-DKWBL | Male | 1 | 2 | No | DSL | Yes | No | No | No | No | No | Month-to-month | Electronic check | 49.25 | 91.1 | |||||
| 42 | 0068-FIGTF | Female | 0 | 27 | No | DSL | No | Yes | Yes | Yes | Yes | Yes | One year | Mailed check | 78.2 | 2078.95 | |||||
| 43 | 0071-NDAFP | Male | 0 | 25 | Yes | No | No internet service | No internet service | No internet service | No internet service | No internet service | No internet service | Two year | Credit card (automatic) | 25.5 | 630.6 | |||||
| 44 | 0074-HDKDG | Male | 0 | 25 | No | DSL | Yes | Yes | Yes | No | No | No | One year | Bank transfer (automatic) | 61.6 | 1611.0 | |||||
| 45 | 0076-LVEPS | Male | 0 | 29 | No phone service | DSL | Yes | Yes | Yes | Yes | No | No | Month-to-month | Mailed check | 45.0 | 1242.45 | |||||
| 46 | 0078-XZMHT | Male | 0 | 72 | Yes | DSL | No | Yes | Yes | Yes | Yes | Yes | Two year | Bank transfer (automatic) | 85.15 | 6316.2 | |||||
| 47 | 0080-EMYVY | Female | 0 | 14 | No | DSL | No | Yes | No | No | No | No | One year | Credit card (automatic) | 51.45 | 727.85 | |||||
| 48 | 0080-OROZO | Female | 0 | 35 | No | Fiber optic | No | No | Yes | Yes | Yes | Yes | One year | Electronic check | 99.25 | 3532.0 | |||||
| 49 | 0082-LDZUE | Male | 0 | 1 | No | DSL | No | No | No | No | No | No | Month-to-month | Mailed check | 44.3 | 44.3 | |||||
| 50 | 0082-OQIQY | Male | 0 | 29 | No | Fiber optic | No | No | No | Yes | Yes | Yes | Month-to-month | Electronic check | 94.2 | 2607.6 | |||||
| 51 | 0083-PIVIK | Male | 0 | 64 | Yes | DSL | Yes | Yes | Yes | Yes | Yes | No | One year | Electronic check | 81.25 | 5567.55 | |||||
| 52 | 0089-IIQKO | Female | 0 | 39 | Yes | Fiber optic | No | No | No | Yes | Yes | Yes | Month-to-month | Credit card (automatic) | 99.95 | 3767.4 | |||||
| 53 | 0093-EXYQL | Female | 1 | 40 | No | Fiber optic | No | No | No | No | Yes | Yes | Month-to-month | Electronic check | 91.55 | 3673.6 | |||||
| 54 | 0093-XWZFY | Male | 0 | 40 | Yes | Fiber optic | No | Yes | Yes | No | Yes | Yes | Month-to-month | Credit card (automatic) | 104.5 | 4036.85 | |||||
| 55 | 0094-OIFMO | Female | 1 | 11 | No | Fiber optic | No | Yes | No | No | Yes | Yes | Month-to-month | Electronic check | 95.0 | 1120.3 | |||||
| 56 | 0096-BXERS | Female | 0 | 6 | Yes | DSL | No | No | No | No | No | No | Month-to-month | Electronic check | 50.35 | 314.55 | |||||
| 57 | 0096-FCPUF | Male | 0 | 30 | Yes | DSL | Yes | No | No | No | No | Yes | Month-to-month | Mailed check | 64.5 | 1888.45 | |||||
| 58 | 0098-BOWSO | Male | 0 | 27 | No | No | No internet service | No internet service | No internet service | No internet service | No internet service | No internet service | Month-to-month | Electronic check | 19.4 | 529.8 | |||||
| 59 | 0100-DUVFC | Male | 1 | 70 | Yes | Fiber optic | No | Yes | Yes | No | Yes | Yes | One year | Electronic check | 104.8 | 7308.95 | |||||
| 60 | 0103-CSITQ | Female | 0 | 57 | Yes | Fiber optic | No | Yes | Yes | Yes | Yes | Yes | One year | Bank transfer (automatic) | 109.4 | 6252.7 | |||||
| 61 | 0104-PPXDV | Male | 0 | 58 | No | DSL | No | No | Yes | No | No | No | One year | Credit card (automatic) | 50.3 | 2878.55 | |||||
| 62 | 0106-GHRQR | Male | 0 | 16 | Yes | DSL | No | Yes | Yes | No | No | Yes | Month-to-month | Bank transfer (automatic) | 71.4 | 1212.1 | |||||
| 63 | 0106-UGRDO | Female | 0 | 69 | Yes | Fiber optic | Yes | Yes | Yes | Yes | Yes | Yes | Two year | Electronic check | 116.0 | 8182.85 | |||||
| 64 | 0107-WESLM | Male | 0 | 1 | No | No | No internet service | No internet service | No internet service | No internet service | No internet service | No internet service | Month-to-month | Electronic check | 19.85 | 19.85 | |||||
| 65 | 0107-YHINA | Male | 0 | 1 | Yes | Fiber optic | No | No | Yes | No | Yes | Yes | Month-to-month | Electronic check | 99.75 | 99.75 | |||||
| 66 | 0111-KLBQG | Male | 1 | 32 | No | Fiber optic | No | Yes | No | No | Yes | Yes | Month-to-month | Mailed check | 93.95 | 2861.45 | |||||
| 67 | 0112-QAWRZ | Male | 0 | 16 | Yes | Fiber optic | No | No | Yes | No | Yes | No | Month-to-month | Bank transfer (automatic) | 90.8 | 1442.2 | |||||
| 68 | 0112-QWPNC | Male | 0 | 49 | Yes | DSL | Yes | No | Yes | Yes | Yes | Yes | One year | Electronic check | 84.35 | 4059.35 | |||||
| 69 | 0114-IGABW | Female | 0 | 71 | No phone service | DSL | No | Yes | Yes | Yes | Yes | Yes | Two year | Bank transfer (automatic) | 58.25 | 4145.9 | |||||
| 70 | 0114-PEGZZ | Female | 0 | 33 | Yes | Fiber optic | No | Yes | Yes | No | Yes | Yes | Month-to-month | Electronic check | 107.55 | 3645.5 | |||||
| 71 | 0114-RSRRW | Female | 0 | 10 | No | No | No internet service | No internet service | No internet service | No internet service | No internet service | No internet service | Month-to-month | Bank transfer (automatic) | 19.95 | 187.75 | |||||
| 72 | 0115-TFERT | Male | 0 | 21 | Yes | Fiber optic | No | Yes | Yes | Yes | Yes | Yes | Month-to-month | Electronic check | 111.2 | 2317.1 | |||||
| 73 | 0117-LFRMW | Male | 0 | 37 | No phone service | DSL | Yes | Yes | Yes | No | No | No | Month-to-month | Bank transfer (automatic) | 40.2 | 1448.8 | |||||
| 74 | 0118-JPNOY | Female | 1 | 26 | No | Fiber optic | Yes | No | No | No | Yes | No | Month-to-month | Credit card (automatic) | 85.8 | 2193.65 | |||||
| 75 | 0121-SNYRK | Male | 0 | 50 | No phone service | DSL | Yes | No | No | Yes | No | No | One year | Mailed check | 35.4 | 1748.9 | |||||
| 76 | 0122-OAHPZ | Female | 0 | 7 | Yes | Fiber optic | No | No | No | No | No | No | Month-to-month | Electronic check | 73.85 | 511.25 | |||||
| 77 | 0123-CRBRT | Female | 0 | 61 | Yes | DSL | Yes | Yes | Yes | Yes | Yes | Yes | Two year | Mailed check | 88.1 | 5526.75 | |||||
| 78 | 0125-LZQXK | Male | 0 | 15 | No | Fiber optic | No | No | Yes | Yes | Yes | Yes | Month-to-month | Electronic check | 101.35 | 1553.95 | |||||
| 79 | 0128-MKWSG | Female | 0 | 26 | No phone service | DSL | Yes | No | No | Yes | No | Yes | Month-to-month | Mailed check | 45.8 | 1147.0 | |||||
| 80 | 0129-KPTWJ | Male | 0 | 72 | No | Fiber optic | No | No | Yes | No | Yes | Yes | Month-to-month | Electronic check | 94.65 | 6747.35 | |||||
| 81 | 0129-QMPDR | Male | 0 | 44 | No | No | No internet service | No internet service | No internet service | No internet service | No internet service | No internet service | One year | Bank transfer (automatic) | 20.5 | 865.05 | |||||
| 82 | 0130-SXOUN | Male | 0 | 66 | Yes | Fiber optic | No | Yes | No | No | No | Yes | Month-to-month | Credit card (automatic) | 89.4 | 5976.9 | |||||
| 83 | 0133-BMFZO | Female | 0 | 2 | No | Fiber optic | Yes | Yes | No | Yes | No | No | Month-to-month | Electronic check | 86.25 | 181.65 | |||||
| 84 | 0134-XWXCE | Female | 1 | 44 | No | DSL | No | No | Yes | Yes | Yes | Yes | One year | Bank transfer (automatic) | 74.85 | 3268.05 | |||||
| 85 | 0135-NMXAP | Female | 0 | 12 | Yes | Fiber optic | No | Yes | No | No | Yes | No | Month-to-month | Bank transfer (automatic) | 89.75 | 1052.4 | |||||
| 86 | 0136-IFMYD | Male | 1 | 69 | Yes | Fiber optic | No | Yes | Yes | Yes | Yes | Yes | Two year | Electronic check | 109.95 | 7634.25 | |||||
| 87 | 0137-OCGAB | Female | 0 | 1 | Yes | Fiber optic | No | Yes | No | No | No | No | Month-to-month | Mailed check | 80.2 | 80.2 | |||||
| 88 | 0137-UDEUO | Female | 0 | 3 | No | No | No internet service | No internet service | No internet service | No internet service | No internet service | No internet service | Month-to-month | Mailed check | 19.85 | 63.75 | |||||
| 89 | 0139-IVFJG | Female | 0 | 2 | No | Fiber optic | Yes | Yes | No | No | Yes | No | Month-to-month | Electronic check | 90.35 | 190.5 | |||||
| 90 | 0141-YEAYS | Female | 1 | 27 | Yes | Fiber optic | No | Yes | Yes | No | No | No | Month-to-month | Bank transfer (automatic) | 86.45 | 2401.05 | |||||
| 91 | 0142-GVYSN | Male | 0 | 26 | No | No | No internet service | No internet service | No internet service | No internet service | No internet service | No internet service | Month-to-month | Electronic check | 20.3 | 511.25 | |||||
| 92 | 0147-ESWWR | Female | 1 | 39 | Yes | Fiber optic | No | No | No | Yes | Yes | Yes | Month-to-month | Electronic check | 101.25 | 3949.15 | |||||
| 93 | 0148-DCDOS | Male | 0 | 25 | Yes | Fiber optic | No | No | No | No | Yes | Yes | Month-to-month | Bank transfer (automatic) | 94.7 | 2362.1 | |||||
| 94 | 0151-ONTOV | Female | 0 | 1 | No | Fiber optic | No | No | No | No | No | No | Month-to-month | Mailed check | 70.9 | 70.9 | |||||
| 95 | 0156-FVPTA | Male | 0 | 22 | No | DSL | Yes | No | No | Yes | No | No | Month-to-month | Electronic check | 54.2 | 1152.7 | |||||
| 96 | 0164-APGRB | Female | 0 | 72 | Yes | Fiber optic | Yes | Yes | Yes | Yes | Yes | Yes | Two year | Electronic check | 114.9 | 8496.7 | |||||
| 97 | 0164-XAIRP | Female | 0 | 24 | No | No | No internet service | No internet service | No internet service | No internet service | No internet service | No internet service | Two year | Bank transfer (automatic) | 19.55 | 470.2 | |||||
| 98 | 0168-XZKBB | Female | 0 | 19 | Yes | Fiber optic | No | No | No | No | Yes | No | Month-to-month | Electronic check | 86.85 | 1564.4 | |||||
| 99 | 0174-QRVVY | Male | 0 | 71 | Yes | No | No internet service | No internet service | No internet service | No internet service | No internet service | No internet service | Two year | Credit card (automatic) | 25.35 | 1847.55 | |||||
| 100 | 0177-PXBAT | Male | 1 | 33 | Yes | Fiber optic | Yes | No | Yes | Yes | Yes | Yes | Month-to-month | Bank transfer (automatic) | 109.9 | 3694.7 |
Data Exploration and Preparation¶
Let's examine our data.
