Examen Grupal 2
Layza N. Frias Rivera y Tania M. Sánchez Pantojas
2024-05-10
I. Clasificación supervisada: La clave del éxito en cualquier organización es atraer y retener a los mejores talentos. Una de las tareas es determinar qué factores mantienen a los empleados en la empresa y cuáles lo impulsan a irse. Se necesita saber qué factores puedo cambiar para evitar la pérdida de buenas personas. Para este análisis se adjuntan los datos Employee-IBM. Esta base de datos esta compuesta por diversas variables que se midieron a los emleados y se quiere ver que tanto se puede predecir el nivel de satisfacción. Aplique por lo menos tres metodologías vistas en clase sobre clasificación supervisada donde puedan explicar a detalle los hallazgos encontrados.
## Satisfaction Age Gender HourlyRate JobInvolvement MonthlyIncome
## 1 1 41 Female 94 3 5993
## 2 4 49 Male 61 2 5130
## 3 2 37 Male 92 2 2090
## 4 3 33 Female 56 3 2909
## 5 4 27 Male 40 3 3468
## 6 3 32 Male 79 3 3068
## NumCompaniesWorked PercentSalaryHike StockOptionLevel TotalWorkingYears
## 1 8 11 0 8
## 2 1 23 1 10
## 3 6 15 0 7
## 4 1 11 0 8
## 5 9 12 1 6
## 6 0 13 0 8
## TrainingTimesLastYear WorkLifeBalance YearsAtCompany YearsInCurrentRole
## 1 0 1 6 4
## 2 3 3 10 7
## 3 3 3 0 0
## 4 3 3 8 7
## 5 3 3 2 2
## 6 2 2 7 7
## YearsSinceLastPromotion YearsWithCurrManager
## 1 0 5
## 2 1 7
## 3 0 0
## 4 3 0
## 5 2 2
## 6 3 6K-vecinos más cercanos
## Satisfaction Age Gender HourlyRate JobInvolvement MonthlyIncome
## 1 1 41 Female 94 3 5993
## 2 4 49 Male 61 2 5130
## 3 2 37 Male 92 2 2090
## 4 3 33 Female 56 3 2909
## 5 4 27 Male 40 3 3468
## 6 3 32 Male 79 3 3068
## NumCompaniesWorked PercentSalaryHike StockOptionLevel TotalWorkingYears
## 1 8 11 0 8
## 2 1 23 1 10
## 3 6 15 0 7
## 4 1 11 0 8
## 5 9 12 1 6
## 6 0 13 0 8
## TrainingTimesLastYear WorkLifeBalance YearsAtCompany YearsInCurrentRole
## 1 0 1 6 4
## 2 3 3 10 7
## 3 3 3 0 0
## 4 3 3 8 7
## 5 3 3 2 2
## 6 2 2 7 7
## YearsSinceLastPromotion YearsWithCurrManager
## 1 0 5
## 2 1 7
## 3 0 0
## 4 3 0
## 5 2 2
## 6 3 6## Satisfaction Age Gender HourlyRate JobInvolvement MonthlyIncome
## 1 1 41 Female 94 3 5993
## 2 4 49 Male 61 2 5130
## 3 2 37 Male 92 2 2090
## 4 3 33 Female 56 3 2909
## 5 4 27 Male 40 3 3468
## 6 3 32 Male 79 3 3068
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## 9 2 38 Male 44 2 9526
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## 11 3 35 Male 84 4 2426
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## Call:
