Optimus Analysis
ENACOM
21 de fevereiro de 2017
1. Missing Values
Original data.
Removing the missing values.
2. Descriptive Statistics
With missing values.
After removing the missing values.
3. Factorial Analysis of Mixed Data
##
## Call:
## FAMD(base = finalData[, -c(1, 2)], ncp = 25, graph = FALSE)
##
##
## Eigenvalues
## Dim.1 Dim.2 Dim.3 Dim.4 Dim.5 Dim.6
## Variance 5.553 2.656 2.172 1.868 1.351 1.165
## % of var. 22.211 10.624 8.689 7.471 5.404 4.658
## Cumulative % of var. 22.211 32.835 41.525 48.996 54.400 59.058
## Dim.7 Dim.8 Dim.9 Dim.10 Dim.11 Dim.12
## Variance 1.079 1.001 1.000 0.998 0.927 0.862
## % of var. 4.315 4.004 4.001 3.990 3.708 3.449
## Cumulative % of var. 63.373 67.378 71.379 75.369 79.077 82.526
## Dim.13 Dim.14 Dim.15 Dim.16 Dim.17 Dim.18
## Variance 0.795 0.696 0.625 0.433 0.416 0.396
## % of var. 3.181 2.785 2.499 1.732 1.662 1.583
## Cumulative % of var. 85.707 88.492 90.991 92.723 94.385 95.968
## Dim.19 Dim.20 Dim.21 Dim.22 Dim.23 Dim.24
## Variance 0.311 0.273 0.213 0.143 0.062 0.006
## % of var. 1.243 1.093 0.853 0.572 0.247 0.022
## Cumulative % of var. 97.211 98.304 99.158 99.730 99.976 99.999
## Dim.25
## Variance 0.000
## % of var. 0.001
## Cumulative % of var. 100.000
##
## Individuals (the 10 first)
## Dist Dim.1 ctr cos2 Dim.2 ctr cos2 Dim.3
## 1 | 3.811 | -1.463 0.000 0.147 | -0.307 0.000 0.007 | 0.369
## 2 | 3.825 | -1.454 0.000 0.144 | -0.310 0.000 0.007 | 0.371
## 3 | 3.801 | -1.499 0.000 0.155 | -0.292 0.000 0.006 | 0.435
## 4 | 3.835 | -1.600 0.000 0.174 | -0.300 0.000 0.006 | 0.480
## 5 | 3.840 | -2.025 0.001 0.278 | 0.522 0.000 0.019 | -0.094
## 6 | 3.862 | -1.916 0.001 0.246 | 0.533 0.000 0.019 | -0.143
## 7 | 3.822 | -1.963 0.001 0.264 | 0.468 0.000 0.015 | -0.200
## 8 | 3.843 | -1.960 0.001 0.260 | 0.510 0.000 0.018 | -0.148
## 9 | 3.843 | -1.986 0.001 0.267 | 0.499 0.000 0.017 | -0.136
## 10 | 3.868 | -1.923 0.001 0.247 | 0.509 0.000 0.017 | -0.165
## ctr cos2
## 1 0.000 0.009 |
## 2 0.000 0.009 |
## 3 0.000 0.013 |
## 4 0.000 0.016 |
## 5 0.000 0.001 |
## 6 0.000 0.001 |
## 7 0.000 0.003 |
## 8 0.000 0.001 |
## 9 0.000 0.001 |
## 10 0.000 0.002 |
##
## Continuous variables (the 10 first)
## Dim.1 ctr cos2 Dim.2 ctr cos2 Dim.3 ctr
## num 1 | 0.019 0.006 0.000 | -0.006 0.001 0.000 | 0.011 0.006
## num 2 | -0.111 0.220 0.012 | -0.047 0.083 0.002 | -0.248 2.825
## num 3 | 0.097 0.169 0.009 | 0.386 5.624 0.149 | 0.454 9.479
## num 4 | 0.086 0.132 0.007 | 0.241 2.195 0.058 | -0.091 0.381
## num 5 | 0.803 11.599 0.644 | 0.110 0.458 0.012 | -0.023 0.024
## num 6 | 0.916 15.114 0.839 | 0.135 0.686 0.018 | -0.098 0.443
## num 7 | -0.797 11.437 0.635 | -0.216 1.760 0.047 | 0.171 1.350
## num 8 | -0.309 1.722 0.096 | 0.582 12.765 0.339 | -0.107 0.526
## num 9 | 0.052 0.048 0.003 | 0.444 7.406 0.197 | 0.435 8.700
## num 10 | 0.134 0.321 0.018 | 0.259 2.529 0.067 | 0.392 7.062
## cos2
## num 1 0.000 |
## num 2 0.061 |
## num 3 0.206 |
## num 4 0.008 |
## num 5 0.001 |
## num 6 0.010 |
## num 7 0.029 |
## num 8 0.011 |
## num 9 0.189 |
## num 10 0.153 |
##
## Categories (the 10 first)
## Dim.1 ctr cos2 v.test Dim.2 ctr cos2
## 0 | 0.700 1.114 0.498 142.587 | -0.536 2.856 0.292
## 1 | -1.639 2.608 0.498 -142.587 | 1.256 6.688 0.292
## 0 | 1.557 0.002 0.001 3.100 | 1.546 0.008 0.001
## 1 | 0.000 0.000 0.001 -3.100 | 0.000 0.000 0.001
## 0 | -1.409 1.230 0.323 -91.123 | -0.217 0.127 0.008
## 1 | 0.333 0.290 0.323 91.123 | 0.051 0.030 0.008
## 0 | -2.073 7.333 0.963 -290.827 | -0.241 0.433 0.013
## 1 | 2.303 8.149 0.963 290.827 | 0.268 0.482 0.013
## 0 | 1.260 0.077 0.022 20.651 | -1.558 0.514 0.034
## 1 | -0.019 0.001 0.022 -20.651 | 0.024 0.008 0.034
## v.test Dim.3 ctr cos2 v.test
## 0 -157.921 | 0.227 0.762 0.052 73.765 |
## 1 157.921 | -0.530 1.784 0.052 -73.765 |
## 0 4.450 | -1.776 0.015 0.001 -5.653 |
## 1 -4.450 | 0.000 0.000 0.001 5.653 |
## 0 -20.247 | -0.625 1.579 0.064 -64.592 |
## 1 20.247 | 0.147 0.373 0.064 64.592 |
## 0 -48.905 | 0.159 0.283 0.006 35.732 |
## 1 48.905 | -0.177 0.314 0.006 -35.732 |
## 0 -36.916 | -1.453 0.668 0.030 -38.060 |
## 1 36.916 | 0.022 0.010 0.030 38.060 |Dim = coordenate for each dimension.