churn.describe(method = "categorical", unique = True)
| dtype | count | top | top_percent | unique | |
| "customerID" | varchar(20) | 7043 | 0002-ORFBO | 0.014 | 7043.0 |
| "gender" | varchar(20) | 7043 | Male | 50.476 | 2.0 |
| "SeniorCitizen" | int | 7043 | 0 | 83.785 | 2.0 |
| "Partner" | boolean | 7043 | 0 | 51.697 | 2.0 |
| "Dependents" | boolean | 7043 | 0 | 70.041 | 2.0 |
| "tenure" | int | 7043 | 1 | 8.704 | 73.0 |
| "PhoneService" | boolean | 7043 | 1 | 90.317 | 2.0 |
| "MultipleLines" | varchar(100) | 7043 | No | 48.133 | 3.0 |
| "InternetService" | varchar(22) | 7043 | Fiber optic | 43.959 | 3.0 |
| "OnlineSecurity" | varchar(38) | 7043 | No | 49.666 | 3.0 |
| "OnlineBackup" | varchar(38) | 7043 | No | 43.845 | 3.0 |
| "DeviceProtection" | varchar(38) | 7043 | No | 43.944 | 3.0 |
| "TechSupport" | varchar(38) | 7043 | No | 49.311 | 3.0 |
| "StreamingTV" | varchar(38) | 7043 | No | 39.898 | 3.0 |
| "StreamingMovies" | varchar(38) | 7043 | No | 39.543 | 3.0 |
| "Contract" | varchar(28) | 7043 | Month-to-month | 55.019 | 3.0 |
| "PaperlessBilling" | boolean | 7043 | 1 | 59.222 | 2.0 |
| "PaymentMethod" | varchar(50) | 7043 | Electronic check | 33.579 | 4.0 |
| "MonthlyCharges" | numeric(8,3) | 7043 | 20.05 | 0.866 | 1585.0 |
| "TotalCharges" | numeric(9,3) | 7032 | [null] | 0.156 | 6530.0 |
| "Churn" | boolean | 7043 | 0 | 73.463 | 2.0 |
Several variables are categorical, and since they all have low cardinalities, we can compute their dummies. We can also convert all booleans to numeric.
for column in ["DeviceProtection",
"MultipleLines",
"PaperlessBilling",
"Churn",
"TechSupport",
"Partner",
"StreamingTV",
"OnlineBackup",
"Dependents",
"OnlineSecurity",
"PhoneService",
"StreamingMovies"]:
churn[column].decode("Yes", 1, 0)
churn.one_hot_encode().drop(["customerID",
"gender",
"Contract",
"PaymentMethod",
"InternetService"])
123 SeniorCitizenInt | 123 PartnerInteger | 123 DependentsInteger | 123 tenureInt | 123 PhoneServiceInteger | 123 MultipleLinesInteger | 123 OnlineSecurityInteger | 123 OnlineBackupInteger | 123 DeviceProtectionInteger | 123 TechSupportInteger | 123 StreamingTVInteger | 123 StreamingMoviesInteger | 123 PaperlessBillingInteger | 123 MonthlyChargesNumeric(8,3) | 123 TotalChargesNumeric(9,3) | 123 ChurnInteger | 123 gender_FemaleBool | 123 InternetService_DSLBool | 123 InternetService_Fiber_opticBool | 123 Contract_Month-to-monthBool | 123 Contract_One_yearBool | 123 Bool | 123 Bool | 123 PaymentMethod_Electronic_checkBool | |
| 1 | 0 | 1 | 1 | 9 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 65.6 | 593.3 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | ||
| 2 | 0 | 0 | 0 | 9 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 59.9 | 542.4 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | ||
| 3 | 0 | 0 | 0 | 4 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 73.9 | 280.85 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | ||
| 4 | 1 | 1 | 0 | 13 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 98.0 | 1237.85 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | ||
| 5 | 1 | 1 | 0 | 3 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 83.9 | 267.4 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | ||
| 6 | 0 | 0 | 1 | 9 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 69.4 | 571.45 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | ||
| 7 | 1 | 1 | 0 | 71 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 109.7 | 7904.25 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | ||
| 8 | 0 | 1 | 0 | 63 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 84.65 | 5377.8 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | ||
| 9 | 1 | 0 | 0 | 7 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 48.2 | 340.35 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | ||
| 10 | 0 | 1 | 1 | 65 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 90.45 | 5957.9 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | ||
| 11 | 0 | 0 | 0 | 54 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 45.2 | 2460.55 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | ||
| 12 | 0 | 1 | 1 | 72 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 116.8 | 8456.75 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | ||
| 13 | 0 | 1 | 0 | 5 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 68.95 | 351.5 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | ||
| 14 | 0 | 0 | 0 | 72 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 101.3 | 7261.25 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | ||
| 15 | 0 | 0 | 0 | 56 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 45.05 | 2560.1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | ||
| 16 | 0 | 1 | 1 | 71 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 95.75 | 6849.4 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | ||
| 17 | 0 | 1 | 1 | 34 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 61.25 | 1993.2 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | ||
| 18 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 72.1 | 72.1 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | ||
| 19 | 1 | 0 | 0 | 45 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 62.7 | 2791.5 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | ||
| 20 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 25.1 | 25.1 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | ||
| 21 | 1 | 1 | 0 | 50 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 25.2 | 1306.3 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | ||
| 22 | 0 | 1 | 0 | 13 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 94.1 | 1215.6 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | ||
| 23 | 0 | 1 | 1 | 23 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 83.75 | 1849.95 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | ||
| 24 | 0 | 0 | 0 | 3 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 19.85 | 57.2 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | ||
| 25 | 0 | 1 | 1 | 4 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 20.35 | 76.35 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | ||
| 26 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 30.5 | 30.5 | 1 | 1 | 1 | 0 | 1 | 0 | 0 | ||
| 27 | 0 | 1 | 1 | 55 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 103.7 | 5656.75 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | ||
| 28 | 0 | 1 | 1 | 54 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 20.4 | 1090.6 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ||
| 29 | 0 | 0 | 0 | 26 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 19.6 | 471.85 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | ||
| 30 | 0 | 1 | 1 | 69 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 19.7 | 1396.9 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | ||
| 31 | 0 | 1 | 1 | 37 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 91.2 | 3247.55 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | ||
| 32 | 0 | 1 | 0 | 49 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 20.45 | 900.9 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | ||
| 33 | 0 | 1 | 0 | 66 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 115.8 | 7942.15 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | ||
| 34 | 0 | 0 | 0 | 67 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 20.55 | 1343.4 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | ||
| 35 | 0 | 1 | 1 | 20 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 39.4 | 825.4 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | ||
| 36 | 0 | 0 | 1 | 43 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 25.1 | 1070.15 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | ||
| 37 | 0 | 1 | 0 | 55 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 89.8 | 4959.6 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | ||
| 38 | 0 | 1 | 0 | 59 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 94.75 | 5597.65 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | ||
| 39 | 0 | 1 | 1 | 12 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 20.3 | 224.5 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | ||
| 40 | 0 | 1 | 1 | 27 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 75.75 | 1929.0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | ||
| 41 | 1 | 0 | 0 | 2 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 49.25 | 91.1 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | ||
| 42 | 0 | 0 | 0 | 27 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 78.2 | 2078.95 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | ||
| 43 | 0 | 1 | 1 | 25 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 25.5 | 630.6 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ||
| 44 | 0 | 1 | 1 | 25 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 61.6 | 1611.0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | ||
| 45 | 0 | 0 | 1 | 29 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 45.0 | 1242.45 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | ||
| 46 | 0 | 1 | 0 | 72 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 85.15 | 6316.2 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | ||
| 47 | 0 | 0 | 0 | 14 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 51.45 | 727.85 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | ||
| 48 | 0 | 0 | 0 | 35 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 99.25 | 3532.0 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | ||
| 49 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 44.3 | 44.3 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | ||
| 50 | 0 | 0 | 0 | 29 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 94.2 | 2607.6 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | ||
| 51 | 0 | 0 | 0 | 64 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 81.25 | 5567.55 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | ||
| 52 | 0 | 1 | 1 | 39 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 99.95 | 3767.4 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | ||
| 53 | 1 | 0 | 0 | 40 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 91.55 | 3673.6 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | ||
| 54 | 0 | 0 | 0 | 40 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 104.5 | 4036.85 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | ||
| 55 | 1 | 0 | 0 | 11 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 95.0 | 1120.3 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | ||
| 56 | 0 | 1 | 0 | 6 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 50.35 | 314.55 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | ||
| 57 | 0 | 0 | 0 | 30 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 64.5 | 1888.45 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | ||
| 58 | 0 | 0 | 0 | 27 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 19.4 | 529.8 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | ||
| 59 | 1 | 1 | 0 | 70 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 104.8 | 7308.95 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | ||
| 60 | 0 | 1 | 0 | 57 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 109.4 | 6252.7 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | ||
| 61 | 0 | 1 | 0 | 58 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 50.3 | 2878.55 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | ||
| 62 | 0 | 0 | 0 | 16 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 71.4 | 1212.1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | ||
| 63 | 0 | 1 | 0 | 69 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 116.0 | 8182.85 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | ||
| 64 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 19.85 | 19.85 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | ||
| 65 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 99.75 | 99.75 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | ||
| 66 | 1 | 1 | 1 | 32 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 93.95 | 2861.45 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | ||
| 67 | 0 | 1 | 1 | 16 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 90.8 | 1442.2 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | ||
| 68 | 0 | 1 | 0 | 49 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 84.35 | 4059.35 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | ||
| 69 | 0 | 1 | 0 | 71 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 58.25 | 4145.9 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | ||
| 70 | 0 | 0 | 0 | 33 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 107.55 | 3645.5 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | ||
| 71 | 0 | 1 | 0 | 10 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 19.95 | 187.75 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | ||
| 72 | 0 | 1 | 0 | 21 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 111.2 | 2317.1 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | ||
| 73 | 0 | 1 | 1 | 37 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 40.2 | 1448.8 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | ||
| 74 | 1 | 0 | 0 | 26 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 85.8 | 2193.65 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | ||
| 75 | 0 | 0 | 0 | 50 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 35.4 | 1748.9 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | ||
| 76 | 0 | 0 | 0 | 7 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 73.85 | 511.25 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | ||
| 77 | 0 | 1 | 1 | 61 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 88.1 | 5526.75 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | ||
| 78 | 0 | 0 | 0 | 15 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 101.35 | 1553.95 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | ||
| 79 | 0 | 0 | 1 | 26 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 45.8 | 1147.0 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | ||
| 80 | 0 | 1 | 0 | 72 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 94.65 | 6747.35 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | ||
| 81 | 0 | 1 | 1 | 44 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 20.5 | 865.05 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | ||
| 82 | 0 | 0 | 0 | 66 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 89.4 | 5976.9 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | ||
| 83 | 0 | 0 | 0 | 2 | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 86.25 | 181.65 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | ||
| 84 | 1 | 0 | 0 | 44 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 74.85 | 3268.05 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | ||
| 85 | 0 | 0 | 0 | 12 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 89.75 | 1052.4 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | ||
| 86 | 1 | 1 | 0 | 69 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 109.95 | 7634.25 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | ||
| 87 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 80.2 | 80.2 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | ||
| 88 | 0 | 0 | 0 | 3 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 19.85 | 63.75 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | ||
| 89 | 0 | 1 | 0 | 2 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 90.35 | 190.5 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | ||
| 90 | 1 | 0 | 0 | 27 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 86.45 | 2401.05 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | ||
| 91 | 0 | 0 | 0 | 26 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 20.3 | 511.25 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | ||
| 92 | 1 | 1 | 0 | 39 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 101.25 | 3949.15 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | ||
| 93 | 0 | 0 | 0 | 25 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 94.7 | 2362.1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | ||
| 94 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 70.9 | 70.9 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | ||
| 95 | 0 | 1 | 0 | 22 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 54.2 | 1152.7 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | ||
| 96 | 0 | 0 | 0 | 72 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 114.9 | 8496.7 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | ||
| 97 | 0 | 0 | 0 | 24 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 19.55 | 470.2 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | ||
| 98 | 0 | 1 | 0 | 19 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 86.85 | 1564.4 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | ||
| 99 | 0 | 1 | 1 | 71 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 25.35 | 1847.55 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ||
| 100 | 1 | 1 | 0 | 33 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 109.9 | 3694.7 | 0 | 0 | 0 | 1 | 1 | 0 | 0 |
Let's compute the correlations between the different variables and the response column.
%matplotlib inline
churn.corr(focus = "Churn")
| "Churn" | |
| 1.0 | |
| 0.405 | |
| -0.352 | |
| 0.308 | |
| 0.302 | |
| -0.199 | |
| 0.193 | |
| 0.192 | |
| -0.178 | |
| -0.171 | |
| -0.165 | |
| -0.164 | |
| 0.151 | |
| -0.15 | |
| -0.134 | |
| -0.124 | |
| -0.118 | |
| -0.082 | |
| -0.066 | |
| 0.063 | |
| 0.061 | |
| 0.04 | |
| 0.012 | |
| 0.009 |
Many features have a strong correlation with the 'Churn' variable. For example, the customers that have a 'Month to Month' contract are more likely to churn. Having this type of contract gives customers a lot of flexibility and allows them to leave at any time. New customers are also likely to churn.
# No lock-in = Churn
churn.hist(["Contract_Month-to-month", "tenure"], method = "avg", of = "Churn")
<AxesSubplot:xlabel='"Contract_Month-to-month"', ylabel='avg("Churn")'>
The following scatter plot shows that providing better tariff plans can prevent churning. Indeed, customers having high total charges are more likely to churn even if they've been with the company for a long time.
churn.scatter(["TotalCharges", "tenure"], catcol = "Churn")
<AxesSubplot:xlabel='"TotalCharges"', ylabel='"tenure"'>
Let's move on to machine learning.