## train.kknn(formula = Satisfaction ~ ., data = entrenamiento, kmax = 16)
##
## Type of response variable: continuous
## minimal mean absolute error: 0.9491035
## Minimal mean squared error: 1.265616
## Best kernel: optimal
## Best k: 16## Pres
## 1.6859355984822 1.69465303849977 1.83022107067109 1.84565775291778
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## Pres
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## Pres
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## Pres
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## Pres
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## Pres
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## Pres
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## Pres
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## Pres
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## Pres
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## Pres
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## Pres
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## Pres
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## Pres
## 2.30640040194758 2.3072278945853 2.32103210053905 2.32743552676206
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## Pres
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## Pres
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## Pres
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## Pres
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## Pres
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## Pres
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## Pres
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## Pres
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## Pres
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## 10 0 0 0 0
## 11 0 0 0 0
## 12 0 0 0 0
## 13 0 0 0 0
## 14 0 0 0 0
## 15 0 0 0 0
## 16 0 0 0 0
## 17 0 0 0 0
## Pres
## 3.03011120400301 3.03193704284058 3.03270142883149 3.03740548506131
## 0 1 0 0 0
## 1 0 0 0 0
## 2 0 1 1 1
## 3 0 0 0 0
## 4 0 0 0 0
## 5 0 0 0 0
## 6 0 0 0 0
## 7 0 0 0 0
## 8 0 0 0 0
## 9 0 0 0 0
## 10 0 0 0 0
## 11 0 0 0 0
## 12 0 0 0 0
## 13 0 0 0 0
## 14 0 0 0 0
## 15 0 0 0 0
## 16 0 0 0 0
## 17 0 0 0 0
## Pres
## 3.03966558588923 3.04180142192377 3.04306495713058 3.0435362788439
## 0 0 0 0 0
## 1 0 0 0 0
## 2 0 1 1 1
## 3 0 0 0 0
## 4 0 0 0 0
## 5 0 0 0 0
## 6 0 0 0 0
## 7 0 0 0 0
## 8 0 0 0 0
## 9 1 0 0 0
## 10 0 0 0 0
## 11 0 0 0 0
## 12 0 0 0 0
## 13 0 0 0 0
## 14 0 0 0 0
## 15 0 0 0 0
## 16 0 0 0 0
## 17 0 0 0 0
## Pres
## 3.04566654841179 3.04651390108364 3.05023920369411 3.05214000468775
## 0 0 0 0 1
## 1 0 0 0 0
## 2 0 1 0 0
## 3 0 0 1 0
## 4 0 0 0 0
## 5 0 0 0 0
## 6 0 0 0 0
## 7 1 0 0 0
## 8 0 0 0 0
## 9 0 0 0 0
## 10 0 0 0 0
## 11 0 0 0 0
## 12 0 0 0 0
## 13 0 0 0 0
## 14 0 0 0 0
## 15 0 0 0 0
## 16 0 0 0 0
## 17 0 0 0 0
## Pres
## 3.05240648011982 3.05313391465212 3.05658518936533 3.06244480146716
## 0 0 0 0 0
## 1 0 0 0 0
## 2 0 0 0 1
## 3 0 1 0 0
## 4 0 0 0 0
## 5 0 0 1 0
## 6 0 0 0 0
## 7 0 0 0 0
## 8 0 0 0 0
## 9 1 0 0 0
## 10 0 0 0 0
## 11 0 0 0 0
## 12 0 0 0 0
## 13 0 0 0 0
## 14 0 0 0 0
## 15 0 0 0 0
## 16 0 0 0 0
## 17 0 0 0 0
## Pres
## 3.06454957261851 3.06685741794217 3.06703232250698 3.06720182778914
## 0 0 0 0 0
## 1 0 0 0 0
## 2 1 1 0 0
## 3 0 0 0 0
## 4 0 0 0 1
## 5 0 0 0 0
## 6 0 0 0 0
## 7 0 0 0 0
## 8 0 0 1 0
## 9 0 0 0 0
## 10 0 0 0 0
## 11 0 0 0 0
## 12 0 0 0 0
## 13 0 0 0 0
## 14 0 0 0 0
## 15 0 0 0 0
## 16 0 0 0 0
## 17 0 0 0 0
## Pres
## 3.06995825859437 3.07406266697038 3.07643648690087 3.07730302943264
## 0 0 0 0 0
## 1 0 0 0 0
## 2 0 0 1 1
## 3 1 0 0 0
## 4 0 0 0 0
## 5 0 0 0 0
## 6 0 0 0 0
## 7 0 1 0 0
## 8 0 0 0 0
## 9 0 0 0 0
## 10 0 0 0 0
## 11 0 0 0 0
## 12 0 0 0 0
## 13 0 0 0 0
## 14 0 0 0 0
## 15 0 0 0 0
## 16 0 0 0 0
## 17 0 0 0 0
## Pres
## 3.08015207691353 3.09317485512724 3.09616447738324 3.09689778504788
## 0 0 0 0 0
## 1 0 1 0 0
## 2 0 0 0 0
## 3 1 0 0 0
## 4 0 0 0 0
## 5 0 0 0 0
## 6 0 0 0 0
## 7 0 0 0 0
## 8 0 0 0 0
## 9 0 0 0 1
## 10 0 0 1 0
## 11 0 0 0 0
## 12 0 0 0 0
## 13 0 0 0 0
## 14 0 0 0 0
## 15 0 0 0 0
## 16 0 0 0 0
## 17 0 0 0 0
## Pres
## 3.09836972599084 3.1014136914283 3.1029463348965 3.1066841849344
## 0 0 0 0 0
## 1 0 0 0 0
## 2 0 0 1 0
## 3 0 1 0 0
## 4 0 0 0 0
## 5 0 0 0 1
## 6 0 0 0 0
## 7 1 0 0 0
## 8 0 0 0 0
## 9 0 0 0 0
## 10 0 0 0 0
## 11 0 0 0 0
## 12 0 0 0 0
## 13 0 0 0 0
## 14 0 0 0 0
## 15 0 0 0 0
## 16 0 0 0 0
## 17 0 0 0 0
## Pres
## 3.10820717074375 3.11107086441622 3.11850071226895 3.11879890509715
## 0 1 0 0 0
## 1 0 0 1 0
## 2 0 0 0 1
## 3 0 0 0 0
## 4 0 0 0 0
## 5 0 0 0 0
## 6 0 1 0 0
## 7 0 0 0 0
## 8 0 0 0 0
## 9 0 0 0 0
## 10 0 0 0 0
## 11 0 0 0 0
## 12 0 0 0 0
## 13 0 0 0 0
## 14 0 0 0 0
## 15 0 0 0 0
## 16 0 0 0 0
## 17 0 0 0 0
## Pres
## 3.13555435219832 3.13600402091249 3.1361160052409 3.14909602313464
## 0 0 0 0 0
## 1 0 0 0 0
## 2 0 1 1 0
## 3 0 0 0 0
## 4 0 0 0 0
## 5 0 0 0 0
## 6 0 0 0 0
## 7 0 0 0 0
## 8 0 0 0 0
## 9 1 0 0 1
## 10 0 0 0 0
## 11 0 0 0 0
## 12 0 0 0 0
## 13 0 0 0 0
## 14 0 0 0 0
## 15 0 0 0 0
## 16 0 0 0 0
## 17 0 0 0 0
## Pres
## 3.1552975827015 3.1580256174748 3.15805794915456 3.16523304093676
## 0 0 0 0 0
## 1 0 0 0 0
## 2 0 1 0 0
## 3 0 0 0 0
## 4 0 0 0 0
## 5 0 0 0 0
## 6 0 0 0 0
## 7 0 0 1 1
## 8 1 0 0 0
## 9 0 0 0 0
## 10 0 0 0 0
## 11 0 0 0 0
## 12 0 0 0 0
## 13 0 0 0 0
## 14 0 0 0 0
## 15 0 0 0 0
## 16 0 0 0 0
## 17 0 0 0 0
## Pres
## 3.17063203320703 3.17425475207417 3.18703099369217 3.19947148591077
## 0 0 0 0 0
## 1 0 0 0 0
## 2 1 0 0 0
## 3 0 0 0 0
## 4 0 0 0 0
## 5 0 0 0 0
## 6 0 0 0 0
## 7 0 0 1 0
## 8 0 0 0 0
## 9 0 0 0 1
## 10 0 0 0 0
## 11 0 1 0 0
## 12 0 0 0 0
## 13 0 0 0 0
## 14 0 0 0 0
## 15 0 0 0 0
## 16 0 0 0 0
## 17 0 0 0 0
## Pres
## 3.20227293637446 3.20304139756384 3.20404400114396 3.20555562688051
## 0 1 0 0 1
## 1 0 0 0 0
## 2 0 0 0 0
## 3 0 0 0 0
## 4 0 0 0 0
## 5 0 0 0 0
## 6 0 0 0 0
## 7 0 0 1 0
## 8 0 1 0 0
## 9 0 0 0 0
## 10 0 0 0 0
## 11 0 0 0 0
## 12 0 0 0 0
## 13 0 0 0 0
## 14 0 0 0 0
## 15 0 0 0 0
## 16 0 0 0 0
## 17 0 0 0 0
## Pres
## 3.20583862707475 3.20588696504502 3.20632133182788 3.21025392976252
## 0 0 0 0 0
## 1 0 0 0 0
## 2 0 0 0 0
## 3 1 1 0 0
## 4 0 0 1 0
## 5 0 0 0 0
## 6 0 0 0 0
## 7 0 0 0 0
## 8 0 0 0 0
## 9 0 0 0 0
## 10 0 0 0 0
## 11 0 0 0 1
## 12 0 0 0 0
## 13 0 0 0 0
## 14 0 0 0 0
## 15 0 0 0 0
## 16 0 0 0 0
## 17 0 0 0 0
## Pres
## 3.21142072487911 3.2135517785381 3.21650909772368 3.21786258035903
## 0 1 0 0 0
## 1 0 0 0 0
## 2 0 1 0 0
## 3 0 0 0 0
## 4 0 0 1 0
## 5 0 0 0 0
## 6 0 0 0 1
## 7 0 0 0 0
## 8 0 0 0 0
## 9 0 0 0 0
## 10 0 0 0 0
## 11 0 0 0 0
## 12 0 0 0 0
## 13 0 0 0 0
## 14 0 0 0 0
## 15 0 0 0 0
## 16 0 0 0 0
## 17 0 0 0 0
## Pres
## 3.21950570550819 3.21970053733847 3.22127330720808 3.22228408959361
## 0 0 0 1 0
## 1 0 0 0 0
## 2 1 1 0 1
## 3 0 0 0 0
## 4 0 0 0 0
## 5 0 0 0 0
## 6 0 0 0 0
## 7 0 0 0 0
## 8 0 0 0 0
## 9 0 0 0 0
## 10 0 0 0 0
## 11 0 0 0 0
## 12 0 0 0 0
## 13 0 0 0 0
## 14 0 0 0 0
## 15 0 0 0 0
## 16 0 0 0 0
## 17 0 0 0 0
## Pres
## 3.22862393671975 3.23510245454318 3.24783654036428 3.25161802015536
## 0 1 0 0 0
## 1 0 0 0 0
## 2 0 1 0 0
## 3 0 0 1 0
## 4 0 0 0 1
## 5 0 0 0 0
## 6 0 0 0 0
## 7 0 0 0 0
## 8 0 0 0 0
## 9 0 0 0 0
## 10 0 0 0 0
## 11 0 0 0 0
## 12 