Machine Learning¶
Logistic regression is a very powerful algorithm and we can use it to detect churns. Let's split our vDataFrame into training and testing set to evaluate our model.
train, test = churn.train_test_split(test_size = 0.2,
random_state = 0)
Let's train and evaluate our model.
from verticapy.learn.linear_model import LogisticRegression
model = LogisticRegression("churn_model",
penalty = 'L2',
tol = 1e-6,
max_iter = 1000,
solver = "BFGS")
model.fit(train,
churn.get_columns(exclude_columns = ["churn"]),
'churn',
test)
model.classification_report()
| value | |
| auc | 0.8554368006422792 |
| prc_auc | 0.6822415600545241 |
| accuracy | 0.8031161473087819 |
| log_loss | 0.1717601946823 |
| precision | 0.6761006289308176 |
| recall | 0.5512820512820513 |
| f1_score | 0.6073446327683616 |
| mcc | 0.48220268504473107 |
| informedness | 0.45049927241708065 |
| markedness | 0.5161371920021156 |
| csi | 0.43610547667342797 |
| cutoff | 0.5 |
The model is excellent! Let's run some machine learning on the entire dataset and compute the importance of each feature.
model.fit(churn,
churn.get_columns(exclude_columns = ["churn"]),
'churn')
model.features_importance()
| importance | sign | |
| 28.58 | -1 | |
| 18.43 | 1 | |
| 8.66 | 1 | |
| 7.0 | 1 | |
| 5.79 | 1 | |
| 5.26 | -1 | |
| 4.31 | 1 | |
| 3.58 | 1 | |
| 2.93 | -1 | |
| 2.81 | -1 | |
| 2.4 | 1 | |
| 2.29 | 1 | |
| 1.45 | 1 | |
| 1.4 | -1 | |
| 1.34 | 1 | |
| 0.97 | -1 | |
| 0.73 | 1 | |
| 0.68 | 1 | |
| 0.63 | -1 | |
| 0.39 | 1 | |
| 0.21 | -1 | |
| 0.17 | 1 | |
| 0.0 | -1 |
Based on our model, most churning customers are at least one of the following:
- Paying higher bills
- New Telco customers
- Have a monthly contract
Notice that customers have a 'Fiber Optic' option are also likely to churn. Let's check if this relationship is causal by computing some aggregations.
import verticapy.stats as st
# Is Fiber optic a Bad Option? - VerticaPy
churn.groupby(["InternetService_Fiber_optic"],
[st.avg(churn["tenure"])._as("tenure"),
st.avg(churn["totalcharges"])._as("totalcharges"),
st.avg(churn["contract_month-to-month"])._as("contract_month_to_month"),
st.avg(churn["monthlycharges"])._as("monthlycharges")])
123 InternetService_Fiber_opticInteger | 123 tenureFloat | 123 totalchargesFloat | 123 contract_month_to_monthFloat | 123 monthlychargesFloat | |
| 1 | 0 | 31.9422346085635 | 1558.06548526423 | 0.442614644033443 | 43.7882442361287 |
| 2 | 1 | 32.9179586563307 | 3205.30457041344 | 0.68733850129199 | 91.5001291989664 |
It seems like the 'Fiber Optic' option in and of itself doesn't lead to churning, but customers that have this option tend to churn because their contract puts them into one of the three categories we listed before: they're paying more.
To retain these customers, we'll need to make some changes to what types of contracts we offer.
We'll use a lift chart to help us identify which of our customers are likely to churn.
model.lift_chart()
| decision_boundary | positive_prediction_ratio | lift | |
| 1 | 0.0 | 0.0 | 3.76243980738363 |
| 2 | 0.001 | 0.0 | 3.76243980738363 |
| 3 | 0.002 | 0.0 | 3.76243980738363 |
| 4 | 0.003 | 0.0 | 3.76243980738363 |
| 5 | 0.004 | 0.0 | 3.76243980738363 |
| 6 | 0.005 | 0.0 | 3.76243980738363 |
| 7 | 0.006 | 0.0 | 3.76243980738363 |
| 8 | 0.007 | 0.0 | 3.76243980738363 |
| 9 | 0.008 | 0.0 | 3.76243980738363 |
| 10 | 0.009 | 0.0 | 3.76243980738363 |
| 11 | 0.01 | 0.0 | 3.76243980738363 |
| 12 | 0.011 | 0.0 | 3.76243980738363 |
| 13 | 0.012 | 0.0 | 3.76243980738363 |
| 14 | 0.013 | 0.0 | 3.76243980738363 |
| 15 | 0.014 | 0.0 | 3.76243980738363 |
| 16 | 0.015 | 0.0 | 3.76243980738363 |
| 17 | 0.016 | 0.0 | 3.76243980738363 |
| 18 | 0.017 | 0.0 | 3.76243980738363 |
| 19 | 0.018 | 0.0 | 3.76243980738363 |
| 20 | 0.019 | 0.0 | 3.76243980738363 |
| 21 | 0.02 | 0.0 | 3.76243980738363 |
| 22 | 0.021 | 0.0 | 3.76243980738363 |
| 23 | 0.022 | 0.0 | 3.76243980738363 |
| 24 | 0.023 | 0.0 | 3.76243980738363 |
| 25 | 0.024 | 0.0 | 3.76243980738363 |
| 26 | 0.025 | 0.0 | 3.76243980738363 |
| 27 | 0.026 | 0.0 | 3.76243980738363 |
| 28 | 0.027 | 0.0 | 3.76243980738363 |
| 29 | 0.028 | 0.0 | 3.76243980738363 |
| 30 | 0.029 | 0.0 | 3.76243980738363 |
| 31 | 0.03 | 0.0 | 3.76243980738363 |
| 32 | 0.031 | 0.0 | 3.76243980738363 |
| 33 | 0.032 | 0.0 | 3.76243980738363 |
| 34 | 0.033 | 0.0 | 3.76243980738363 |
| 35 | 0.034 | 0.0 | 3.76243980738363 |
| 36 | 0.035 | 0.0 | 3.76243980738363 |
| 37 | 0.036 | 0.0 | 3.76243980738363 |
| 38 | 0.037 | 0.0 | 3.76243980738363 |
| 39 | 0.038 | 0.0 | 3.76243980738363 |
| 40 | 0.039 | 0.0 | 3.76243980738363 |
| 41 | 0.04 | 0.0 | 3.76243980738363 |
| 42 | 0.041 | 0.0 | 3.76243980738363 |
| 43 | 0.042 | 0.0 | 3.76243980738363 |
| 44 | 0.043 | 0.0 | 3.76243980738363 |
| 45 | 0.044 | 0.0 | 3.76243980738363 |
| 46 | 0.045 | 0.0 | 3.76243980738363 |
| 47 | 0.046 | 0.0 | 3.76243980738363 |
| 48 | 0.047 | 0.0 | 3.76243980738363 |
| 49 | 0.048 | 0.0 | 3.76243980738363 |
| 50 | 0.049 | 0.0 | 3.76243980738363 |
| 51 | 0.05 | 0.0 | 3.76243980738363 |
| 52 | 0.051 | 0.0 | 3.76243980738363 |
| 53 | 0.052 | 0.0 | 3.76243980738363 |
| 54 | 0.053 | 0.0 | 3.76243980738363 |
| 55 | 0.054 | 0.0 | 3.76243980738363 |
| 56 | 0.055 | 0.0 | 3.76243980738363 |
| 57 | 0.056 | 0.0 | 3.76243980738363 |
| 58 | 0.057 | 0.0 | 3.76243980738363 |
| 59 | 0.058 | 0.0 | 3.76243980738363 |
| 60 | 0.059 | 0.0 | 3.76243980738363 |
| 61 | 0.06 | 0.0 | 3.76243980738363 |
| 62 | 0.061 | 0.0 | 3.76243980738363 |
| 63 | 0.062 | 0.0 | 3.76243980738363 |
| 64 | 0.063 | 0.0 | 3.76243980738363 |
| 65 | 0.064 | 0.0 | 3.76243980738363 |
| 66 | 0.065 | 0.0 | 3.76243980738363 |
| 67 | 0.066 | 0.0 | 3.76243980738363 |
| 68 | 0.067 | 0.0 | 3.76243980738363 |
| 69 | 0.068 | 0.0 | 3.76243980738363 |
| 70 | 0.069 | 0.0 | 3.76243980738363 |
| 71 | 0.07 | 0.0 | 3.76243980738363 |
| 72 | 0.071 | 0.0 | 3.76243980738363 |
| 73 | 0.072 | 0.0 | 3.76243980738363 |
| 74 | 0.073 | 0.0 | 3.76243980738363 |
| 75 | 0.074 | 0.0 | 3.76243980738363 |
| 76 | 0.075 | 0.0 | 3.76243980738363 |
| 77 | 0.076 | 0.0 | 3.76243980738363 |
| 78 | 0.077 | 0.0 | 3.76243980738363 |
| 79 | 0.078 | 0.0 | 3.76243980738363 |
| 80 | 0.079 | 0.0 | 3.76243980738363 |
| 81 | 0.08 | 0.0 | 3.76243980738363 |
| 82 | 0.081 | 0.0 | 3.76243980738363 |
| 83 | 0.082 | 0.0 | 3.76243980738363 |
| 84 | 0.083 | 0.0 | 3.76243980738363 |
| 85 | 0.084 | 0.0 | 3.76243980738363 |
| 86 | 0.085 | 0.0 | 3.76243980738363 |
| 87 | 0.086 | 0.0 | 3.76243980738363 |
| 88 | 0.087 | 0.0 | 3.76243980738363 |
| 89 | 0.088 | 0.0 | 3.76243980738363 |
| 90 | 0.089 | 0.0 | 3.76243980738363 |
| 91 | 0.09 | 0.0 | 3.76243980738363 |
| 92 | 0.091 | 0.0 | 3.76243980738363 |
| 93 | 0.092 | 0.0 | 3.76243980738363 |
| 94 | 0.093 | 0.0 | 3.76243980738363 |
| 95 | 0.094 | 0.0 | 3.76243980738363 |
| 96 | 0.095 | 0.0 | 3.76243980738363 |
| 97 | 0.096 | 0.0 | 3.76243980738363 |
| 98 | 0.097 | 0.0 | 3.76243980738363 |
| 99 | 0.098 | 0.0 | 3.76243980738363 |
| 100 | 0.099 | 0.0 | 3.76243980738363 |
| 101 | 0.1 | 0.0 | 3.76243980738363 |
| 102 | 0.101 | 0.0 | 3.76243980738363 |
| 103 | 0.102 | 0.0 | 3.76243980738363 |
| 104 | 0.103 | 0.0 | 3.76243980738363 |
| 105 | 0.104 | 0.0 | 3.76243980738363 |
| 106 | 0.105 | 0.0 | 3.76243980738363 |
| 107 | 0.106 | 0.0 | 3.76243980738363 |
| 108 | 0.107 | 0.0 | 3.76243980738363 |
| 109 | 0.108 | 0.0 | 3.76243980738363 |
| 110 | 0.109 | 0.0 | 3.76243980738363 |
| 111 | 0.11 | 0.0 | 3.76243980738363 |
| 112 | 0.111 | 0.0 | 3.76243980738363 |
| 113 | 0.112 | 0.0 | 3.76243980738363 |
| 114 | 0.113 | 0.0 | 3.76243980738363 |
| 115 | 0.114 | 0.0 | 3.76243980738363 |
| 116 | 0.115 | 0.0 | 3.76243980738363 |
| 117 | 0.116 | 0.0 | 3.76243980738363 |
| 118 | 0.117 | 0.0 | 3.76243980738363 |
| 119 | 0.118 | 0.0 | 3.76243980738363 |
| 120 | 0.119 | 0.0 | 3.76243980738363 |
| 121 | 0.12 | 0.0 | 3.76243980738363 |
| 122 | 0.121 | 0.0 | 3.76243980738363 |
| 123 | 0.122 | 0.0 | 3.76243980738363 |
| 124 | 0.123 | 0.0 | 3.76243980738363 |
| 125 | 0.124 | 0.0 | 3.76243980738363 |
| 126 | 0.125 | 0.0 | 3.76243980738363 |
| 127 | 0.126 | 0.0 | 3.76243980738363 |
| 128 | 0.127 | 0.0 | 3.76243980738363 |
| 129 | 0.128 | 0.0 | 3.76243980738363 |
| 130 | 0.129 | 0.0 | 3.76243980738363 |
| 131 | 0.13 | 0.0 | 3.76243980738363 |
| 132 | 0.131 | 0.0 | 3.76243980738363 |
| 133 | 0.132 | 0.0 | 3.76243980738363 |
| 134 | 0.133 | 0.0 | 3.76243980738363 |
| 135 | 0.134 | 0.0 | 3.76243980738363 |
| 136 | 0.135 | 0.0 | 3.76243980738363 |
| 137 | 0.136 | 0.0 | 3.76243980738363 |
| 138 | 0.137 | 0.0 | 3.76243980738363 |
| 139 | 0.138 | 0.0 | 3.76243980738363 |
| 140 | 0.139 | 0.0 | 3.76243980738363 |
| 141 | 0.14 | 0.0 | 3.76243980738363 |
| 142 | 0.141 | 0.0 | 3.76243980738363 |
| 143 | 0.142 | 0.0 | 3.76243980738363 |
| 144 | 0.143 | 0.0 | 3.76243980738363 |
| 145 | 0.144 | 0.0 | 3.76243980738363 |
| 146 | 0.145 | 0.0 | 3.76243980738363 |
| 147 | 0.146 | 0.0 | 3.76243980738363 |
| 148 | 0.147 | 0.0 | 3.76243980738363 |
| 149 | 0.148 | 0.0 | 3.76243980738363 |
| 150 | 0.149 | 0.0 | 3.76243980738363 |
| 151 | 0.15 | 0.0 | 3.76243980738363 |
| 152 | 0.151 | 0.0 | 3.76243980738363 |
| 153 | 0.152 | 0.0 | 3.76243980738363 |
| 154 | 0.153 | 0.0 | 3.76243980738363 |
| 155 | 0.154 | 0.000535045478865704 | 3.76243980738363 |
| 156 | 0.155 | 0.00107009095773141 | 3.76243980738363 |
| 157 | 0.156 | 0.00214018191546281 | 3.76243980738363 |