0 0 0 0
## 13 0 0 0 0
## 14 0 0 0 0
## 15 0 0 0 0
## 16 0 0 0 0
## 17 0 0 0 0
## Pres
## 3.25404821518767 3.26097529945151 3.26698828709231 3.26782370648452
## 0 0 1 0 1
## 1 0 0 0 0
## 2 1 0 1 0
## 3 0 0 0 0
## 4 0 0 0 0
## 5 0 0 0 0
## 6 0 0 0 0
## 7 0 0 0 0
## 8 0 0 0 0
## 9 0 0 0 0
## 10 0 0 0 0
## 11 0 0 0 0
## 12 0 0 0 0
## 13 0 0 0 0
## 14 0 0 0 0
## 15 0 0 0 0
## 16 0 0 0 0
## 17 0 0 0 0
## Pres
## 3.26872790679202 3.28839476458777 3.29363849262062 3.29584161381328
## 0 0 1 0 0
## 1 0 0 0 1
## 2 1 0 0 0
## 3 0 0 0 0
## 4 0 0 0 0
## 5 0 0 1 0
## 6 0 0 0 0
## 7 0 0 0 0
## 8 0 0 0 0
## 9 0 0 0 0
## 10 0 0 0 0
## 11 0 0 0 0
## 12 0 0 0 0
## 13 0 0 0 0
## 14 0 0 0 0
## 15 0 0 0 0
## 16 0 0 0 0
## 17 0 0 0 0
## Pres
## 3.29804283617596 3.30318012579207 3.30751082674096 3.31055461964296
## 0 0 0 0 0
## 1 0 0 0 0
## 2 0 0 1 1
## 3 0 0 0 0
## 4 0 0 0 0
## 5 1 0 0 0
## 6 0 0 0 0
## 7 0 0 0 0
## 8 0 1 0 0
## 9 0 0 0 0
## 10 0 0 0 0
## 11 0 0 0 0
## 12 0 0 0 0
## 13 0 0 0 0
## 14 0 0 0 0
## 15 0 0 0 0
## 16 0 0 0 0
## 17 0 0 0 0
## Pres
## 3.31404510339611 3.31965812626224 3.35947757802274 3.36080480625119
## 0 0 0 0 0
## 1 0 0 1 0
## 2 0 0 0 0
## 3 0 0 0 0
## 4 0 0 0 0
## 5 0 0 0 0
## 6 0 0 0 0
## 7 0 0 0 0
## 8 0 0 0 0
## 9 1 0 0 0
## 10 0 0 0 1
## 11 0 0 0 0
## 12 0 0 0 0
## 13 0 0 0 0
## 14 0 0 0 0
## 15 0 1 0 0
## 16 0 0 0 0
## 17 0 0 0 0
## Pres
## 3.36579043051551 3.39053834022538 3.39054787587905 3.39461552929056
## 0 0 0 0 0
## 1 0 0 0 0
## 2 0 0 0 0
## 3 0 1 0 0
## 4 0 0 0 0
## 5 0 0 0 1
## 6 0 0 0 0
## 7 0 0 0 0
## 8 0 0 1 0
## 9 0 0 0 0
## 10 0 0 0 0
## 11 0 0 0 0
## 12 0 0 0 0
## 13 1 0 0 0
## 14 0 0 0 0
## 15 0 0 0 0
## 16 0 0 0 0
## 17 0 0 0 0
## Pres
## 3.40726883535781 3.46952968671101 3.47353007055513 3.51055009378861
## 0 0 0 0 0
## 1 0 0 0 0
## 2 1 1 1 0
## 3 0 0 0 0
## 4 0 0 0 0
## 5 0 0 0 0
## 6 0 0 0 0
## 7 0 0 0 1
## 8 0 0 0 0
## 9 0 0 0 0
## 10 0 0 0 0
## 11 0 0 0 0
## 12 0 0 0 0
## 13 0 0 0 0
## 14 0 0 0 0
## 15 0 0 0 0
## 16 0 0 0 0
## 17 0 0 0 0
## Pres
## 3.57882363955204 3.67289527936115 3.74596061448574
## 0 1 0 0
## 1 0 1 0
## 2 0 0 1
## 3 0 0 0
## 4 0 0 0
## 5 0 0 0
## 6 0 0 0
## 7 0 0 0
## 8 0 0 0
## 9 0 0 0
## 10 0 0 0
## 11 0 0 0
## 12 0 0 0
## 13 0 0 0
## 14 0 0 0
## 15 0 0 0
## 16 0 0 0
## 17 0 0 0## [1] 0## Pred
## 2.06928969797454 2.25526250336779 2.27524697662313 2.28471373859386
## 0 0 0 0 0
## 1 0 0 0 0
## 2 1 0 1 1
## 3 0 0 0 0
## 4 0 0 0 0
## 5 0 0 0 0
## 6 0 1 0 0
## 7 0 0 0 0
## 8 0 0 0 0
## 9 0 0 0 0
## 10 0 0 0 0
## 11 0 0 0 0
## 12 0 0 0 0
## Pred
## 2.28676736322755 2.33631632641548 2.36491083605442 2.37745283899743
## 0 0 0 0 0
## 1 0 1 0 0
## 2 0 0 0 0
## 3 1 0 1 0
## 4 0 0 0 0
## 5 0 0 0 1
## 6 0 0 0 0
## 7 0 0 0 0
## 8 0 0 0 0
## 9 0 0 0 0
## 10 0 0 0 0
## 11 0 0 0 0
## 12 0 0 0 0
## Pred
## 2.38155508151129 2.38508828814415 2.38636393088374 2.39524804814811
## 0 0 0 0 0
## 1 0 0 0 0
## 2 0 0 1 0
## 3 0 1 0 1
## 4 1 0 0 0
## 5 0 0 0 0
## 6 0 0 0 0
## 7 0 0 0 0
## 8 0 0 0 0
## 9 0 0 0 0
## 10 0 0 0 0
## 11 0 0 0 0
## 12 0 0 0 0
## Pred
## 2.40162415996319 2.42469379538702 2.42649650704503 2.43787555038249
## 0 0 0 0 1
## 1 0 0 0 0
## 2 0 0 1 0
## 3 0 1 0 0
## 4 0 0 0 0
## 5 0 0 0 0
## 6 0 0 0 0
## 7 1 0 0 0
## 8 0 0 0 0
## 9 0 0 0 0
## 10 0 0 0 0
## 11 0 0 0 0
## 12 0 0 0 0
## Pred
## 2.44051515009478 2.44110284916393 2.44126934988976 2.44200149038398
## 0 0 0 1 0
## 1 0 0 0 0
## 2 0 0 0 1
## 3 0 0 0 0
## 4 0 1 0 0
## 5 0 0 0 0
## 6 0 0 0 0
## 7 1 0 0 0
## 8 0 0 0 0
## 9 0 0 0 0
## 10 0 0 0 0
## 11 0 0 0 0
## 12 0 0 0 0
## Pred
## 2.4487607427613 2.45119309434193 2.45546822629669 2.4594496497446
## 0 1 0 0 0
## 1 0 0 0 0
## 2 0 0 0 1
## 3 0 0 0 0
## 4 0 0 0 0
## 5 0 0 0 0
## 6 0 0 0 0
## 7 0 0 1 0
## 8 0 0 0 0
## 9 0 1 0 0
## 10 0 0 0 0
## 11 0 0 0 0
## 12 0 0 0 0
## Pred
## 2.50124285684968 2.51492589210529 2.52781807385065 2.57558044873566
## 0 0 0 0 0
## 1 0 0 0 0
## 2 0 0 0 1
## 3 1 0 0 0
## 4 0 0 1 0
## 5 0 0 0 0
## 6 0 0 0 0
## 7 0 0 0 0
## 8 0 0 0 0
## 9 0 1 0 0
## 10 0 0 0 0
## 11 0 0 0 0
## 12 0 0 0 0
## Pred
## 2.57843590367104 2.58948498745346 2.59145443552361 2.60294943386796
## 0 0 0 1 0
## 1 0 0 0 0
## 2 0 0 0 0
## 3 0 0 0 0
## 4 0 0 0 0
## 5 0 0 0 0
## 6 0 0 0 0
## 7 0 1 0 0
## 8 1 0 0 0
## 9 0 0 0 0
## 10 0 0 0 1
## 11 0 0 0 0
## 12 0 0 0 0
## Pred
## 2.61796887720593 2.62073486211803 2.63065370517744 2.63116788704466
## 0 1 0 0 0
## 1 0 0 0 0
## 2 0 0 1 0
## 3 0 1 0 0
## 4 0 0 0 0
## 5 0 0 0 0
## 6 0 0 0 0
## 7 0 0 0 0
## 8 0 0 0 0
## 9 0 0 0 0
## 10 0 0 0 0
## 11 0 0 0 0
## 12 0 0 0 1
## Pred
## 2.64035136796794 2.64881689664933 2.66793720858657 2.6716017781004
## 0 1 1 1 0
## 1 0 0 0 0
## 2 0 0 0 1
## 3 0 0 0 0
## 4 0 0 0 0
## 5 0 0 0 0
## 6 0 0 0 0
## 7 0 0 0 0
## 8 0 0 0 0
## 9 0 0 0 0
## 10 0 0 0 0
## 11 0 0 0 0
## 12 0 0 0 0
## Pred
## 2.67455087658109 2.68654432824965 2.68707099294937 2.70003071165102
## 0 0 0 0 1
## 1 0 0 0 0
## 2 0 0 1 0
## 3 0 1 0 0
## 4 0 0 0 0
## 5 0 0 0 0
## 6 0 0 0 0
## 7 0 0 0 0
## 8 1 0 0 0
## 9 0 0 0 0
## 10 0 0 0 0
## 11 0 0 0 0
## 12 0 0 0 0
## Pred
## 2.71827741756374 2.72141618820304 2.72486090693039 2.7331830337357
## 0 0 0 0 0
## 1 0 0 0 0
## 2 0 0 0 1
## 3 0 0 0 0
## 4 0 0 1 0
## 5 0 0 0 0
## 6 0 0 0 0
## 7 0 0 0 0
## 8 1 1 0 0
## 9 0 0 0 0
## 10 0 0 0 0
## 11 0 0 0 0
## 12 0 0 0 0
## Pred
## 2.74558073400253 2.74872300677126 2.75137160777622 2.762950154055
## 0 1 0 0 0
## 1 0 0 0 0
## 2 0 0 0 0
## 3 0 1 0 0
## 4 0 0 0 0
## 5 0 0 1 0
## 6 0 0 0 0
## 7 0 0 0 0
## 8 0 0 0 0
## 9 0 0 0 0
## 10 0 0 0 0
## 11 0 0 0 1
## 12 0 0 0 0
## Pred
## 2.76536301240049 2.77377774079935 2.77903620372991 2.78201272294772
## 0 0 0 0 1
## 1 1 0 1 0
## 2 0 0 0 0
## 3 0 0 0 0
## 4 0 0 0 0
## 5 0 0 0 0
## 6 0 0 0 0
## 7 0 0 0 0
## 8 0 0 0 0
## 9 0 1 0 0
## 10 0 0 0 0
## 11 0 0 0 0
## 12 0 0 0 0
## Pred
## 2.78523593135465 2.79752861327058 2.8079495568106 2.81181178731702
## 0 0 0 1 0
## 1 0 0 0 0
## 2 0 0 0 1
## 3 0 0 0 0
## 4 0 0 0 0
## 5 0 0 0 0
## 6 0 0 0 0
## 7 0 0 0 0
## 8 0 0 0 0
## 9 1 0 0 0
## 10 0 1 0 0
## 11 0 0 0 0
## 12 0 0 0 0
## Pred
## 2.81311066731357 2.84975123363262 2.85818386910142 2.87600296101816
## 0 0 1 1 0
## 1 0 0 0 0
## 2 0 0 0 1
## 3 0 0 0 0
## 4 1 0 0 0
## 5 0 0 0 0
## 6 0 0 0 0
## 7 0 0 0 0
## 8 0 0 0 0
## 9 0 0 0 0
## 10 0 0 0 0
## 11 0 0 0 0
## 12 0 0 0 0
## Pred
## 2.90699236255219 2.91765923121115 2.95487715073694 2.95771509899489
## 0 0 0 0 0
## 1 0 1 0 0
## 2 1 0 0 1
## 3 0 0 0 0
## 4 0 0 0 0
## 5 0 0 0 0
## 6 0 0 0 0
## 7 0 0 1 0
## 8 0 0 0 0
## 9 0 0 0 0
## 10 0 0 0 0
## 11 0 0 0 0
## 12 0 0 0 0
## Pred
## 2.95828434608187 2.97419532428453 2.98026536435541 2.99583878971087
## 0 0 0 0 0
## 1 0 0 0 0
## 2 0 1 0 1
## 3 0 0 1 0
## 4 1 0 0 0
## 5 0 0 0 0
## 6 0 0 0 0
## 7 0 0 0 0
## 8 0 0 0 0
## 9 0 0 0 0
## 10 0 0 0 0
## 11 0 0 0 0
## 12 0 0 0 0
## Pred
## 3.00046917053378 3.01606910763772 3.02234732399477 3.05743127762876
## 0 0 0 0 1
## 1 0 0 0 0
## 2 0 0 0 0
## 3 0 0 0 0
## 4 0 0 0 0
## 5 0 0 0 0
## 6 0 1 0 0
## 7 1 0 0 0
## 8 0 0 0 0
## 9 0 0 0 0
## 10 0 0 1 0
## 11 0 0 0 0
## 12 0 0 0 0
## Pred
## 3.07998795798804 3.09086101537953 3.09715485350379 3.10150142885025
## 0 1 0 0 1
## 1 0 0 0 0
## 2 0 1 1 0
## 3 0 0 0 0
## 4 0 0 0 0
## 5 0 0 0 0
## 6 0 0 0 0
## 7 0 0 0 0
## 8 0 0 0 0
## 9 0 0 0 0
## 10 0 0 0 0
## 11 0 0 0 0
## 12 0 0 0 0
## Pred
## 3.10464975422351 3.17858576386102 3.24977790648416 3.25307428255527
## 0 0 0 0 0
## 1 0 0 0 0
## 2 1 0 0 0
## 3 0 0 0 0
## 4 0 0 0 0
## 5 0 0 0 0
## 6 0 0 0 0
## 7 0 1 1 1
## 8 0 0 0 0
## 9 0 0 0 0
## 10 0 0 0 0
## 11 0 0 0 0
## 12 0 0 0 0
## Pred
## 3.26681806697915 3.27712470599333 3.29131711062081 3.34264595489915
## 0 0 1 1 0
## 1 0 0 0 0
## 2 1 0 0 0
## 3 0 0 0 1
## 4 0 0 0 0
## 5 0 0 0 0
## 6 0 0 0 0
## 7 0 0 0 0
## 8 0 0 0 0
## 9 0 0 0 0
## 10 0 0 0 0
## 11 0 0 0 0
## 12 0 0 0 0
## Pred
## 3.38586919191745 3.44455154981844 3.45721968700537 3.51280093776696
## 0 0 0 0 0
## 1 0 0 0 0
## 2 0 1 1 1
## 3 0 0 0 0
## 4 0 0 0 0
## 5 0 0 0 0
## 6 0 0 0 0
## 7 0 0 0 0
## 8 1 0 0 0
## 9 0 0 0 0
## 10 0 0 0 0
## 11 0 0 0 0
## 12 0 0 0 0## [1] 0.01086957##
## F M
## 588 882##
## F M
## 0.4 0.6## 'data.frame': 1470 obs. of 16 variables:
## $ Satisfaction : int 1 4 2 3 4 3 1 2 2 2 ...