| 158 | 0.157 | 0.00267522739432852 | 3.76243980738363 |
| 159 | 0.158 | 0.00267522739432852 | 3.76243980738363 |
| 160 | 0.159 | 0.00374531835205993 | 3.76243980738363 |
| 161 | 0.16 | 0.00374531835205993 | 3.29213483146067 |
| 162 | 0.161 | 0.00481540930979133 | 3.38619582664526 |
| 163 | 0.162 | 0.00481540930979133 | 3.38619582664526 |
| 164 | 0.163 | 0.00535045478865704 | 3.42039982489421 |
| 165 | 0.164 | 0.00535045478865704 | 3.42039982489421 |
| 166 | 0.165 | 0.00535045478865704 | 3.42039982489421 |
| 167 | 0.166 | 0.00535045478865704 | 3.42039982489421 |
| 168 | 0.167 | 0.00535045478865704 | 3.42039982489421 |
| 169 | 0.168 | 0.00535045478865704 | 3.42039982489421 |
| 170 | 0.169 | 0.00535045478865704 | 3.42039982489421 |
| 171 | 0.17 | 0.00535045478865704 | 3.42039982489421 |
| 172 | 0.171 | 0.00535045478865704 | 3.42039982489421 |
| 173 | 0.172 | 0.00535045478865704 | 3.42039982489421 |
| 174 | 0.173 | 0.00535045478865704 | 3.42039982489421 |
| 175 | 0.174 | 0.00535045478865704 | 3.42039982489421 |
| 176 | 0.175 | 0.00535045478865704 | 3.42039982489421 |
| 177 | 0.176 | 0.00535045478865704 | 3.42039982489421 |
| 178 | 0.177 | 0.00642054574638844 | 3.47302136066181 |
| 179 | 0.178 | 0.00642054574638844 | 3.47302136066181 |
| 180 | 0.179 | 0.00642054574638844 | 3.47302136066181 |
| 181 | 0.18 | 0.00642054574638844 | 3.47302136066181 |
| 182 | 0.181 | 0.00695559122525415 | 3.49369410685623 |
| 183 | 0.182 | 0.00856072766185126 | 3.541119818714 |
| 184 | 0.183 | 0.00963081861958266 | 3.38619582664526 |
| 185 | 0.184 | 0.0101658640984484 | 3.40411220668042 |
| 186 | 0.185 | 0.0112359550561798 | 3.4352711284807 |
| 187 | 0.186 | 0.0117710005350455 | 3.44890315676833 |
| 188 | 0.187 | 0.0133761369716426 | 3.48374056239225 |
| 189 | 0.188 | 0.0133761369716426 | 3.48374056239225 |
| 190 | 0.189 | 0.0139111824505083 | 3.49369410685623 |
| 191 | 0.19 | 0.014446227929374 | 3.50296119997786 |
| 192 | 0.191 | 0.0165864098448368 | 3.53441315239068 |
| 193 | 0.192 | 0.0171214553237025 | 3.541119818714 |
| 194 | 0.193 | 0.0171214553237025 | 3.541119818714 |
| 195 | 0.194 | 0.0181915462814339 | 3.55341537364009 |
| 196 | 0.195 | 0.0181915462814339 | 3.55341537364009 |
| 197 | 0.196 | 0.0181915462814339 | 3.55341537364009 |
| 198 | 0.197 | 0.0187265917602996 | 3.46540508574808 |
| 199 | 0.198 | 0.0192616372391653 | 3.47302136066181 |
| 200 | 0.199 | 0.0203317281968967 | 3.48713933367263 |
| 201 | 0.2 | 0.0208667736757624 | 3.49369410685623 |
| 202 | 0.201 | 0.0208667736757624 | 3.49369410685623 |
| 203 | 0.202 | 0.0214018191546281 | 3.49994400686849 |
| 204 | 0.203 | 0.0219368646334938 | 3.50590982051656 |
| 205 | 0.204 | 0.0219368646334938 | 3.50590982051656 |
| 206 | 0.205 | 0.0230069555912253 | 3.51706329820643 |
| 207 | 0.206 | 0.0240770465489567 | 3.52728731942215 |
| 208 | 0.207 | 0.0251471375066881 | 3.53669341894061 |
| 209 | 0.208 | 0.0256821829855538 | 3.541119818714 |
| 210 | 0.209 | 0.0267522739432852 | 3.42039982489421 |
| 211 | 0.21 | 0.0278223649010166 | 3.43240122778857 |
| 212 | 0.211 | 0.028892455858748 | 3.44358897624942 |
| 213 | 0.212 | 0.0304975922953451 | 3.40411220668042 |
| 214 | 0.213 | 0.0315676832530765 | 3.26446983287697 |
| 215 | 0.214 | 0.0331728196896736 | 3.28551081771528 |
| 216 | 0.215 | 0.034242910647405 | 3.29857736537743 |
| 217 | 0.216 | 0.0358480470840021 | 3.3168877249303 |
| 218 | 0.217 | 0.0369181380417336 | 3.3283121373009 |
| 219 | 0.218 | 0.037988228999465 | 3.33916532905297 |
| 220 | 0.219 | 0.0385232744783307 | 3.30360568453197 |
| 221 | 0.22 | 0.0406634563937935 | 3.32494680652507 |
| 222 | 0.221 | 0.0422685928303906 | 3.33969376161019 |
| 223 | 0.222 | 0.0422685928303906 | 3.26629389871765 |
| 224 | 0.223 | 0.0438737292669877 | 3.24757962321534 |
| 225 | 0.224 | 0.0476190476190476 | 3.28291316526611 |
| 226 | 0.225 | 0.048689138576779 | 3.26078116639914 |
| 227 | 0.226 | 0.0529695024077047 | 3.23896992113895 |
| 228 | 0.227 | 0.0540395933654361 | 3.24791812432262 |
| 229 | 0.228 | 0.0561797752808989 | 3.23816540799411 |
| 230 | 0.229 | 0.0567148207597646 | 3.21627919018278 |
| 231 | 0.23 | 0.057784911717496 | 3.17455858747994 |
| 232 | 0.231 | 0.057784911717496 | 3.17455858747994 |
| 233 | 0.232 | 0.0593900481540931 | 3.18802151618002 |
| 234 | 0.233 | 0.0609951845906902 | 3.17717139290173 |
| 235 | 0.234 | 0.0626003210272873 | 3.18989461930351 |
| 236 | 0.235 | 0.0636704119850187 | 3.17539246155072 |
| 237 | 0.236 | 0.0636704119850187 | 3.17539246155072 |
| 238 | 0.237 | 0.0658105939004815 | 3.16972668704237 |
| 239 | 0.238 | 0.066880684858213 | 3.17773632380374 |
| 240 | 0.239 | 0.0674157303370786 | 3.1816605082573 |
| 241 | 0.24 | 0.0674157303370786 | 3.1816605082573 |
| 242 | 0.241 | 0.0679507758159444 | 3.18553237025147 |
| 243 | 0.242 | 0.0684858212948101 | 3.18935294930533 |
| 244 | 0.243 | 0.0706260032102729 | 3.20414228757832 |
| 245 | 0.244 | 0.07223113964687 | 3.2147428733974 |
| 246 | 0.245 | 0.0738362760834671 | 3.22494840632882 |
| 247 | 0.246 | 0.0743713215623328 | 3.2084609400388 |
| 248 | 0.247 | 0.077581594435527 | 3.22812882882027 |
| 249 | 0.248 | 0.0781166399143927 | 3.21237550805854 |
| 250 | 0.249 | 0.0781166399143927 | 3.21237550805854 |
| 251 | 0.25 | 0.0797217763509898 | 3.16725158926644 |
| 252 | 0.251 | 0.0829320492241841 | 3.16944657687208 |
| 253 | 0.252 | 0.0893525949705725 | 3.14163723916533 |
| 254 | 0.253 | 0.0947030497592295 | 3.1561698858147 |
| 255 | 0.254 | 0.0963081861958267 | 3.14994960618164 |
| 256 | 0.255 | 0.0973782771535581 | 3.14111947221936 |
| 257 | 0.256 | 0.0979133226324237 | 3.14395655137536 |
| 258 | 0.257 | 0.102193686463349 | 3.15186843513278 |
| 259 | 0.258 | 0.106474050294275 | 3.17256576978535 |
| 260 | 0.259 | 0.108614232209738 | 3.18239700374532 |
| 261 | 0.26 | 0.109684323167469 | 3.17407473462405 |
| 262 | 0.261 | 0.111824505082932 | 3.17076580541604 |
| 263 | 0.262 | 0.115569823434992 | 3.16220621943527 |
| 264 | 0.263 | 0.118780096308186 | 3.16386983802714 |
| 265 | 0.264 | 0.124130551096843 | 3.18571545734672 |
| 266 | 0.265 | 0.126270733012306 | 3.19401364943358 |
| 267 | 0.266 | 0.128410914927769 | 3.17952659778898 |
| 268 | 0.267 | 0.128945960406635 | 3.18157190729633 |
| 269 | 0.268 | 0.130551096843232 | 3.17659277855227 |
| 270 | 0.269 | 0.132691278758694 | 3.18459069020867 |
| 271 | 0.27 | 0.133761369716426 | 3.17773632380374 |
| 272 | 0.271 | 0.134831460674157 | 3.17101950321296 |
| 273 | 0.272 | 0.135901551631889 | 3.1333105281162 |
| 274 | 0.273 | 0.138576779026217 | 3.13335019328733 |
| 275 | 0.274 | 0.138576779026217 | 3.11332878630147 |
| 276 | 0.275 | 0.139646869983949 | 3.10758477761749 |
| 277 | 0.276 | 0.142322097378277 | 3.06996622320259 |
| 278 | 0.277 | 0.142857142857143 | 3.06271777003484 |
| 279 | 0.278 | 0.144997324772606 | 3.06192548889178 |
| 280 | 0.279 | 0.147672552166934 | 3.06322532990525 |
| 281 | 0.28 | 0.149277688603531 | 3.06935879023401 |
| 282 | 0.281 | 0.15195291599786 | 3.07049685430158 |
| 283 | 0.282 | 0.154628143392188 | 3.0802977459883 |
| 284 | 0.283 | 0.156768325307651 | 3.07073778151366 |
| 285 | 0.284 | 0.157303370786517 | 3.05568315848284 |
| 286 | 0.285 | 0.162118780096308 | 3.07282819848312 |
| 287 | 0.286 | 0.164794007490637 | 3.07382350311448 |
| 288 | 0.287 | 0.167469234884965 | 3.07478762326652 |
| 289 | 0.288 | 0.168004280363831 | 3.06063756351932 |
| 290 | 0.289 | 0.170679507758159 | 3.06961201676567 |
| 291 | 0.29 | 0.170679507758159 | 3.05399058156585 |
| 292 | 0.291 | 0.172284644194757 | 3.03635493227451 |
| 293 | 0.292 | 0.174959871589085 | 3.03782177040604 |
| 294 | 0.293 | 0.176565008025682 | 3.03570938004058 |
| 295 | 0.294 | 0.178170144462279 | 3.02631027985205 |
| 296 | 0.295 | 0.180310326377742 | 3.03335458155092 |
| 297 | 0.296 | 0.184055644729802 | 3.03109904857135 |
| 298 | 0.297 | 0.188336008560728 | 3.02369591826264 |
| 299 | 0.298 | 0.191546281433922 | 3.02686168773784 |
| 300 | 0.299 | 0.192081326912788 | 3.01499082779179 |
| 301 | 0.3 | 0.193686463349385 | 3.0132814386568 |
| 302 | 0.301 | 0.195291599785982 | 3.01160203880488 |
| 303 | 0.302 | 0.202782236490102 | 3.0211116249966 |
| 304 | 0.303 | 0.208132691278759 | 3.02394439064511 |
| 305 | 0.304 | 0.208132691278759 | 2.99302471384914 |
| 306 | 0.305 | 0.210272873194221 | 2.96320409679713 |
| 307 | 0.306 | 0.210807918673087 | 2.95888479862106 |
| 308 | 0.307 | 0.211878009630819 | 2.95620270580142 |
| 309 | 0.308 | 0.213483146067416 | 2.94933886669168 |
| 310 | 0.309 | 0.215088282504013 | 2.93120310575236 |
| 311 | 0.31 | 0.21669341894061 | 2.92473727829246 |
| 312 | 0.311 | 0.219903691813804 | 2.92871735006566 |
| 313 | 0.312 | 0.221508828250401 | 2.92242041323982 |
| 314 | 0.313 | 0.222578919208133 | 2.90924713730779 |
| 315 | 0.314 | 0.223113964686998 | 2.90543962903513 |
| 316 | 0.315 | 0.225789192081327 | 2.90265008906013 |
| 317 | 0.316 | 0.227394328517924 | 2.90733985116008 |
| 318 | 0.317 | 0.228464419475655 | 2.90517504114432 |
| 319 | 0.318 | 0.228999464954521 | 2.90148511272107 |
| 320 | 0.319 | 0.230069555912253 | 2.90457651198377 |
| 321 | 0.32 | 0.230069555912253 | 2.8993711777329 |
| 322 | 0.321 | 0.234884965222044 | 2.91307067979085 |
| 323 | 0.322 | 0.235955056179775 | 2.91094027202839 |
| 324 | 0.323 | 0.239165329052969 | 2.91474972946357 |
| 325 | 0.324 | 0.242375601926164 | 2.92347381259826 |
| 326 | 0.325 | 0.242910647405029 | 2.91492776886035 |
| 327 | 0.326 | 0.243980738362761 | 2.90791957994396 |
| 328 | 0.327 | 0.245585874799358 | 2.91224261650773 |
| 329 | 0.328 | 0.249331193151418 | 2.91245340571557 |
| 330 | 0.329 | 0.251471375066881 | 2.90846498268142 |
| 331 | 0.33 | 0.254146602461209 | 2.89652983550603 |
| 332 | 0.331 | 0.258426966292135 | 2.90761348314607 |
| 333 | 0.332 | 0.261102193686463 | 2.90977912203361 |
| 334 | 0.333 | 0.266987693953986 | 2.91078676571229 |
| 335 | 0.334 | 0.268592830390583 | 2.90576120508705 |
| 336 | 0.335 | 0.269662921348315 | 2.90838905356035 |
| 337 | 0.336 | 0.272338148742643 | 2.91488867877971 |
| 338 | 0.337 | 0.27394328517924 | 2.90992323471362 |
| 339 | 0.338 | 0.276618512573569 | 2.90759548642352 |
| 340 | 0.339 | 0.278758694489032 | 2.90835480659773 |
| 341 | 0.34 | 0.28143392188336 | 2.91035785100557 |
| 342 | 0.341 | 0.282504012841092 | 2.90009958875702 |
| 343 | 0.342 | 0.283574103798823 | 2.89839113068797 |
| 344 | 0.343 | 0.285714285714286 | 2.88669950738916 |
| 345 | 0.344 | 0.287854467629749 | 2.88757862535291 |
| 346 | 0.345 | 0.289994649545211 | 2.88844529122086 |
| 347 | 0.346 | 0.29266987693954 | 2.88647205419193 |
| 348 | 0.347 | 0.293204922418406 | 2.87963270174054 |
| 349 | 0.348 | 0.293739967897271 | 2.87285042316219 |
| 350 | 0.349 | 0.294810058855003 | 2.87133564247698 |
| 351 | 0.35 | 0.295345104333868 | 2.86464382575967 |
| 352 | 0.351 | 0.297485286249331 | 2.86563908617164 |
| 353 | 0.352 | 0.298020331728197 | 2.85904361898046 |
| 354 | 0.353 | 0.299090422685928 | 2.85761392979273 |
| 355 | 0.354 | 0.302835741037988 | 2.8622861975526 |
| 356 | 0.355 | 0.30390583199572 | 2.86086453894766 |
| 357 | 0.356 | 0.305510968432317 | 2.85685256651071 |
| 358 | 0.357 | 0.306581059390048 | 2.85169048892965 |
| 359 | 0.358 | 0.309256286784377 | 2.8501837597218 |
| 360 | 0.359 | 0.310326377742108 | 2.85256874285295 |
| 361 | 0.36 | 0.31139646869984 | 2.84751621313039 |
| 362 | 0.361 | 0.313001605136437 | 2.84738329536795 |
| 363 | 0.362 | 0.314071696094168 | 2.83875599863006 |
| 364 | 0.363 | 0.315141787051899 | 2.8338581157915 |
| 365 | 0.364 | 0.316746923488497 | 2.83019614481716 |
| 366 | 0.365 | 0.318352059925094 | 2.83373631062438 |
| 367 | 0.366 | 0.323702514713751 | 2.82767215337527 |
| 368 | 0.367 | 0.324237560192616 | 2.81834180874472 |
| 369 | 0.368 | 0.326377742108079 | 2.81951877457495 |
| 370 | 0.369 | 0.328517924023542 | 2.81381003865231 |
| 371 | 0.37 | 0.331193151417871 | 2.80934890322131 |
| 372 | 0.371 | 0.333333333333333 | 2.80718562874251 |
| 373 | 0.372 | 0.334403424291065 | 2.80946819547762 |
| 374 | 0.373 | 0.336543606206528 | 2.80732460123879 |
| 375 | 0.374 | 0.337613697164259 | 2.80626420621639 |
| 376 | 0.375 | 0.340823970037453 | 2.80312766936067 |
| 377 | 0.376 | 0.341894060995185 | 2.80536643747741 |
| 378 | 0.377 | 0.344034242910647 | 2.80330103840982 |
| 379 | 0.378 | 0.345639379347245 | 2.78731205913971 |
| 380 | 0.379 | 0.34991974317817 | 2.79300298981713 |
| 381 | 0.38 | 0.352594970572499 | 2.79217098318222 |
| 382 | 0.381 | 0.354200107009096 | 2.78917710245012 |
| 383 | 0.382 | 0.356875334403424 | 2.78220327220053 |
| 384 | 0.383 | 0.359550561797753 | 2.77841708852945 |
| 385 | 0.384 | 0.363295880149813 | 2.77986575540096 |
| 386 | 0.385 | 0.36864633493847 | 2.77550431187079 |
| 387 | 0.386 | 0.370786516853933 | 2.77379870906048 |
| 388 | 0.387 | 0.372926698769395 | 2.76918748230875 |
| 389 | 0.388 | 0.374531835205993 | 2.76649985837031 |
| 390 | 0.389 | 0.375066880684858 | 2.75886015164845 |
| 391 | 0.39 | 0.376672017121455 | 2.7533863039481 |
| 392 | 0.391 | 0.377207062600321 | 2.7402066778982 |
| 393 | 0.392 | 0.377742108079187 | 2.73843557114726 |
| 394 | 0.393 | 0.378812199036918 | 2.74054257574857 |
| 395 | 0.394 | 0.37988228999465 | 2.72863356817403 |
| 396 | 0.395 | 0.382022471910112 | 2.7272913933725 |
| 397 | 0.396 | 0.384697699304441 | 2.72426406999882 |
| 398 | 0.397 | 0.385767790262172 | 2.72088174636268 |
| 399 | 0.398 | 0.386302835741038 | 2.71920074167265 |
| 400 | 0.399 | 0.387372926698769 | 2.71315380532445 |
| 401 | 0.4 | 0.389513108614232 | 2.71193681165869 |
| 402 | 0.401 | 0.393258426966292 | 2.71649632458445 |
| 403 | 0.402 | 0.395933654360621 | 2.70311209462513 |
| 404 | 0.403 | 0.397538790797218 | 2.69056090171899 |
| 405 | 0.404 | 0.399678972712681 | 2.68181539705684 |
| 406 | 0.405 | 0.401284109149278 | 2.67980043260942 |
| 407 | 0.406 | 0.401819154628143 | 2.67321882246462 |
| 408 | 0.407 | 0.404494382022472 | 2.67331249471995 |
| 409 | 0.408 | 0.405564472980203 | 2.66784787090439 |
| 410 | 0.409 | 0.4071696094168 | 2.66593733093011 |
| 411 | 0.41 | 0.407704654895666 | 2.66695733323379 |
| 412 | 0.411 | 0.409309791332263 | 2.67000598575925 |
| 413 | 0.412 | 0.410379882289995 | 2.67202901135485 |
| 414 | 0.413 | 0.413590155163189 | 2.67313048815032 |
| 415 | 0.414 | 0.415730337078652 | 2.66978605510235 |
| 416 | 0.415 | 0.417335473515249 | 2.66791186341748 |
| 417 | 0.416 | 0.419475655430712 | 2.66704593941118 |
| 418 | 0.417 | 0.424826110219369 | 2.67207263601306 |
| 419 | 0.418 | 0.426431246655966 | 2.66311236810369 |
| 420 | 0.419 | 0.429106474050294 | 2.6656154819096 |
| 421 | 0.42 | 0.430176565008026 | 2.66051152606547 |
| 422 | 0.421 | 0.430711610486891 | 2.65914314744848 |
| 423 | 0.422 | 0.433921883360086 | 2.65796052594784 |
| 424 | 0.423 | 0.437667201712146 | 2.66234927546696 |
| 425 | 0.424 | 0.438737292669877 | 2.66424925911449 |
| 426 | 0.425 | 0.440342429106474 | 2.66021302532365 |
| 427 | 0.426 | 0.443017656500803 | 2.64681407010505 |
| 428 | 0.427 | 0.444087747458534 | 2.64422103313159 |
| 429 | 0.428 | 0.445692883895131 | 2.64036424561968 |
| 430 | 0.429 | 0.447833065810594 | 2.64191452917793 |
| 431 | 0.43 | 0.449973247726057 | 2.64124530718667 |
| 432 | 0.431 | 0.45211342964152 | 2.64277775331601 |
| 433 | 0.432 | 0.453718566078117 | 2.64337113227947 |
| 434 | 0.433 | 0.454788657035848 | 2.64522236251124 |
| 435 | 0.434 | 0.455323702514714 | 2.63960121688662 |
| 436 | 0.435 | 0.456928838951311 | 2.64020016064554 |
| 437 | 0.436 | 0.457998929909042 | 2.64204140698965 |
| 438 | 0.437 | 0.458533975387908 | 2.64079518012102 |
| 439 | 0.438 | 0.460674157303371 | 2.64014724870196 |
| 440 | 0.439 | 0.462279293739968 | 2.63431766092338 |
| 441 | 0.44 | 0.464419475655431 | 2.6358335373761 |
| 442 | 0.441 | 0.466024612092028 | 2.63431275902825 |
| 443 | 0.442 | 0.466559657570894 | 2.62677943317736 |
| 444 | 0.443 | 0.471375066880685 | 2.62863558311259 |
| 445 | 0.444 | 0.474585339753879 | 2.63400482174371 |
| 446 | 0.445 | 0.476190476190476 | 2.63045673886208 |
| 447 | 0.446 | 0.477260567148208 | 2.62605344928497 |
| 448 | 0.447 | 0.47940074906367 | 2.62141995911021 |
| 449 | 0.448 | 0.481540930979133 | 2.62292473016674 |
| 450 | 0.449 | 0.482611021936865 | 2.62063375000775 |
| 451 | 0.45 | 0.482611021936865 | 2.61659268023133 |
| 452 | 0.451 | 0.483681112894596 | 2.6143317339545 |
| 453 | 0.452 | 0.483681112894596 | 2.60631845660904 |
| 454 | 0.453 | 0.485821294810059 | 2.60388364718318 |
| 455 | 0.454 | 0.487961476725522 | 2.60344848583753 |
| 456 | 0.455 | 0.49063670411985 | 2.59410323561713 |
| 457 | 0.456 | 0.492776886035313 | 2.59760649370339 |
| 458 | 0.457 | 0.493311931514179 | 2.5965340586884 |
| 459 | 0.458 | 0.493846976993044 | 2.59352646916735 |
| 460 | 0.459 | 0.497057249866239 | 2.59295740434673 |
| 461 | 0.46 | 0.499732477260567 | 2.59727921662698 |
| 462 | 0.461 | 0.500802568218299 | 2.59134927131058 |
| 463 | 0.462 | 0.502407704654896 | 2.58633307403604 |
| 464 | 0.463 | 0.502407704654896 | 2.58444109665927 |
| 465 | 0.464 | 0.505082932049224 | 2.58496592297682 |
| 466 | 0.465 | 0.50561797752809 | 2.58394303632088 |
| 467 | 0.466 | 0.506688068485821 | 2.58377846090812 |
| 468 | 0.467 | 0.508293204922418 | 2.58633706006834 |
| 469 | 0.468 | 0.509898341359015 | 2.5870166929557 |
| 470 | 0.469 | 0.511503477795613 | 2.58397446541577 |
| 471 | 0.47 | 0.513643659711075 | 2.57995872506306 |
| 472 | 0.471 | 0.514713750668807 | 2.57796801617026 |
| 473 | 0.472 | 0.51685393258427 | 2.5721987642835 |
| 474 | 0.473 | 0.517388978063135 | 2.5675930089908 |
| 475 | 0.474 | 0.517388978063135 | 2.56397413230442 |
| 476 | 0.475 | 0.518994114499732 | 2.56469895513852 |
| 477 | 0.476 | 0.521669341894061 | 2.55458134554251 |
| 478 | 0.477 | 0.522739432851792 | 2.54917038267254 |
| 479 | 0.478 | 0.523274478330658 | 2.54120589200358 |
| 480 | 0.479 | 0.524344569288389 | 2.53764006279143 |
| 481 | 0.48 | 0.527554842161584 | 2.53919620128697 |
| 482 | 0.481 | 0.528624933119315 | 2.53566884699524 |
| 483 | 0.482 | 0.529695024077046 | 2.5321654719985 |
| 484 | 0.483 | 0.531300160513644 | 2.5295211433527 |
| 485 | 0.484 | 0.532905296950241 | 2.52179680225713 |
| 486 | 0.485 | 0.535045478865704 | 2.51668214540711 |
| 487 | 0.486 | 0.536650615302301 | 2.51749641548084 |
| 488 | 0.487 | 0.538790797217763 | 2.51578810493713 |
| 489 | 0.488 | 0.539860888175495 | 2.51577320453948 |
| 490 | 0.489 | 0.539860888175495 | 2.50912211873766 |
| 491 | 0.49 | 0.540930979133226 | 2.50746647677314 |
| 492 | 0.491 | 0.540930979133226 | 2.50416500675763 |
| 493 | 0.492 | 0.540930979133226 | 2.50087221910904 |
| 494 | 0.493 | 0.542001070090958 | 2.4992469015604 |
| 495 | 0.494 | 0.543071161048689 | 2.49436734454238 |
| 496 | 0.495 | 0.543071161048689 | 2.49436734454238 |
| 497 | 0.496 | 0.54414125200642 | 2.49276956619489 |
| 498 | 0.497 | 0.546281433921883 | 2.49283000865586 |
| 499 | 0.498 | 0.548956661316212 | 2.49210022103009 |