## $ Age : int 41 49 37 33 27 32 59 30 38 36 ...
## $ Gender : chr "F" "M" "M" "F" ...
## $ HourlyRate : int 94 61 92 56 40 79 81 67 44 94 ...
## $ JobInvolvement : int 3 2 2 3 3 3 4 3 2 3 ...
## $ MonthlyIncome : int 5993 5130 2090 2909 3468 3068 2670 2693 9526 5237 ...
## $ NumCompaniesWorked : int 8 1 6 1 9 0 4 1 0 6 ...
## $ PercentSalaryHike : int 11 23 15 11 12 13 20 22 21 13 ...
## $ StockOptionLevel : int 0 1 0 0 1 0 3 1 0 2 ...
## $ TotalWorkingYears : int 8 10 7 8 6 8 12 1 10 17 ...
## $ TrainingTimesLastYear : int 0 3 3 3 3 2 3 2 2 3 ...
## $ WorkLifeBalance : int 1 3 3 3 3 2 2 3 3 2 ...
## $ YearsAtCompany : int 6 10 0 8 2 7 1 1 9 7 ...
## $ YearsInCurrentRole : int 4 7 0 7 2 7 0 0 7 7 ...
## $ YearsSinceLastPromotion: int 0 1 0 3 2 3 0 0 1 7 ...
## $ YearsWithCurrManager : int 5 7 0 0 2 6 0 0 8 7 ...##
## Call:
## train.kknn(formula = entrenamiento_labels ~ ., data = entrenamiento, kmax = 10)
##
## Type of response variable: nominal
## Minimal misclassification: 0.376588
## Best kernel: optimal
## Best k: 10## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 0.333333333333333 0.666666666666667 1
## 0 65 4 0 0
## 0.333333333333333 14 59 2 0
## 0.666666666666667 0 9 113 5
## 1 0 0 9 88
##
## Overall Statistics
##
## Accuracy : 0.8832
## 95% CI : (0.8458, 0.9141)
## No Information Rate : 0.337
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 0.8414
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: 0 Class: 0.333333333333333 Class: 0.666666666666667
## Sensitivity 0.8228 0.8194 0.9113
## Specificity 0.9862 0.9459 0.9426
## Pos Pred Value 0.9420 0.7867 0.8898
## Neg Pred Value 0.9532 0.9556 0.9544
## Prevalence 0.2147 0.1957 0.3370
## Detection Rate 0.1766 0.1603 0.3071
## Detection Prevalence 0.1875 0.2038 0.3451
## Balanced Accuracy 0.9045 0.8827 0.9270
## Class: 1
## Sensitivity 0.9462
## Specificity 0.9673
## Pos Pred Value 0.9072
## Neg Pred Value 0.9815
## Prevalence 0.2527
## Detection Rate 0.2391
## Detection Prevalence 0.2636
## Balanced Accuracy 0.9568## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 0.333333333333333 0.666666666666667 1
## 0 53 11 0 0
## 0.333333333333333 24 36 9 0
## 0.666666666666667 2 25 93 15
## 1 0 0 22 78
##
## Overall Statistics
##
## Accuracy : 0.7065
## 95% CI : (0.6571, 0.7526)
## No Information Rate : 0.337
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 0.6
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: 0 Class: 0.333333333333333 Class: 0.666666666666667
## Sensitivity 0.6709 0.50000 0.7500
## Specificity 0.9619 0.88851 0.8279
## Pos Pred Value 0.8281 0.52174 0.6889
## Neg Pred Value 0.9145 0.87960 0.8670
## Prevalence 0.2147 0.19565 0.3370
## Detection Rate 0.1440 0.09783 0.2527
## Detection Prevalence 0.1739 0.18750 0.3668
## Balanced Accuracy 0.8164 0.69426 0.7889
## Class: 1
## Sensitivity 0.8387
## Specificity 0.9200
## Pos Pred Value 0.7800
## Neg Pred Value 0.9440
## Prevalence 0.2527
## Detection Rate 0.2120
## Detection Prevalence 0.2717
## Balanced Accuracy 0.8794Mediante un muestreo aleatorio separamos los datos en dos grupos, entrenamiento y prueba, de las cuales 15 se utilizaron para el modelo de entrenamiento y 1 para el modelo de prueba. Utilizando la paquetería kknn podemos descubrir el valor óptimo y el valor máximo de k. Al correr este código descubrimos que el valor máximo de k debe ser 16 vecinos. Este modelo el cual tomamos logra predecir 1% aproximadamente de los datos de prueba. Luego, fueron modificados los nombres de las variables de femenino y masculino para que asi fueran más claros. Podemos identificar un total de 588 féminas y 882 hombres, lo que nos lleva a una proporcion de 0.4 féminas y 0.6 hombres. Dividimos nuevamente la muestra en dos conjuntos, uno para entrenamiento y el otro para prueba. Volvemos a utilizar la paquetería kknn para verificar el valor máximo de k, el cual en este caso resultó ser 10. Hemos obtenido una exactitud del 88%. Al reescalar los valores podemos notar que la exactitud de los datos disminuyó a un 71%, lo cual demuestra que el modelo no se ha logrado mejorar.
Árboles de decisión
## n= 1176
##
## node), split, n, loss, yval, (yprob)
## * denotes terminal node
##
## 1) root 1176 460 Male (0.3911565 0.6088435)
## 2) YearsInCurrentRole>=11.5 45 16 Female (0.6444444 0.3555556) *
## 3) YearsInCurrentRole< 11.5 1131 431 Male (0.3810787 0.6189213)
## 6) HourlyRate< 31.5 24 8 Female (0.6666667 0.3333333) *
## 7) HourlyRate>=31.5 1107 415 Male (0.3748871 0.6251129)
## 14) MonthlyIncome< 19035.5 1075 410 Male (0.3813953 0.6186047)
## 28) MonthlyIncome>=18518 8 1 Female (0.8750000 0.1250000) *
## 29) MonthlyIncome< 18518 1067 403 Male (0.3776945 0.6223055)
## 58) Satisfaction< 1.5 205 95 Male (0.4634146 0.5365854)
## 116) MonthlyIncome>=4776 96 41 Female (0.5729167 0.4270833)
## 232) MonthlyIncome< 6558 40 10 Female (0.7500000 0.2500000) *
## 233) MonthlyIncome>=6558 56 25 Male (0.4464286 0.5535714)
## 466) WorkLifeBalance< 1.5 7 1 Female (0.8571429 0.1428571) *
## 467) WorkLifeBalance>=1.5 49 19 Male (0.3877551 0.6122449) *
## 117) MonthlyIncome< 4776 109 40 Male (0.3669725 0.6330275) *
## 59) Satisfaction>=1.5 862 308 Male (0.3573086 0.6426914) *
## 15) MonthlyIncome>=19035.5 32 5 Male (0.1562500 0.8437500) *
##
## pred 1 2 3 4
## Female 8 30 76 10
## Male 62 274 614 102## [1] 0.24## Pred1
## Female Male
## 1 3 10
## 2 6 65
## 3 21 157
## 4 1 31## [1] 0.2312925## [1] "integer"##
## Call:
## C5.0.formula(formula = pred ~ ., data = entrenamiento)
##
## Classification Tree
## Number of samples: 1176
## Number of predictors: 16
##
## Tree size: 10
##
## Non-standard options: attempt to group attributes
##
## pred 1 2 3 4
## Female 6 30 76 10
## Male 64 274 614 102## [1] 0.24## Pred2
## Female Male
## 1 3 10
## 2 5 66
## 3 20 158
## 4 1 31## [1] 0.2346939Nuevamente los datos fueron separados en dos conjuntos, entrenamiento y prueba. Al analizar el primer árbol de decisión vemos que los hombres dominan en la gráfica. Algunas de las variables que se utilizan para categorizar estos dos grupos son años en la posición actual, satisfacción, ingreso mensual y balance vida trabajo. La tasa de aciertos para el modelo de entrenamiento es de 24%, la de prueba es de un 23%. Podemos notar que hay un total de 16 predictores. También podemos ver un nodo específicamente del árbol, en este caso el nodo 6.