| 500 | 0.499 | 0.550026752273943 | 2.48892414542495 |
| 501 | 0.5 | 0.553237025147137 | 2.48585479925538 |
| 502 | 0.501 | 0.555912252541466 | 2.48517162102453 |
| 503 | 0.502 | 0.558052434456929 | 2.48368653107666 |
| 504 | 0.503 | 0.55912252541466 | 2.48373316406563 |
| 505 | 0.504 | 0.560192616372392 | 2.47753111844696 |
| 506 | 0.505 | 0.56286784376672 | 2.47845126948502 |
| 507 | 0.506 | 0.56286784376672 | 2.47690029872815 |
| 508 | 0.507 | 0.56286784376672 | 2.47225901147256 |
| 509 | 0.508 | 0.563937934724452 | 2.47078601681143 |
| 510 | 0.509 | 0.564472980203317 | 2.46851616715779 |
| 511 | 0.51 | 0.56661316211878 | 2.46866403718666 |
| 512 | 0.511 | 0.567683253076511 | 2.46264567281556 |
| 513 | 0.512 | 0.568753344034243 | 2.45818900752846 |
| 514 | 0.513 | 0.569823434991974 | 2.45526862430365 |
| 515 | 0.514 | 0.571963616907437 | 2.45396470658517 |
| 516 | 0.515 | 0.575708935259497 | 2.45356680772411 |
| 517 | 0.516 | 0.578919208132691 | 2.45682551091677 |
| 518 | 0.517 | 0.578919208132691 | 2.45386369595484 |
| 519 | 0.518 | 0.579454253611557 | 2.45169814163446 |
| 520 | 0.519 | 0.580524344569288 | 2.44739040228491 |
| 521 | 0.52 | 0.582129481005885 | 2.44828619045059 |
| 522 | 0.521 | 0.582664526484751 | 2.44614743297956 |
| 523 | 0.522 | 0.584804708400214 | 2.44636925013106 |
| 524 | 0.523 | 0.584804708400214 | 2.44056184538297 |
| 525 | 0.524 | 0.586409844836811 | 2.43569641399436 |
| 526 | 0.525 | 0.588014981273408 | 2.42944850077239 |
| 527 | 0.526 | 0.588014981273408 | 2.4265970353959 |
| 528 | 0.527 | 0.588550026752274 | 2.42595767181828 |
| 529 | 0.528 | 0.58908507223114 | 2.42106734537076 |
| 530 | 0.529 | 0.590155163188871 | 2.41839808131943 |
| 531 | 0.53 | 0.590690208667737 | 2.41496136473926 |
| 532 | 0.531 | 0.591760299625468 | 2.40674287273932 |
| 533 | 0.532 | 0.593365436062065 | 2.40770095002218 |
| 534 | 0.533 | 0.593900481540931 | 2.40709405544428 |
| 535 | 0.534 | 0.594970572498662 | 2.40588445417515 |
| 536 | 0.535 | 0.594970572498662 | 2.4031206581336 |
| 537 | 0.536 | 0.595505617977528 | 2.40252180471485 |
| 538 | 0.537 | 0.596040663456394 | 2.3991745537638 |
| 539 | 0.538 | 0.597110754414125 | 2.39799133354662 |
| 540 | 0.539 | 0.598180845371857 | 2.39408520469829 |
| 541 | 0.54 | 0.598715890850722 | 2.39078372769011 |
| 542 | 0.541 | 0.600321027287319 | 2.39040626494022 |
| 543 | 0.542 | 0.600321027287319 | 2.38905346003646 |
| 544 | 0.543 | 0.600321027287319 | 2.38770218545499 |
| 545 | 0.544 | 0.602996254681648 | 2.38619564598838 |
| 546 | 0.545 | 0.602996254681648 | 2.38083641938313 |
| 547 | 0.546 | 0.604601391118245 | 2.37517149851592 |
| 548 | 0.547 | 0.605136436597111 | 2.36933152681007 |
| 549 | 0.548 | 0.606206527554842 | 2.3656183694593 |
| 550 | 0.549 | 0.606206527554842 | 2.35907266284762 |
| 551 | 0.55 | 0.606206527554842 | 2.35256308044462 |
| 552 | 0.551 | 0.607276618512574 | 2.35023069971404 |
| 553 | 0.552 | 0.607811663991439 | 2.34455930948316 |
| 554 | 0.553 | 0.608881754949171 | 2.34482831369253 |
| 555 | 0.554 | 0.609416800428036 | 2.33792631784504 |
| 556 | 0.555 | 0.609416800428036 | 2.33029849951602 |
| 557 | 0.556 | 0.613162118780096 | 2.33446454751578 |
| 558 | 0.557 | 0.614767255216693 | 2.32922593679083 |
| 559 | 0.558 | 0.615837346174425 | 2.32951491032736 |
| 560 | 0.559 | 0.61637239165329 | 2.32528468782507 |
| 561 | 0.56 | 0.618512573568753 | 2.32711632816237 |
| 562 | 0.561 | 0.620652755484216 | 2.32397772980032 |
| 563 | 0.562 | 0.622792937399679 | 2.32703503495991 |
| 564 | 0.563 | 0.62386302835741 | 2.32239534960789 |
| 565 | 0.564 | 0.625468164794007 | 2.32222393602506 |
| 566 | 0.565 | 0.627073301230605 | 2.31352542195887 |
| 567 | 0.566 | 0.628143392188336 | 2.31140990783275 |
| 568 | 0.567 | 0.629748528624933 | 2.30645398608882 |
| 569 | 0.568 | 0.630818619582664 | 2.30437222488587 |
| 570 | 0.569 | 0.632423756019262 | 2.30186534799557 |
| 571 | 0.57 | 0.634563937934724 | 2.30369313967836 |
| 572 | 0.571 | 0.634563937934724 | 2.2989457040479 |
| 573 | 0.572 | 0.635634028892456 | 2.29219409803679 |
| 574 | 0.573 | 0.636704119850187 | 2.29370049732916 |
| 575 | 0.574 | 0.638309256286784 | 2.29243651185325 |
| 576 | 0.575 | 0.638309256286784 | 2.29009729092279 |
| 577 | 0.576 | 0.640449438202247 | 2.29076319910387 |
| 578 | 0.577 | 0.64258962011771 | 2.28794440945202 |
| 579 | 0.578 | 0.643659711075441 | 2.28827860883848 |
| 580 | 0.579 | 0.643659711075441 | 2.28596721630429 |
| 581 | 0.58 | 0.644194756554307 | 2.2844062168885 |
| 582 | 0.581 | 0.64633493846977 | 2.28278618147635 |
| 583 | 0.582 | 0.648475120385233 | 2.28117911283089 |
| 584 | 0.583 | 0.649545211342964 | 2.27924247812561 |
| 585 | 0.584 | 0.652220438737293 | 2.28066341382429 |
| 586 | 0.585 | 0.653290529695024 | 2.2798704738538 |
| 587 | 0.586 | 0.654360620652755 | 2.27908067579504 |
| 588 | 0.587 | 0.655430711610487 | 2.27829400101085 |
| 589 | 0.588 | 0.655965757089353 | 2.2790272746306 |
| 590 | 0.589 | 0.655965757089353 | 2.27565426929074 |
| 591 | 0.59 | 0.658105939004815 | 2.27410366736209 |
| 592 | 0.591 | 0.660781166399144 | 2.27440683412569 |
| 593 | 0.592 | 0.662921348314607 | 2.27065899724711 |
| 594 | 0.593 | 0.663456393793472 | 2.26807261115979 |
| 595 | 0.594 | 0.664526484751204 | 2.26732180532288 |
| 596 | 0.595 | 0.665596575708935 | 2.26219193832056 |
| 597 | 0.596 | 0.666666666666667 | 2.25818882466281 |
| 598 | 0.597 | 0.668271803103264 | 2.25385482945907 |
| 599 | 0.598 | 0.668806848582129 | 2.24703762982778 |
| 600 | 0.599 | 0.670411985018727 | 2.24492241840556 |
| 601 | 0.6 | 0.670411985018727 | 2.24171996131797 |
| 602 | 0.601 | 0.670947030497592 | 2.2381876273525 |
| 603 | 0.602 | 0.672017121455324 | 2.23645262568568 |
| 604 | 0.603 | 0.672017121455324 | 2.23222692398386 |
| 605 | 0.604 | 0.672552166934189 | 2.2276904559026 |
| 606 | 0.605 | 0.672552166934189 | 2.22245622080884 |
| 607 | 0.606 | 0.673087212413055 | 2.22109304443388 |
| 608 | 0.607 | 0.674157303370786 | 2.21734057872 |
| 609 | 0.608 | 0.674692348849652 | 2.21392281713054 |
| 610 | 0.609 | 0.675227394328518 | 2.21258109828431 |
| 611 | 0.61 | 0.676832530765115 | 2.21268542833114 |
| 612 | 0.611 | 0.677367576243981 | 2.21135041603885 |
| 613 | 0.612 | 0.678972712680578 | 2.20941051160103 |
| 614 | 0.613 | 0.680042803638309 | 2.20778439297534 |
| 615 | 0.614 | 0.680042803638309 | 2.20269967534988 |
| 616 | 0.615 | 0.680042803638309 | 2.19662884482526 |
| 617 | 0.616 | 0.680577849117175 | 2.19533185091375 |
| 618 | 0.617 | 0.681112894596041 | 2.19504393895479 |
| 619 | 0.618 | 0.682718031032638 | 2.19217954074041 |
| 620 | 0.619 | 0.685393258426966 | 2.19375757544762 |
| 621 | 0.62 | 0.687533440342429 | 2.19162971554305 |
| 622 | 0.621 | 0.688068485821295 | 2.18639746601688 |
| 623 | 0.622 | 0.689138576779026 | 2.18289300536492 |
| 624 | 0.623 | 0.690208667736758 | 2.18333214193652 |
| 625 | 0.624 | 0.690743713215623 | 2.18207987031997 |
| 626 | 0.625 | 0.690743713215623 | 2.17718950754472 |
| 627 | 0.626 | 0.691813804173355 | 2.17471375545241 |
| 628 | 0.627 | 0.69234884965222 | 2.17154197625085 |
| 629 | 0.628 | 0.692883895131086 | 2.16934975537035 |
| 630 | 0.629 | 0.693953986088818 | 2.16594959173394 |
| 631 | 0.63 | 0.695559122525415 | 2.1623217283814 |
| 632 | 0.631 | 0.69609416800428 | 2.16016513212979 |
| 633 | 0.632 | 0.69609416800428 | 2.15826022460586 |
| 634 | 0.633 | 0.696629213483146 | 2.15801613621739 |
| 635 | 0.634 | 0.697164258962012 | 2.15398025879651 |
| 636 | 0.635 | 0.698234349919743 | 2.15539242696911 |
| 637 | 0.636 | 0.698769395398609 | 2.15326309747722 |
| 638 | 0.637 | 0.700374531835206 | 2.1516093088096 |
| 639 | 0.638 | 0.701444622792937 | 2.15207617254796 |
| 640 | 0.639 | 0.703049759229534 | 2.14949822039221 |
| 641 | 0.64 | 0.703049759229534 | 2.14576645264847 |
| 642 | 0.641 | 0.7035848047084 | 2.14274939225183 |
| 643 | 0.642 | 0.704119850187266 | 2.13882107408935 |
| 644 | 0.643 | 0.705189941144997 | 2.13561398196883 |
| 645 | 0.644 | 0.706795077581594 | 2.13495832712791 |
| 646 | 0.645 | 0.709470304975923 | 2.13204922418406 |
| 647 | 0.646 | 0.710540395933654 | 2.13071218089785 |
| 648 | 0.647 | 0.712145532370251 | 2.13007545028822 |
| 649 | 0.648 | 0.712145532370251 | 2.12375207108889 |
| 650 | 0.649 | 0.713750668806849 | 2.12223877507389 |
| 651 | 0.65 | 0.71482075976458 | 2.12093653276984 |
| 652 | 0.651 | 0.715355805243446 | 2.11984071743443 |
| 653 | 0.652 | 0.716425896201177 | 2.12033118774692 |
| 654 | 0.653 | 0.716960941680043 | 2.1183484629807 |
| 655 | 0.654 | 0.718031032637774 | 2.11706256667037 |
| 656 | 0.655 | 0.71856607811664 | 2.11775216316689 |
| 657 | 0.656 | 0.720171214553237 | 2.11627412483843 |
| 658 | 0.657 | 0.721241305510968 | 2.11411790760864 |
| 659 | 0.658 | 0.721776350989834 | 2.11128589856927 |
| 660 | 0.659 | 0.724986623863028 | 2.10927014439587 |
| 661 | 0.66 | 0.72605671482076 | 2.10802263361667 |
| 662 | 0.661 | 0.728196896736223 | 2.10467759056684 |
| 663 | 0.662 | 0.729266987693954 | 2.10344768558814 |
| 664 | 0.663 | 0.72980203317282 | 2.10154295547554 |
| 665 | 0.664 | 0.731942215088282 | 2.09996640412109 |
| 666 | 0.665 | 0.732477260567148 | 2.09893239458361 |
| 667 | 0.666 | 0.73354735152488 | 2.09943222463287 |
| 668 | 0.667 | 0.734082397003745 | 2.09840138850827 |
| 669 | 0.668 | 0.734082397003745 | 2.09329578902285 |
| 670 | 0.669 | 0.735687533440342 | 2.08940013536046 |
| 671 | 0.67 | 0.736757624398074 | 2.0873809890279 |
| 672 | 0.671 | 0.73729266987694 | 2.08553582243549 |
| 673 | 0.672 | 0.738897806313537 | 2.0867186240951 |
| 674 | 0.673 | 0.739967897271268 | 2.08471724904309 |
| 675 | 0.674 | 0.741037988228999 | 2.08355822999853 |
| 676 | 0.675 | 0.741573033707865 | 2.08090246330156 |
| 677 | 0.676 | 0.742108079186731 | 2.07577725252231 |
| 678 | 0.677 | 0.742643124665597 | 2.07315063622409 |
| 679 | 0.678 | 0.743178170144462 | 2.07217640462167 |
| 680 | 0.679 | 0.744248261102194 | 2.07105412428596 |
| 681 | 0.68 | 0.745318352059925 | 2.06830254604791 |
| 682 | 0.681 | 0.747993579454254 | 2.0700082057152 |
| 683 | 0.682 | 0.748528624933119 | 2.06904610476796 |
| 684 | 0.683 | 0.750133761369716 | 2.06860416076543 |
| 685 | 0.684 | 0.752808988764045 | 2.0694889792763 |
| 686 | 0.685 | 0.754414125200642 | 2.06743574762701 |
| 687 | 0.686 | 0.757624398073836 | 2.0689766086428 |
| 688 | 0.687 | 0.758694489031568 | 2.06868540010469 |
| 689 | 0.688 | 0.759764579989299 | 2.06839509349003 |
| 690 | 0.689 | 0.761904761904762 | 2.06861555432984 |
| 691 | 0.69 | 0.763509898341359 | 2.06818243649323 |
| 692 | 0.691 | 0.764044943820225 | 2.06485935624282 |
| 693 | 0.692 | 0.765650080256822 | 2.0612754074908 |
| 694 | 0.693 | 0.765650080256822 | 2.05969830312394 |
| 695 | 0.694 | 0.766185125735688 | 2.05956185174822 |
| 696 | 0.695 | 0.766720171214553 | 2.05863926841571 |
| 697 | 0.696 | 0.767255216693419 | 2.05536711763357 |
| 698 | 0.697 | 0.76832530765115 | 2.05198008484728 |
| 699 | 0.698 | 0.769395398608882 | 2.04938956174911 |
| 700 | 0.699 | 0.769930444087747 | 2.04307580483964 |
| 701 | 0.7 | 0.771000535045479 | 2.04206243406396 |
| 702 | 0.701 | 0.772605671482076 | 2.04016638447689 |
| 703 | 0.702 | 0.774210807918673 | 2.0405736136747 |
| 704 | 0.703 | 0.775280898876405 | 2.03728523202499 |
| 705 | 0.704 | 0.776350989834136 | 2.03325890521923 |
| 706 | 0.705 | 0.776886035313002 | 2.02861589317528 |
| 707 | 0.706 | 0.777421080791867 | 2.02475001486237 |
| 708 | 0.707 | 0.777421080791867 | 2.02250278954066 |
| 709 | 0.708 | 0.777421080791867 | 2.02100740855024 |
| 710 | 0.709 | 0.777956126270733 | 2.0179223459741 |
| 711 | 0.71 | 0.780631353665062 | 2.01741994817079 |
| 712 | 0.711 | 0.781166399143927 | 2.01362247755869 |
| 713 | 0.712 | 0.782236490101659 | 2.00901643476803 |
| 714 | 0.713 | 0.78330658105939 | 2.00590381573548 |
| 715 | 0.714 | 0.784376672017121 | 2.00353678082978 |
| 716 | 0.715 | 0.786516853932584 | 2.0024571024091 |
| 717 | 0.716 | 0.787586944890316 | 2.00083504207684 |
| 718 | 0.717 | 0.788657035848047 | 2.00066243725955 |
| 719 | 0.718 | 0.789192081326913 | 1.99697686789883 |
| 720 | 0.719 | 0.789727126805779 | 1.9968936194528 |
| 721 | 0.72 | 0.790262172284644 | 1.99537651544187 |
| 722 | 0.721 | 0.79079721776351 | 1.9888719725726 |
| 723 | 0.722 | 0.791867308721241 | 1.98375878693544 |
| 724 | 0.723 | 0.792402354200107 | 1.98156947181193 |
| 725 | 0.724 | 0.793472445157838 | 1.97931828107482 |
| 726 | 0.725 | 0.794007490636704 | 1.9785473685887 |
| 727 | 0.726 | 0.796682718031033 | 1.97890246315585 |
| 728 | 0.727 | 0.798822899946495 | 1.97862720409431 |
| 729 | 0.728 | 0.800963081861958 | 1.97835349197516 |
| 730 | 0.729 | 0.800963081861958 | 1.97557782941189 |
| 731 | 0.73 | 0.802568218298555 | 1.97261786475898 |
| 732 | 0.731 | 0.802568218298555 | 1.96780324653955 |
| 733 | 0.732 | 0.803638309256287 | 1.96221687176743 |
| 734 | 0.733 | 0.806848582129481 | 1.96052495837405 |
| 735 | 0.734 | 0.80952380952381 | 1.95822890559733 |
| 736 | 0.735 | 0.811128945960407 | 1.95605581206913 |
| 737 | 0.736 | 0.812199036918138 | 1.95394581854545 |
| 738 | 0.737 | 0.812734082397004 | 1.95122774578891 |
| 739 | 0.738 | 0.814874264312467 | 1.94772121911804 |
| 740 | 0.739 | 0.815409309791332 | 1.94371466659412 |
| 741 | 0.74 | 0.815944355270198 | 1.93907425017237 |
| 742 | 0.741 | 0.817549491706795 | 1.93765016032429 |
| 743 | 0.742 | 0.818084537185661 | 1.93695975269009 |
| 744 | 0.743 | 0.818084537185661 | 1.93110791053695 |
| 745 | 0.744 | 0.818619582664527 | 1.9291330111585 |
| 746 | 0.745 | 0.819689673622258 | 1.92777852338185 |
| 747 | 0.746 | 0.820759764579989 | 1.92514431772064 |
| 748 | 0.747 | 0.821829855537721 | 1.92380410923477 |
| 749 | 0.748 | 0.822899946495452 | 1.92246924377276 |
| 750 | 0.749 | 0.822899946495452 | 1.92119270377026 |
| 751 | 0.75 | 0.822899946495452 | 1.91673813307586 |
| 752 | 0.751 | 0.823970037453184 | 1.91542390194076 |
| 753 | 0.752 | 0.824505082932049 | 1.90846601157938 |
| 754 | 0.753 | 0.825575173889781 | 1.90654995822428 |
| 755 | 0.754 | 0.827180310326378 | 1.90650014494103 |
| 756 | 0.755 | 0.828250401284109 | 1.90148769893237 |
| 757 | 0.756 | 0.828785446762975 | 1.89961514394956 |
| 758 | 0.757 | 0.830390583199572 | 1.89772719566441 |
| 759 | 0.758 | 0.830925628678438 | 1.89525430453025 |
| 760 | 0.759 | 0.831460674157303 | 1.89279101996574 |
| 761 | 0.76 | 0.832530765115035 | 1.89216429873592 |
| 762 | 0.761 | 0.833600856072766 | 1.88910126326255 |
| 763 | 0.762 | 0.834135901551632 | 1.88605905456948 |
| 764 | 0.763 | 0.834670947030498 | 1.88182305210595 |
| 765 | 0.764 | 0.83681112894596 | 1.88001784624537 |
| 766 | 0.765 | 0.83681112894596 | 1.87941739340402 |
| 767 | 0.766 | 0.83681112894596 | 1.87582271557156 |
| 768 | 0.767 | 0.837881219903692 | 1.87165843022959 |
| 769 | 0.768 | 0.837881219903692 | 1.8686903705559 |
| 770 | 0.769 | 0.838951310861423 | 1.86870624579586 |
| 771 | 0.77 | 0.838951310861423 | 1.86339406758608 |
| 772 | 0.771 | 0.84055644729802 | 1.86166706689754 |
| 773 | 0.772 | 0.841091492776886 | 1.85933837699059 |
| 774 | 0.773 | 0.841091492776886 | 1.85293088258367 |
| 775 | 0.774 | 0.841626538255752 | 1.85063096216837 |
| 776 | 0.775 | 0.842161583734617 | 1.84891672083104 |
| 777 | 0.776 | 0.843231674692349 | 1.84780465454553 |
| 778 | 0.777 | 0.843231674692349 | 1.84435618551683 |
| 779 | 0.778 | 0.843231674692349 | 1.8426367732867 |
| 780 | 0.779 | 0.84430176565008 | 1.83982956803575 |
| 781 | 0.78 | 0.844836811128946 | 1.83417488603234 |
| 782 | 0.781 | 0.844836811128946 | 1.83021948732555 |
| 783 | 0.782 | 0.845906902086677 | 1.82971926652523 |
| 784 | 0.783 | 0.845906902086677 | 1.82578800966038 |
| 785 | 0.784 | 0.846976993044409 | 1.82361978416665 |
| 786 | 0.785 | 0.846976993044409 | 1.81916377980705 |
| 787 | 0.786 | 0.847512038523275 | 1.81532277030023 |
| 788 | 0.787 | 0.849652220438737 | 1.81493147452163 |
| 789 | 0.788 | 0.849652220438737 | 1.8127288877807 |
| 790 | 0.789 | 0.850722311396469 | 1.80952186743496 |
| 791 | 0.79 | 0.851257356875334 | 1.80519955776458 |
| 792 | 0.791 | 0.852327447833066 | 1.8036613340843 |
| 793 | 0.792 | 0.853932584269663 | 1.80109596058316 |
| 794 | 0.793 | 0.853932584269663 | 1.79839890164249 |
| 795 | 0.794 | 0.854467629748529 | 1.79308157934696 |
| 796 | 0.795 | 0.856607811663991 | 1.78903063012212 |
| 797 | 0.796 | 0.858212948100589 | 1.78337867938633 |
| 798 | 0.797 | 0.85928303905832 | 1.77667695697092 |
| 799 | 0.798 | 0.860353130016051 | 1.77471493407828 |
| 800 | 0.799 | 0.861423220973783 | 1.76965471512931 |
| 801 | 0.8 | 0.86677367576244 | 1.76415412097293 |
| 802 | 0.801 | 0.869448903156768 | 1.75840226833431 |
| 803 | 0.802 | 0.872124130551097 | 1.75774631299378 |
| 804 | 0.803 | 0.873194221508828 | 1.75839111272912 |
| 805 | 0.804 | 0.873729266987694 | 1.75244272831074 |
| 806 | 0.805 | 0.875334403424291 | 1.75066880684858 |
| 807 | 0.806 | 0.877474585339754 | 1.75046844939267 |
| 808 | 0.807 | 0.879079721776351 | 1.7501949613622 |
| 809 | 0.808 | 0.880149812734082 | 1.74639206635047 |
| 810 | 0.809 | 0.880684858212948 | 1.7400887673373 |
| 811 | 0.81 | 0.882289994649545 | 1.73642967880649 |
| 812 | 0.811 | 0.883360085607277 | 1.7341675382441 |
| 813 | 0.812 | 0.884965222043874 | 1.73199984453452 |
| 814 | 0.813 | 0.886035313001605 | 1.73024168870516 |
| 815 | 0.814 | 0.887105403959337 | 1.72753397968487 |
| 816 | 0.815 | 0.887640449438202 | 1.72475480531899 |
| 817 | 0.816 | 0.889245585874799 | 1.72548977921401 |
| 818 | 0.817 | 0.891385767790262 | 1.72583279710934 |
| 819 | 0.818 | 0.892990904226859 | 1.72561473990747 |
| 820 | 0.819 | 0.892990904226859 | 1.72182945942508 |
| 821 | 0.82 | 0.894596040663456 | 1.72114893514239 |
| 822 | 0.821 | 0.896736222578919 | 1.71915188581651 |
| 823 | 0.822 | 0.898341359015516 | 1.71754661136409 |
| 824 | 0.823 | 0.899946495452113 | 1.7150199880811 |
| 825 | 0.824 | 0.900481540930979 | 1.71325384086219 |
| 826 | 0.825 | 0.900481540930979 | 1.71047709233567 |
| 827 | 0.826 | 0.901016586409845 | 1.70734266656805 |
| 828 | 0.827 | 0.901551631888711 | 1.70559889035281 |
| 829 | 0.828 | 0.902086677367576 | 1.70248886614299 |
| 830 | 0.829 | 0.902621722846442 | 1.69802995052332 |
| 831 | 0.83 | 0.904226859283039 | 1.69605848879123 |
| 832 | 0.831 | 0.904761904761905 | 1.69209726443769 |
| 833 | 0.832 | 0.905296950240771 | 1.68950322560857 |
| 834 | 0.833 | 0.906902086677368 | 1.68936039033517 |
| 835 | 0.834 | 0.907972177635099 | 1.6882232557192 |
| 836 | 0.835 | 0.90904226859283 | 1.68442298623051 |
| 837 | 0.836 | 0.910647405029428 | 1.68340498216796 |
| 838 | 0.837 | 0.911182450508293 | 1.68085912696073 |
| 839 | 0.838 | 0.911182450508293 | 1.67909722011906 |
| 840 | 0.839 | 0.911182450508293 | 1.67733900313464 |
| 841 | 0.84 | 0.911182450508293 | 1.67339644606276 |
| 842 | 0.841 | 0.911717495987159 | 1.67045269197022 |
| 843 | 0.842 | 0.91278758694489 | 1.66850073080231 |