Redes Neuronales Artificiales
## pred
## 3 4
## 1 223 0
## 2 235 0
## 3 365 0
## 4 346 7## [1] 0.19## pred
## 3
## Female 126
## Male 168## [1] 0.43En este método fue utilizado las redes neuronales artificiales para poder determinar el comportamiento de las variables en los modelos. En la red, podemos notar en la segunda capa una variación del peso entre -0.60951 hasta 2.37108. Como bien se sabe los valores negativos afectan de manera negativa al modelo y los positivos de manera positiva. Con los datos de entrenamiento descubrimos una tasa de aciertos del 19% y con los datos de prueba se puede observar una tasa de aciertos del 43%
- Clasificación no supervisada: La economía brinda una ventana a la economía global y la actividad económica de los más de 200 países y territorios que producen, comercian y consumen la producción mundial. En la base de datos se encuentran algunas variables con las que se establece el tamaño de la economía de un país. Los indicadores del desarrollo mundial monitorean los cambios en el tamaño y la estructura de la economía global y sus efectos en las economías nacionales. Para este ejercicio adjuntamos la base de datos Size of the economy. Aplique las dos metodologías vistas en clase sobre clasificación no supervisada donde puedan explicar a detalle los hallazgos encontrados.
## Country Population..millions. Surface_area Population_density
## 1 Afghanistan 40.09946 652.86 59.75228
## 2 Albania 2.81167 28.75 103.57113
## 3 Algeria 44.17797 2381.74 18.24366
## 4 American Samoa 0.04504 0.20 230.94500
## 5 Andorra 0.07903 0.47 165.31915
## 6 Angola 34.50377 1246.70 26.81358
## Gross_national_income Purchasing_power_parity Gross_domestic_product
## 1 15.69540 67.3584 -22.96530
## 2 17.18400 43.8569 9.52603
## 3 161.49500 524.0170 1.79842
## 4 NA NA 0.64838
## 5 3.55199 NA 7.11048
## 6 58.87880 206.2780 -2.05072| Name | Economy |
| Number of rows | 210 |
| Number of columns | 7 |
| _______________________ | |
| Column type frequency: | |
| character | 1 |
| numeric | 6 |
| ________________________ | |
| Group variables | None |
Variable type: character
| skim_variable | n_missing | complete_rate | min | max | empty | n_unique | whitespace |
|---|---|---|---|---|---|---|---|
| Country | 0 | 1 | 4 | 30 | 0 | 210 | 0 |
Variable type: numeric
| skim_variable | n_missing | complete_rate | mean | sd | p0 | p25 | p50 | p75 | p100 | hist |
|---|---|---|---|---|---|---|---|---|---|---|
| Population..millions. | 0 | 1.00 | 149.47 | 671.44 | 0.01 | 1.82 | 9.13 | 35.69 | 7888.41 | ▇▁▁▁▁ |
| Surface_area | 1 | 1.00 | 2559.54 | 11152.31 | 0.00 | 20.48 | 130.37 | 625.22 | 134664.14 | ▇▁▁▁▁ |
| Population_density | 1 | 1.00 | 340.35 | 1599.81 | 2.12 | 39.65 | 87.42 | 218.60 | 20555.71 | ▇▁▁▁▁ |
| Gross_national_income | 1 | 1.00 | 1805.52 | 8710.00 | 0.08 | 10.80 | 39.79 | 340.81 | 94862.36 | ▇▁▁▁▁ |
| Purchasing_power_parity | 5 | 0.98 | 2830.87 | 12841.66 | 0.08 | 23.76 | 97.88 | 532.80 | 146022.36 | ▇▁▁▁▁ |
| Gross_domestic_product | 0 | 1.00 | 3.95 | 6.15 | -22.97 | 1.19 | 3.88 | 6.36 | 39.84 | ▁▅▇▁▁ |
En esta base de datos, tuvimos que limpiar los datos debido a la gran cantidad de valores faltantes. Una vez completada la limpieza, procedimos a analizar los datos utilizando métodos de clasificación no supervisada para identificar patrones y estructuras en la economía global.
Cluster jerárquico
## Population..millions. Surface_area Population_density
## [1,] -0.1628973 -0.1702608 -0.17477993
## [2,] -0.2184316 -0.2263505 -0.14732711
## [3,] -0.1568230 -0.0148837 -0.20078537
## [4,] -0.2225520 -0.2289163 -0.06752649
## [5,] -0.2225014 -0.2288921 -0.10864155
## [6,] -0.1712312 -0.1168915 -0.19541625
## Gross_national_income Purchasing_power_parity Gross_domestic_product
## [1,] -0.2049734 -0.2123841 -4.3767025
## [2,] -0.2048021 -0.2142354 0.9066078
## [3,] -0.1881956 -0.1764111 -0.3499539
## [4,] -0.2067795 -0.2176902 -0.5369582
## [5,] -0.2063708 -0.2176902 0.5138230
## [6,] -0.2000041 -0.2014408 -0.9758502Matriz de distancias
## 1 2 3 4 5
## 2 5.284
## 3 4.030 1.278
## 4 3.842 1.446 0.324
## 5 4.892 0.395 0.898 1.052
## 6 3.401 1.887 0.635 0.474 1.497
En resumen, el análisis realizado se centró en determinar el número óptimo de clústeres para agrupar los países según sus características económicas. Se utilizó una matriz de distancias para medir la similitud entre los países en función de variables como población, área, ingreso nacional, poder adquisitivo y producto interno bruto.
Se aplicaron tres métodos diferentes para determinar el número óptimo de clústeres: el método de silhouette, el método de la suma de cuadrados dentro de clústeres (wss) y el método de gap statistics.
Los resultados mostraron discrepancias en la cantidad de clústeres óptimos: el método de silhouette y el método wss sugirieron dos clústeres, mientras que el método de gap statistics sugirió un solo clúster. Además, al visualizar los datos con un dendrograma de clúster jerárquico, se observó que la mayoría de los países pertenecían a un solo grupo, lo que respaldaría la sugerencia de un solo clúster según el método de gap statistics filogenetico
Los resultados mostraron que la mayoría de los países pertenecían al mismo clúster, con solo unos pocos países asignados a clústeres diferentes. Esto sugiere una fuerte cohesión entre la mayoría de los países en términos de sus características económicas, con solo algunas excepciones que muestran diferencias significativas respecto al resto de países. circular
## grupos
## 1 2 3 4
## 204 1 1 4## Country Population..millions. Surface_area
## 1 Afghanistan 40.09946 652.86
## 2 Albania 2.81167 28.75
## 3 Algeria 44.17797 2381.74
## 4 American Samoa 0.04504 0.20
## 5 Andorra 0.07903 0.47
## 6 Angola 34.50377 1246.70
## 7 Antigua and Barbuda 0.09322 0.44
## 8 Argentina 45.80875 2780.40
## 9 Armenia 2.79097 29.74
## 10 Aruba 0.10654 0.18
## 11 Australia 25.68808 7741.22
## 12 Austria 8.95580 83.88
## 13 Azerbaijan 10.13775 86.60
## 14 Bahamas, The 0.40791 13.88
## 15 Bahrain 1.46327 0.78
## 16 Bangladesh 169.35625 147.57
## 17 Barbados 0.28120 0.43
## 18 Belarus 9.30000 207.60
## 19 Belgium 11.60000 30.53
## 20 Belize 0.40003 22.97
## 21 Benin 12.99690 114.76
## 22 Bermuda 0.10000 4.29
## 23 Bhutan 0.77749 38.39
## 24 Bolivia 12.07947 1098.58
## 25 Bosnia and Herzegovina 3.27094 51.21
## 26 Botswana 2.58842 581.73
## 27 Brazil 214.32622 8515.77
## 28 Brunei Darussalam 0.44537 5.77
## 29 Bulgaria 6.87774 111.00
## 30 Burkina Faso 22.10068 274.22
## 31 Burundi 12.55121 27.83
## 32 Cambodia 16.58902 181.04
## 33 Cameroon 27.19863 475.44
## 34 Canada 38.24611 9879.75
## 35 Cabo Verde 0.58793 4.03
## 36 Cayman Islands 0.06814 0.26
## 37 Central African Republic 5.45715 622.98
## 38 Chad 17.17974 1284.00
## 39 Chile 19.49318 756.70
## 40 China 1412.36000 9600.00
## 41 Hong Kong SAR, China 7.41310 1.11
## 42 Macao SAR, China 0.68661 0.00
## 43 Colombia 51.51656 1141.75
## 44 Comoros 0.82163 1.86
## 45 Congo, Dem. Rep. 95.89412 2344.86
## 46 Congo, Rep. 5.83581 342.00
## 47 Costa Rica 5.15396 51.10
## 48 Cote d'Ivoire 27.47825 322.46
## 49 Croatia 3.90000 88.07
## 50 Cuba 11.25637 109.88
## 51 Curacao 0.15237 0.44
## 52 Cyprus 1.24419 9.25
## 53 Czechia 10.50000 78.87
## 54 Denmark 5.85673 42.92
## 55 Djibouti 1.10556 23.20
## 56 Dominica 0.07241 0.75
## 57 Dominican Republic 11.11787 48.67
## 58 Ecuador 17.79774 256.37
## 59 Egypt, Arab Rep. 109.26218 1001.45
## 60 El Salvador 6.31417 21.04
## 61 Equatorial Guinea 1.63447 28.05
## 62 Estonia 1.33093 45.34