| 844 | 0.843 | 0.914927768860353 | 1.66850935441546 |
| 845 | 0.844 | 0.915462814339219 | 1.66732310552535 |
| 846 | 0.845 | 0.915462814339219 | 1.66473610303424 |
| 847 | 0.846 | 0.915462814339219 | 1.6621571160427 |
| 848 | 0.847 | 0.915997859818085 | 1.65970032214398 |
| 849 | 0.848 | 0.918138041733547 | 1.66101021596869 |
| 850 | 0.849 | 0.918673087212413 | 1.66112346342959 |
| 851 | 0.85 | 0.918673087212413 | 1.65856460828695 |
| 852 | 0.851 | 0.919208132691279 | 1.65570481277794 |
| 853 | 0.852 | 0.92027822364901 | 1.65466542283299 |
| 854 | 0.853 | 0.920813269127876 | 1.65140497539077 |
| 855 | 0.854 | 0.920813269127876 | 1.64804248116753 |
| 856 | 0.855 | 0.920813269127876 | 1.64469365214814 |
| 857 | 0.856 | 0.920813269127876 | 1.64135840519828 |
| 858 | 0.857 | 0.920813269127876 | 1.63762238454912 |
| 859 | 0.858 | 0.921348314606742 | 1.63320427232534 |
| 860 | 0.859 | 0.921348314606742 | 1.62705207139995 |
| 861 | 0.86 | 0.922418405564473 | 1.62567574634821 |
| 862 | 0.861 | 0.922418405564473 | 1.62080115640414 |
| 863 | 0.862 | 0.922953451043339 | 1.61769906972501 |
| 864 | 0.863 | 0.924558587479936 | 1.61527850612644 |
| 865 | 0.864 | 0.925093632958802 | 1.61260744347206 |
| 866 | 0.865 | 0.925628678437667 | 1.60875453948929 |
| 867 | 0.866 | 0.925628678437667 | 1.60637237580792 |
| 868 | 0.867 | 0.926163723916533 | 1.60216071502609 |
| 869 | 0.868 | 0.926163723916533 | 1.59979938751684 |
| 870 | 0.869 | 0.926698769395399 | 1.59954485674729 |
| 871 | 0.87 | 0.926698769395399 | 1.59601904148627 |
| 872 | 0.871 | 0.927233814874264 | 1.59303889230291 |
| 873 | 0.872 | 0.927233814874264 | 1.59070704713243 |
| 874 | 0.873 | 0.927233814874264 | 1.5860637767443 |
| 875 | 0.874 | 0.927233814874264 | 1.58259907431938 |
| 876 | 0.875 | 0.928303905831996 | 1.5802065034642 |
| 877 | 0.876 | 0.928838951310861 | 1.57653765523002 |
| 878 | 0.877 | 0.928838951310861 | 1.57463729643635 |
| 879 | 0.878 | 0.930979133226324 | 1.57295657492732 |
| 880 | 0.879 | 0.933119315141787 | 1.57053495071255 |
| 881 | 0.88 | 0.933119315141787 | 1.56603699858641 |
| 882 | 0.881 | 0.933119315141787 | 1.56193644943515 |
| 883 | 0.882 | 0.933119315141787 | 1.56045065970917 |
| 884 | 0.883 | 0.934189406099519 | 1.55816411377889 |
| 885 | 0.884 | 0.93525949705725 | 1.55736319756253 |
| 886 | 0.885 | 0.93525949705725 | 1.55368409716669 |
| 887 | 0.886 | 0.93525949705725 | 1.54965711199495 |
| 888 | 0.887 | 0.936329588014981 | 1.54778318357342 |
| 889 | 0.888 | 0.936864633493847 | 1.54539810056972 |
| 890 | 0.889 | 0.937399678972713 | 1.54157964044343 |
| 891 | 0.89 | 0.937934724451578 | 1.53850174535654 |
| 892 | 0.891 | 0.937934724451578 | 1.53635149833298 |
| 893 | 0.892 | 0.93900481540931 | 1.53381692496127 |
| 894 | 0.893 | 0.940074906367041 | 1.53058734465687 |
| 895 | 0.894 | 0.941144997324773 | 1.52596993801886 |
| 896 | 0.895 | 0.94275013376137 | 1.52295404103146 |
| 897 | 0.896 | 0.943285179240235 | 1.52032578052197 |
| 898 | 0.897 | 0.943820224719101 | 1.51701573033708 |
| 899 | 0.898 | 0.944890315676833 | 1.51630960744854 |
| 900 | 0.899 | 0.945425361155698 | 1.51302483833566 |
| 901 | 0.9 | 0.945425361155698 | 1.50856163822257 |
| 902 | 0.901 | 0.945960406634564 | 1.50565721581128 |
| 903 | 0.902 | 0.94649545211343 | 1.50141123827242 |
| 904 | 0.903 | 0.947030497592295 | 1.49887878889692 |
| 905 | 0.904 | 0.948100588550027 | 1.49653049128705 |
| 906 | 0.905 | 0.949705724986624 | 1.49436801479211 |
| 907 | 0.906 | 0.950775815944355 | 1.49005026470263 |
| 908 | 0.907 | 0.951310861423221 | 1.4872427695705 |
| 909 | 0.908 | 0.951310861423221 | 1.48295676735271 |
| 910 | 0.909 | 0.952380952380952 | 1.48068601749787 |
| 911 | 0.91 | 0.953451043338684 | 1.4777755646369 |
| 912 | 0.911 | 0.953451043338684 | 1.47484992009627 |
| 913 | 0.912 | 0.95398608881755 | 1.47050201152236 |
| 914 | 0.913 | 0.954521134296415 | 1.46778758284986 |
| 915 | 0.914 | 0.956126270733012 | 1.46704777128399 |
| 916 | 0.915 | 0.956126270733012 | 1.46353503173586 |
| 917 | 0.916 | 0.957731407169609 | 1.46217265636489 |
| 918 | 0.917 | 0.957731407169609 | 1.45805742697915 |
| 919 | 0.918 | 0.959336543606207 | 1.45703122562394 |
| 920 | 0.919 | 0.959336543606207 | 1.45389107212044 |
| 921 | 0.92 | 0.959336543606207 | 1.45170100594767 |
| 922 | 0.921 | 0.960406634563938 | 1.44926597730764 |
| 923 | 0.922 | 0.960941680042804 | 1.44696828566617 |
| 924 | 0.923 | 0.961476725521669 | 1.4428306303603 |
| 925 | 0.924 | 0.962546816479401 | 1.43738144265941 |
| 926 | 0.925 | 0.962546816479401 | 1.43190802062262 |
| 927 | 0.926 | 0.962546816479401 | 1.42587512396949 |
| 928 | 0.927 | 0.963616907437132 | 1.42416017089069 |
| 929 | 0.928 | 0.963616907437132 | 1.41998199771541 |
| 930 | 0.929 | 0.964686998394864 | 1.41444515694593 |
| 931 | 0.93 | 0.965222043873729 | 1.40789077214687 |
| 932 | 0.931 | 0.966292134831461 | 1.40391865539976 |
| 933 | 0.932 | 0.967362225789192 | 1.3999776027474 |
| 934 | 0.933 | 0.968432316746924 | 1.39721297730085 |
| 935 | 0.934 | 0.968432316746924 | 1.393781426804 |
| 936 | 0.935 | 0.968967362225789 | 1.38858334851676 |
| 937 | 0.936 | 0.970037453183521 | 1.38672562935282 |
| 938 | 0.937 | 0.970037453183521 | 1.38138990902927 |
| 939 | 0.938 | 0.971107544141252 | 1.37872567139134 |
| 940 | 0.939 | 0.972177635098983 | 1.37718636785174 |
| 941 | 0.94 | 0.972712680577849 | 1.37379304475265 |
| 942 | 0.941 | 0.973247726056715 | 1.37042010605343 |
| 943 | 0.942 | 0.973782771535581 | 1.36788662593652 |
| 944 | 0.943 | 0.973782771535581 | 1.36298575824805 |
| 945 | 0.944 | 0.973782771535581 | 1.35811988287152 |
| 946 | 0.945 | 0.973782771535581 | 1.352753941019 |
| 947 | 0.946 | 0.974317817014446 | 1.34923255006806 |
| 948 | 0.947 | 0.975387907972178 | 1.34488779781576 |
| 949 | 0.948 | 0.975922953451043 | 1.33932283541525 |
| 950 | 0.949 | 0.975922953451043 | 1.33385621159723 |
| 951 | 0.95 | 0.976993044408775 | 1.32989064813831 |
| 952 | 0.951 | 0.97752808988764 | 1.32421065846463 |
| 953 | 0.952 | 0.979133226324238 | 1.3220554622719 |
| 954 | 0.953 | 0.979668271803103 | 1.3174655359188 |
| 955 | 0.954 | 0.979668271803103 | 1.31545298593077 |
| 956 | 0.955 | 0.979668271803103 | 1.30945205993526 |
| 957 | 0.956 | 0.980203317281969 | 1.30372417762943 |
| 958 | 0.957 | 0.980738362760835 | 1.29854117245984 |
| 959 | 0.958 | 0.982878544676298 | 1.29722258373944 |
| 960 | 0.959 | 0.982878544676298 | 1.291646781193 |
| 961 | 0.96 | 0.983948635634029 | 1.28823809454077 |
| 962 | 0.961 | 0.983948635634029 | 1.28108254134021 |
| 963 | 0.962 | 0.984483681112895 | 1.27540332453682 |
| 964 | 0.963 | 0.98501872659176 | 1.27164525158679 |
| 965 | 0.964 | 0.98501872659176 | 1.26583546882187 |
| 966 | 0.965 | 0.98501872659176 | 1.26145541529653 |
| 967 | 0.966 | 0.98501872659176 | 1.25551054656394 |
| 968 | 0.967 | 0.98501872659176 | 1.24962144784291 |
| 969 | 0.968 | 0.98501872659176 | 1.24334081590258 |
| 970 | 0.969 | 0.985553772070626 | 1.23978785781765 |
| 971 | 0.97 | 0.986088817549492 | 1.23692054316947 |
| 972 | 0.971 | 0.986623863028357 | 1.23275390988191 |
| 973 | 0.972 | 0.986623863028357 | 1.22686808219547 |
| 974 | 0.973 | 0.987693953986089 | 1.22171748186986 |
| 975 | 0.974 | 0.987693953986089 | 1.215942556798 |
| 976 | 0.975 | 0.987693953986089 | 1.21148855475845 |
| 977 | 0.976 | 0.989299090422686 | 1.207350087444 |
| 978 | 0.977 | 0.989299090422686 | 1.199026405352 |
| 979 | 0.978 | 0.989299090422686 | 1.19367728274748 |
| 980 | 0.979 | 0.989834135901552 | 1.1863837810908 |
| 981 | 0.98 | 0.989834135901552 | 1.18034825227399 |
| 982 | 0.981 | 0.990904226859283 | 1.17504865485236 |
| 983 | 0.982 | 0.990904226859283 | 1.16913398041518 |
| 984 | 0.983 | 0.991439272338149 | 1.16216052060041 |
| 985 | 0.984 | 0.991974317817014 | 1.15623461012585 |
| 986 | 0.985 | 0.991974317817014 | 1.1471079432477 |
| 987 | 0.986 | 0.99250936329588 | 1.13836663557277 |
| 988 | 0.987 | 0.993579454253612 | 1.12818516426795 |
| 989 | 0.988 | 0.995184590690209 | 1.12131678284466 |
| 990 | 0.989 | 0.99625468164794 | 1.11024768959561 |
| 991 | 0.99 | 0.99625468164794 | 1.09996277615769 |
| 992 | 0.991 | 0.99625468164794 | 1.09088491456685 |
| 993 | 0.992 | 0.997324772605671 | 1.08479316333536 |
| 994 | 0.993 | 0.997324772605671 | 1.07514760094482 |
| 995 | 0.994 | 0.997859818084537 | 1.06398032460507 |
| 996 | 0.995 | 0.998929909042269 | 1.05456765056076 |
| 997 | 0.996 | 0.998929909042269 | 1.04267108807856 |
| 998 | 0.997 | 0.999464954521134 | 1.02857274406448 |
| 999 | 0.998 | 1.0 | 1.01136200201352 |
| 1000 | 0.999 | 1.0 | 1.0 |
| 1001 | 1.0 | 1.0 | 1.0 |
By targeting less than 30% of the entire distribution, our predictions will be more than three times more accurate than the other 70%.
Conclusion¶
We've solved our problem in a Pandas-like way, all without ever loading data into memory!
VerticaPy
About the Author
Badr Ouali
Head of Data Science
Badr Ouali works as a Lead Data Scientist for Vertica worldwide. He can embrace data projects end to end through a clear understanding of the “big picture” as well as attention to details, resulting in achieving great business outcomes – a distinctive differentiator in his role. Badr enjoys sharing knowledge and insights related to data analytics with colleagues & peers and has a sweet spot for Python. He loves helping customers finding the best value from their data and empower them to solve their use-cases.