## 63 Eswatini 1.19227 17.36
## 64 Ethiopia 120.28303 1136.24
## 65 Fiji 0.92461 18.27
## 66 Finland 5.54102 338.45
## 67 France 67.70000 549.09
## 68 Gabon 2.34118 267.67
## 69 Gambia, The 2.63992 11.30
## 70 Georgia 3.70861 69.70
## 71 Germany 83.19608 357.58
## 72 Ghana 32.83303 238.54
## 73 Greece 10.60000 131.96
## 74 Grenada 0.12461 0.34
## 75 Guatemala 17.10975 108.89
## 76 Guinea 13.53191 245.86
## 77 Guinea-Bissau 2.06072 36.13
## 78 Guyana 0.80457 214.97
## 79 Haiti 11.44757 27.75
## 80 Honduras 10.27835 112.49
## 81 Hungary 9.70989 93.03
## 82 Iceland 0.37252 103.00
## 83 India 1407.56000 3287.26
## 84 Indonesia 273.75319 1916.90
## 85 Iran, Islamic Rep. 87.92343 1745.15
## 86 Iraq 43.53359 435.05
## 87 Ireland 5.03317 70.28
## 88 Isle of Man 0.08426 0.57
## 89 Israel 9.40000 22.07
## 90 Italy 59.10000 302.07
## 91 Jamaica 2.82770 10.99
## 92 Japan 125.68159 377.97
## 93 Jordan 11.14828 89.32
## 94 Kazakhstan 19.00100 2724.90
## 95 Kenya 53.00560 580.37
## 96 Kiribati 0.12887 0.81
## 97 Korea, Rep. 51.74488 100.37
## 98 Kosovo 1.80000 0.00
## 99 Kuwait 4.25011 17.82
## 100 Kyrgyz Republic 6.70000 199.95
## 101 Lao PDR 7.42506 236.80
## 102 Latvia 1.88449 64.59
## 103 Lebanon 5.59263 10.45
## 104 Lesotho 2.28145 30.36
## 105 Liberia 5.19342 111.37
## 106 Libya 6.73528 1759.54
## 107 Lithuania 2.80084 65.29
## 108 Luxembourg 0.64006 2.59
## 109 Madagascar 28.91565 587.30
## 110 Malawi 19.88974 118.48
## 111 Malaysia 33.57387 330.52
## 112 Maldives 0.52146 0.30
## 113 Mali 21.90498 1240.19
## 114 Malta 0.51854 0.32
## 115 Marshall Islands 0.04205 0.18
## 116 Mauritania 4.61497 1030.70
## 117 Mauritius 1.30000 2.04
## 118 Mexico 126.70514 1964.38
## 119 Micronesia, Fed. Sts. 0.11313 0.70
## 120 Moldova 2.60000 33.85
## 121 Mongolia 3.34778 1564.12
## 122 Montenegro 0.61921 13.81
## 123 Morocco 37.07658 446.55
## 124 Mozambique 32.07707 799.38
## 125 Myanmar 53.79808 676.59
## 126 Namibia 2.53015 824.29
## 127 Nauru 0.01251 0.02
## 128 Nepal 30.03499 147.18
## 129 Netherlands 17.53304 41.54
## 130 New Zealand 5.12260 267.71
## 131 Nicaragua 6.85054 130.37
## 132 Niger 25.25272 1267.00
## 133 Nigeria 213.40132 923.77
## 134 North Macedonia 2.10000 25.71
## 135 Norway 5.40832 625.22
## 136 Oman 4.52047 309.50
## 137 Pakistan 231.40212 796.10
## 138 Palau 0.01802 0.46
## 139 Panama 4.35127 75.32
## 140 Papua New Guinea 9.94944 462.84
## 141 Paraguay 6.70380 406.75
## 142 Peru 33.71547 1285.22
## 143 Philippines 113.88033 300.00
## 144 Poland 37.70000 312.69
## 145 Portugal 10.30000 92.20
## 146 Puerto Rico 3.26358 8.87
## 147 Qatar 2.68824 11.49
## 148 Romania 19.10000 238.40
## 149 Russian Federation 143.44929 17098.25
## 150 Rwanda 13.46189 26.34
## 151 Samoa 0.21876 2.84
## 152 San Marino 0.03375 0.06
## 153 Sao Tome and Principe 0.22311 0.96
## 154 Saudi Arabia 35.95040 2149.69
## 155 Senegal 16.87672 196.71
## 156 Serbia 6.80000 88.36
## 157 Seychelles 0.09926 0.46
## 158 Sierra Leone 8.42064 72.30
## 159 Singapore 5.45357 0.72
## 160 Slovak Republic 5.40000 49.03
## 161 Slovenia 2.10808 20.48
## 162 Solomon Islands 0.70785 28.90
## 163 Somalia 17.06558 637.66
## 164 South Africa 59.39226 1219.09
## 165 Spain 47.40000 505.96
## 166 Sri Lanka 22.20000 65.61
## 167 St. Kitts and Nevis 0.04761 0.26
## 168 St. Lucia 0.17965 0.62
## 169 St. Vincent and the Grenadines 0.10433 0.39
## 170 Sudan 45.65720 1878.00
## 171 Suriname 0.61299 163.82
## 172 Sweden 10.41581 528.45
## 173 Switzerland 8.70000 41.29
## 174 Syrian Arab Republic 21.32437 185.18
## 175 Tajikistan 9.75006 141.38
## 176 Tanzania 63.58833 947.30
## 177 Thailand 71.60110 513.12
## 178 Timor-Leste 1.32094 14.87
## 179 Togo 8.64483 56.79
## 180 Tonga 0.10602 0.75
## 181 Trinidad and Tobago 1.52566 5.13
## 182 Tunisia 12.26295 163.61
## 183 Turkiye 84.77540 785.35
## 184 Turkmenistan 6.34186 488.10
## 185 Turks and Caicos Islands 0.04511 0.95
## 186 Tuvalu 0.01120 0.03
## 187 Uganda 45.85378 241.55
## 188 Ukraine 43.80000 603.55
## 189 United Arab Emirates 9.36515 98.60
## 190 United Kingdom 67.30000 243.61
## 191 United States 331.89375 9831.51
## 192 Uruguay 3.42626 176.22
## 193 Uzbekistan 34.91510 448.92
## 194 Vanuatu 0.31914 12.19
## 195 Vietnam 97.46803 331.24
## 196 West Bank and Gaza 4.92275 6.02
## 197 Zambia 19.47313 752.61
## 198 Zimbabwe 15.99352 390.76
## 199 World 7888.41000 134664.14
## 200 East Asia & Pacific 2370.20000 24867.83
## 201 Europe & Central Asia 923.77721 28805.61
## 202 Latin America & Caribbean 654.98170 20425.98
## 203 Middle East & North Africa 486.16736 11385.60
## 204 North America 370.20372 19715.55
## 205 South Asia 1901.91000 5135.27
## 206 Sub-Saharan Africa 1181.16000 24328.35
## 207 Low income 709.08850 16027.49
## 208 Lower middle income 3398.19000 25638.20
## 209 Upper middle income 2503.14000 54597.60
## 210 High income 1240.63000 37488.82
## Population_density Gross_national_income Purchasing_power_parity
## 1 59.75228 15.69540 67.3584
## 2 103.57113 17.18400 43.8569
## 3 18.24366 161.49500 524.0170
## 4 230.94500 0.00000 0.0000
## 5 165.31915 3.55199 0.0000
## 6 26.81358 58.87880 206.2780
## 7 210.60000 1.47135 1.9365
## 8 16.58089 456.13900 1061.5400
## 9 98.54612 13.53330 42.2425
## 10 592.13889 3.13083 4.4139
## 11 3.33531 1468.49000 1421.2400
## 12 108.05700 472.47400 532.8050
## 13 122.12474 49.67160 157.3810
## 14 40.60649 10.80470 12.6511
## 15 1882.13000 33.90800 69.2973
## 16 1286.17000 435.53100 1157.6500
## 17 652.77442 4.75208 4.1648
## 18 46.21121 64.82420 194.8300
## 19 381.06354 585.37500 694.6280
## 20 17.31350 2.42920 3.7305
## 21 112.12418 17.60300 48.6847
## 22 1183.20000 7.82193 5.8700
## 23 20.25448 2.36486 8.7460
## 24 11.01833 39.78600 104.1060
## 25 64.81264 22.27340 56.3822
## 26 4.49315 16.63530 39.9099
## 27 25.50763 1658.60000 3343.3100
## 28 83.81879 13.50220 29.6075
## 29 63.87265 77.00460 188.3130
## 30 78.66457 18.39330 50.1903
## 31 475.86554 2.79350 9.7499
## 32 92.88953 26.26680 75.2315
## 33 56.04089 43.21550 108.0550
## 34 4.24258 1847.69000 2000.7700
## 35 144.57568 1.87378 3.8721
## 36 280.46250 4.16500 3.5338
## 37 8.57655 2.61222 5.3636
## 38 13.21847 11.06100 25.9933
## 39 25.95761 288.12500 520.8590
## 40 149.72355 16785.10000 27063.5000
## 41 7124.76000 403.72100 523.3500
## 42 20555.71000 31.89500 50.0790
## 43 45.90416 318.90000 855.4300
## 44 433.18968 1.29948 2.9284
## 45 40.95770 52.54410 106.2300
## 46 16.69743 11.48470 19.8309
## 47 100.33500 63.46960 108.6050
## 48 84.31381 66.45960 155.9020
## 49 72.33167 68.72420 135.8680
## 50 108.86992 100.93300 0.0000
## 51 348.97973 2.80840 3.6243
## 52 133.93258 25.63410 36.6026
## 53 138.57593 256.63100 461.8470
## 54 145.78510 400.03700 390.9950
## 55 47.03003 3.40696 5.8641
## 56 95.99333 0.56376 0.8679
## 57 227.68917 90.00570 216.1400
## 58 70.81895 106.04000 205.3860
## 59 107.95634 365.80000 1345.7400
## 60 303.70323 26.91100 59.4650
## 61 56.90014 8.41801 19.5956
## 62 31.09993 35.21890 55.5920
## 63 68.64273 4.35468 10.6681
## 64 103.84006 113.59300 304.9000
## 65 50.37887 4.16065 9.9095
## 66 18.19288 296.47300 311.1410
## 67 123.40470 2991.55000 3532.1800
## 68 8.89732 15.07630 29.9677
## 69 254.34733 1.95149 5.8710
## 70 65.13027 17.42190 59.1360
## 71 238.01732 4298.33000 4996.1000
## 72 141.43180 74.91060 191.1060
## 73 82.99922 212.81000 336.3850
## 74 363.71471 1.07060 1.7638
## 75 157.31927 84.53480 164.0660
## 76 53.74065 13.78950 34.6785
## 77 71.68663 1.57428 4.1519
## 78 4.04979 7.56730 18.4401
## 79 410.26128 16.42100 36.1350
## 80 90.46173 25.54220 57.8026
## 81 106.83924 172.21100 346.2400
## 82 3.63446 23.63930 20.9535
## 83 469.65957 3023.42000 10034.9000
## 84 144.79639 1143.08000 3471.1700
## 85 53.79981 310.22800 1454.1600
## 86 98.02866 207.08200 424.3800
## 87 72.36728 383.08400 395.8510
## 88 147.44912 7.09904 0.0000
## 89 425.83641 461.51500 409.9300
## 90 200.99910 2127.12000 2774.7400
## 91 260.42807 14.68240 28.9600
## 92 346.39506 5360.68000 5511.5000
## 93 123.07950 46.53500 112.3530
## 94 6.94731 168.69300 478.1560
## 95 91.34094 110.40100 272.0760
## 96 156.12716 0.35493 0.4982
## 97 531.10901 1816.73000 2452.5600
## 98 0.00000 9.16909 23.7619
## 99 244.69383 152.27600 248.3840
## 100 34.30605 7.89397 32.5155
## 101 31.71317 18.58260 60.1424
## 102 30.53911 37.29470 63.2981
## 103 553.56041 28.59380 76.6302
## 104 74.24572 2.75049 6.5529
## 105 52.81960 3.25089 7.6296
## 106 3.78164 58.60780 163.8650
## 107 44.63247 60.88420 116.9670
## 108 244.87426 56.44900 52.9691
## 109 48.51354 14.04950 45.5294
## 110 205.52674 12.31710 31.9935
## 111 101.05005 359.70800 945.1590
## 112 1714.79000 5.00651 9.7885
## 113 17.39405 17.91670 48.6589
## 114 1610.41000 15.94770 23.6835
## 115 241.18333 0.28510 0.3117
## 116 4.36461 9.02090 26.5152
## 117 623.51724 12.56370 29.5968
## 118 64.81561 1215.00000 2415.3700
## 119 160.15143 0.45075 0.4540
## 120 91.74733 14.05000 41.3580
## 121 2.11513 12.47450 36.6495
## 122 46.19375 5.78066 14.8180
## 123 82.20652 136.41000 328.7100
## 124 39.64780 15.35030 42.3304
## 125 81.85331 62.77130 232.0060
## 126 3.02336 11.77240 24.9120
## 127 615.75000 0.21172 0.2730
## 128 204.73406 36.59090 127.1280
## 129 518.01307 967.83700 1110.8100
## 130 19.33159 231.72000 237.1000
## 131 56.14006 13.36010 39.7154
## 132 19.21026 14.82510 33.5218
## 133 228.73767 444.02800 1109.6900
## 134 82.17807 12.77840 36.1933
## 135 14.76722 453.62500 455.6970
## 136 14.67980 81.16460 158.7420
## 137 294.72388 340.80900 1313.3000
## 138 39.06957 0.23044 0.2792
## 139 57.89156 60.57250 129.3300
## 140 21.52904 24.52320 38.5416
## 141 16.65919 38.51310 97.8815
## 142 26.01934 217.75200 430.8290
## 143 376.26514 404.23800 1048.9200
## 144 123.80057 636.06400 1371.7700
## 145 112.40668 246.71000 367.9000
## 146 369.95919 73.67800 80.8160
## 147 240.24238 167.49400 270.0320
## 148 83.73283 270.67700 678.7530
## 149 8.79735 1693.60000 4692.3300
## 150 532.88861 11.25810 32.4360
## 151 77.31259 0.83406 1.3058
## 152 566.78333 1.40969 1.8254
## 153 227.75104 0.50436 1.0039
## 154 16.74525 775.46300 1660.5500
## 155 85.36914 26.46340 63.4382
## 156 78.88322 57.79770 142.2400
## 157 214.04783 1.44337 2.9582
## 158 114.07551 4.21888 14.7658
## 159 7918.95000 349.10100 558.7230
## 160 113.53634 112.42400 178.9690
## 161 104.40888 59.60780 91.1815
## 162 24.69421 1.64100 1.8955
## 163 26.36053 7.40950 21.1943
## 164 48.47285 387.77600 851.9420
## 165 94.81538 1407.94000 1935.0500
## 166 354.33236 89.24370 318.3470
## 167 183.23846 0.89616 1.3531
## 168 293.83115 1.71000 2.4811
## 169 268.28718 0.90957 1.5614
## 170 23.79041 29.89400 178.3700
## 171 3.89144 2.70273 8.6346
## 172 25.42072 620.15400 635.3700
## 173 218.59906 788.51200 658.6600
## 174 113.12201 15.71410 0.0000
## 175 68.76005 11.22450 50.5153
## 176 69.65965 67.78800 174.4900
## 177 139.90421 507.85700 1297.0900
## 178 87.42401 1.50957 3.8080
## 179 155.22302 8.30393 20.2333
## 180 146.18611 0.52227 0.7554
## 181 295.93509 22.88800 38.4691
## 182 78.28092 43.39380 133.8100
## 183 109.31932 839.64500 2543.6700
## 184 13.30079 42.91670 92.7052
## 185 46.60632 0.96571 0.9272
## 186 368.96667 0.08067 0.0808
## 187 221.44729 34.82800 97.9636
## 188 76.16853 170.65500 573.5260
## 189 130.77005 387.96100 661.9950
## 190 277.27442 2994.73000 3406.4000
## 191 36.23984 23539.90000 23393.1200
## 192 19.59254 55.10920 78.6475
## 193 77.68535 68.57890 297.5290
## 194 25.56891 1.03530 1.0707
## 195 308.35910 350.20900 1079.7700
## 196 797.88522 20.77010 36.2674
## 197 25.46135 20.14910 63.2362
## 198 40.50579 24.39300 36.2483
## 199 60.17073 94862.36000 146022.3600
## 200 96.46410 30189.20000 47729.5000
## 201 33.63622 24473.17000 35980.8000
## 202 32.46348 5284.19000 10826.3000
## 203 42.78881 3300.13000 7727.5900
## 204 20.40528 25395.40000 25399.8000
## 205 394.65079 3948.67000 13037.2000
## 206 48.18998 1845.56000 4641.3900
## 207 43.87508 532.35500 1468.6600
## 208 135.14403 8391.83000 26605.4000
## 209 46.83663 25927.80000 49003.8000
## 210 35.20690 59699.60000 68513.9000
## Gross_domestic_product grupos
## 1 -22.96530 1
## 2 9.52603 1
## 3 1.79842 1
## 4 0.64838 1
## 5 7.11048 1
## 6 -2.05072 1
## 7 4.64410 1
## 8 9.35718 1
## 9 6.25422 1
## 10 17.22530 1
## 11 2.10571 1
## 12 4.10232 1
## 13 5.13516 1
## 14 13.31967 1
## 15 3.21766 1
## 16 5.71665 1
## 17 -0.36923 1
## 18 2.73401 1
## 19 5.63631 1
## 20 13.75423 1
## 21 4.23898 1
## 22 5.45645 1
## 23 3.42091 1
## 24 4.84697 1
## 25 9.10616 1
## 26 9.56202 1
## 27 4.06787 1
## 28 -2.39682 1
## 29 8.51525 1
## 30 4.11014 1
## 31 -0.88913 1
## 32 1.83296 1
## 33 0.95358 1
## 34 3.96987 1
## 35 5.99103 1
## 36 0.60617 1
## 37 -1.21028 1
## 38 -4.27698 1
## 39 10.56336 1
## 40 8.01335 1
## 41 7.31715 1
## 42 17.47373 2
## 43 9.41828 1
## 44 0.19094 1
## 45 2.83238 1
## 46 -4.43949 1
## 47 6.93559 1
## 48 4.44186 1
## 49 17.38397 1
## 50 1.65282 1
## 51 5.99596 1
## 52 5.64995 1
## 53 5.43741 1
## 54 4.40223 1
## 55 3.35238 1
## 56 6.06758 1
## 57 11.07828 1
## 58 3.01038 1
## 59 1.62732 1
## 60 9.90409 1
## 61 -3.27359 1
## 62 7.89903 1
## 63 6.83223 1
## 64 2.92169 1
## 65 -5.54140 1
## 66 2.76000 1
## 67 6.53512 1
## 68 -0.64421 1
## 69 1.66189 1
## 70 10.88570 1
## 71 2.58356 1
## 72 3.26228 1
## 73 9.01911 1
## 74 3.89235 1
## 75 6.39408 1
## 76 1.39114 1
## 77 1.53871 1
## 78 18.96098 1
## 79 -3.00580 1
## 80 10.81973 1
## 81 7.56143 1
## 82 2.70550 1
## 83 7.81825 1
## 84 2.97338 1
## 85 3.96557 1
## 86 0.47755 1
## 87 12.50988 1
## 88 0.06614 1
## 89 6.88492 1
## 90 7.33170 1
## 91 4.33148 1
## 92 2.12572 1
## 93 0.21483 1
## 94 2.95338 1
## 95 5.44871 1
## 96 -0.39888 1
## 97 4.32921 1
## 98 10.99953 1
## 99 -7.16936 1
## 100 1.87804 1
## 101 1.06938 1
## 102 4.94939 1
## 103 -5.83237 1
## 104 0.13249 1
## 105 2.84728 1
## 106 29.78597 1
## 107 5.75574 1
## 108 3.51869 1
## 109 1.90932 1
## 110 0.10288 1
## 111 1.94412 1
## 112 39.83716 1
## 113 -0.15090 1
## 114 9.61624 1
## 115 4.39231 1
## 116 -0.13787 1
## 117 3.67740 1
## 118 4.13637 1
## 119 -4.06533 1
## 120 14.81299 1
## 121 0.01415 1
## 122 12.81476 1
## 123 6.79038 1
## 124 -0.50436 1
## 125 -18.48496 1
## 126 0.99040 1
## 127 -0.09012 1
## 128 1.86468 1
## 129 4.31570 1
## 130 3.05803 1
## 131 8.81986 1
## 132 -2.30290 1
## 133 1.18283 1
## 134 4.33877 1
## 135 3.32689 1
## 136 3.61516 1
## 137 4.55185 1
## 138 -13.58337 1
## 139 13.82844 1
## 140 -1.71415 1
## 141 2.78084 1
## 142 11.96871 1
## 143 4.13511 1
## 144 7.27781 1
## 145 5.19567 1
## 146 0.75871 1
## 147 4.31737 1
## 148 5.89921 1
## 149 5.17723 1
## 150 8.28556 1
## 151 -8.71342 1
## 152 -6.17850 1
## 153 -0.16140 1
## 154 3.37507 1
## 155 3.29547 1
## 156 8.56965 1
## 157 6.99688 1
## 158 1.79688 1
## 159 12.19672 1
## 160 3.23330 1
## 161 7.92053 1
## 162 -2.55129 1
## 163 0.82644 1
## 164 3.87032 1
## 165 5.40811 1
## 166 2.22149 1
## 167 -0.80467 1
## 168 11.97123 1
## 169 1.64355 1
## 170 -4.48362 1
## 171 -3.66902 1
## 172 4.44590 1
## 173 3.44050 1
## 174 -6.99425 1
## 175 6.88340 1
## 176 1.19526 1
## 177 1.35596 1
## 178 3.62177 1
## 179 2.79798 1
## 180 -3.36800 1
## 181 -1.51412 1
## 182 3.46166 1
## 183 10.51288 1
## 184 4.68862 1
## 185 0.20347 1
## 186 1.74418 1
## 187 0.26440 1
## 188 4.31846 1
## 189 3.05240 1
## 190 7.13272 1
## 191 5.82014 1
## 192 4.45309 1
## 193 5.31863 1
## 194 -1.89628 1
## 195 1.69939 1
## 196 4.45223 1
## 197 1.66910 1
## 198 6.27161 1
## 199 4.96925 3
## 200 5.52811 4
## 201 5.78024 1
## 202 5.82490 1
## 203 3.20238 1
## 204 5.66579 1
## 205 6.86423 1
## 206 1.56710 1
## 207 -0.15827 1
## 208 4.31219 4
## 209 7.06526 4
## 210 5.25904 4Los resultados mostraron que la mayoría de los países pertenecían al mismo clúster, con solo unos pocos países asignados a clústeres diferentes. Específicamente, se observó que 204 países estaban en el primer clúster, 1 país en el segundo clúster, 1 país en el tercer clúster y 4 países en el cuarto clúster.
Estos resultados refuerzan la idea de que la mayoría de los países tienen características económicas similares, lo que los agrupa en un solo clúster. Sin embargo, la presencia de algunos países en clústeres diferentes indica que existen diferencias económicas significativas entre estos países y el resto del grupo
Metodos de Particionamiento
1. Metodo Silueta
El gráfico de número óptimo de clústeres basado en la medida de silueta sugiere que el número óptimo de clústeres es 2, ya que probablemente haya una buena separación y cohesión de los datos en dos clústeres. Esto significa que los datos pueden agruparse de manera efectiva en dos grupos distintos según sus características económicas.
2. Metodo del codo
Nuevamente se concluye que el número óptimo de clústeres es 2, ya que el punto donde se produce el codo en el gráfico WSS se encuentra en k=2. Esto indica que dividir los datos en dos clústeres explica la mayoría de la variabilidad en los datos sin necesidad de añadir más clústeres.
3. Metodo de brecha
El método de la brecha sugiere que el número óptimo de clústeres es 1, ya que la brecha es mayor cuando k=1 en comparación con otros valores de k. Esto puede indicar que los datos no presentan una estructura clara de clústeres y que un único clúster es suficiente para representar la variabilidad en los datos.
K-medias
La gráfica que estás describiendo muestra que la mayoría de los puntos están cerca del origen (0,0) en el eje de las áreas de superficie, lo que indica que estos países tienen una superficie relativamente pequeña. Además, mencionas que los puntos se distribuyen principalmente en el rango de colores rojo a violeta en el eje de las áreas de superficie, lo que sugiere una variación en las áreas de superficie de los países representados.
El hecho de que la mayoría de los puntos estén cerca del color rojo en la escala de colores podría indicar que estos países tienen áreas de superficie más pequeñas en comparación con aquellos que están más cerca del color violeta. Esto puede deberse a que los países con áreas de superficie más pequeñas tienden a agruparse en un clúster específico.
k-mediana
Al aplicar el método de k-mediana para realizar un análisis de clustering en los datos de tamaño de la economía, se observó que la mayoría de los países se agrupaban cerca del origen en el eje de las áreas de superficie, lo que indica que estos países tenían áreas de superficie relativamente pequeñas.
En el método de k-mediana, se identificó visualmente la presencia de 2 grupos distintos en la gráfica, lo que sugiere que los países pueden dividirse en dos clústeres distintos en función de sus áreas de superficie y posiblemente de otras características.
k-mediodes (pam)
En el método de k-medoides (PAM), nuevamente se observa una distribución donde la mayoría de los países se agrupan cerca del origen en el eje de las áreas de superficie, indicando áreas de superficie relativamente pequeñas.
Al igual que en los métodos anteriores, la visualización de los datos con k-medoides (PAM) parece sugerir la presencia de múltiples grupos distintos.
k-mediodes (clara)
Al igual que en los métodos anteriores, la visualización de los datos con k-medoides con CLARA sugiere la presencia de múltiples grupos distintos.
En general, al utilizar los métodos de clustering k-medias, k-mediana, k-medoides con PAM y k-medoides con CLARA en los datos de tamaño de la economía, se observa una distribución donde la mayoría de los países se agrupan cerca del origen en el eje de las áreas de superficie, indicando áreas de superficie relativamente pequeñas.
La visualización de los datos con estos métodos sugiere la presencia de múltiples grupos distintos, aunque el número exacto de grupos varía entre los métodos.
Numero optimo de particiones
## *** : The Hubert index is a graphical method of determining the number of clusters.
## In the plot of Hubert index, we seek a significant knee that corresponds to a
## significant increase of the value of the measure i.e the significant peak in Hubert
## index second differences plot.
## 
## *** : The D index is a graphical method of determining the number of clusters.
## In the plot of D index, we seek a significant knee (the significant peak in Dindex
## second differences plot) that corresponds to a significant increase of the value of
## the measure.
##
## *******************************************************************
## * Among all indices:
## * 8 proposed 2 as the best number of clusters
## * 5 proposed 3 as the best number of clusters
## * 3 proposed 4 as the best number of clusters
## * 6 proposed 5 as the best number of clusters
## * 2 proposed 10 as the best number of clusters
##
## ***** Conclusion *****
##
## * According to the majority rule, the best number of clusters is 2
##
##
## *******************************************************************##
## Clustering Methods:
## hierarchical kmeans diana fanny pam clara agnes
##
## Cluster sizes:
## 2 3 4 5
##
## Validation Measures:
## 2 3 4 5
##
## hierarchical Connectivity 2.9290 5.8579 9.1798 16.1802
## Dunn 0.9288 0.7045 0.4152 0.1976
## Silhouette 0.9016 0.8384 0.7771 0.6721
## kmeans Connectivity 2.9290 5.8579 13.1944 23.5282
## Dunn 0.9288 0.7045 0.1976 0.0978
## Silhouette 0.9016 0.8384 0.7004 0.5510
## diana Connectivity 2.9290 5.8579 14.3671 19.4115
## Dunn 0.9288 0.7045 0.1694 0.1327
## Silhouette 0.9016 0.8384 0.7399 0.3502
## fanny Connectivity 25.5139 12.5599 27.5337 42.7056
## Dunn 0.0349 0.0377 0.0033 0.0013
## Silhouette 0.4960 0.4639 0.2108 0.4004
## pam Connectivity 0.1667 6.0817 17.1087 15.9544
## Dunn 0.0533 0.0433 0.0471 0.0771
## Silhouette 0.4197 0.4822 0.5579 0.5702
## clara Connectivity 0.1667 6.0817 15.0937 15.9544
## Dunn 0.0533 0.0433 0.0545 0.0771
## Silhouette 0.4197 0.4822 0.5523 0.5702
## agnes Connectivity 2.9290 5.8579 9.1798 16.1802
## Dunn 0.9288 0.7045 0.4152 0.1976
## Silhouette 0.9016 0.8384 0.7771 0.6721
##
## Optimal Scores:
##
## Score Method Clusters
## Connectivity 0.1667 pam 2
## Dunn 0.9288 hierarchical 2
## Silhouette 0.9016 hierarchical 2
En las visualizaciones y análisis realizados para determinar el número óptimo de particiones en los datos de tamaño de la economía, se observa consistentemente que la mayoría de los países se agrupan en un solo grupo. Tanto el método de clustering jerárquico como la evaluación utilizando diferentes métodos de clustering (k-medias, k-medoides, etc.) sugieren que el número óptimo de clústeres es 2.
Esto indica que los datos pueden dividirse efectivamente en dos grupos distintos, posiblemente reflejando diferencias significativas en las características económicas entre estos dos grupos de países.