ctr = contribution for the construction of that dimension.
cos = quality of representation. If it is close to 1 it means that it is well projected on the dimension.
v.test = significant test. If it is smaller than -2 or bigger than 2 it means that the observation’s coordenate is significant smaller or bigger than 0.
4. Dicionário de Variáveis
## [1] "num 1 = LaboratorioPassante150meshpv"
## [2] "num 2 = MoinhoAlimentacaoTaxaMineriomv"
## [3] "num 3 = MoinhoAlimentacaoTaxaMineriopv"
## [4] "num 4 = MoinhoAlimentacaoVazaoAguapv"
## [5] "num 5 = MoinhoCaixaDescargaCaixaABombaRotacaomv"
## [6] "num 6 = MoinhoCaixaDescargaCaixaANivelpv"
## [7] "num 7 = MoinhoCaixaDescargaCaixaRNivelpv"
## [8] "num 8 = MoinhoCaixaDescargaVazaoAguamv"
## [9] "num 9 = MoinhoCaixaDescargaVazaoAguapv"
## [10] "num 10 = MoinhoHidrociclonesDensidadepv"
## [11] "num 11 = MoinhoHidrociclonesPressaopv"
## [12] "num 12 = MoinhoMotorMoinhoPotenciapv"
## [13] "num 13 = PSTPassante150meshMedianapv"
## [14] "ord 1 = LaboratorioPassante150meshhmi"
## [15] "ord 2 = MoinhoAlimentacaoTaxaMineriopermissaohmi"
## [16] "ord 3 = MoinhoBombaDePocoLigada"
## [17] "ord 4 = MoinhoCaixaDescargaCaixaABombaLigado"
## [18] "ord 5 = MoinhoCaixaDescargaCaixaANivelmodo"
## [19] "ord 6 = MoinhoCaixaDescargaCaixaRBombaLigado"
## [20] "ord 7 = MoinhoCaixaDescargaCaixaRNivelmodo"
## [21] "ord 8 = MoinhoHidrociclonesDensidadeLido"
## [22] "ord 9 = MoinhoHidrociclonesDensidadehmi"
## [23] "ord 10 = MoinhoKnelsonBP04ALigado"
## [24] "ord 11 = MoinhoKnelsonBP04RLigado"
## [25] "ord 12 = OptProcessPulsoLido"5. Regressão
##
## Call:
## lm(formula = bcPower(`num 12`, p1$roundlam) ~ . - `ord 2` - `ord 12` -
## `ord 9` - `ord 6` - `num 1` - `num 13` - `ord 3` + LagBC,
## data = finalData[, -c(1, 2)])
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.713e+19 -1.085e+18 4.346e+16 9.625e+17 8.931e+19
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.189e+20 5.968e+17 -199.24 <2e-16 ***
## `num 2` -3.569e+17 3.310e+15 -107.84 <2e-16 ***
## `num 3` 8.146e+16 4.792e+14 170.02 <2e-16 ***
## `num 4` 1.670e+17 1.183e+15 141.25 <2e-16 ***
## `num 5` -7.374e+17 2.065e+15 -357.10 <2e-16 ***
## `num 6` 6.693e+16 1.119e+15 59.81 <2e-16 ***
## `num 7` 6.275e+16 6.175e+14 101.63 <2e-16 ***
## `num 8` -3.344e+16 3.509e+14 -95.31 <2e-16 ***
## `num 9` 3.497e+16 3.467e+14 100.86 <2e-16 ***
## `num 10` 1.600e+20 3.917e+17 408.45 <2e-16 ***
## `num 11` 9.476e+18 1.229e+17 77.13 <2e-16 ***
## `ord 1` 1 -1.642e+18 2.410e+16 -68.12 <2e-16 ***
## `ord 4` 1 4.345e+18 5.974e+16 72.72 <2e-16 ***
## `ord 5` 1 -9.459e+18 7.460e+16 -126.79 <2e-16 ***
## `ord 7` 1 -1.827e+18 3.362e+16 -54.35 <2e-16 ***
## `ord 8` 1 1.980e+18 2.508e+16 78.95 <2e-16 ***
## `ord 10` 1 1.421e+18 4.637e+16 30.64 <2e-16 ***
## `ord 11` 1 5.068e+18 5.193e+16 97.60 <2e-16 ***
## LagBC 9.580e-01 9.198e-04 1041.49 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.628e+18 on 98363 degrees of freedom
## (1 observation deleted due to missingness)
## Multiple R-squared: 0.9463, Adjusted R-squared: 0.9463
## F-statistic: 9.627e+04 on 18 and 98363 DF, p-value: < 2.2e-16##
## Call:
## lm(formula = `num 12` ~ . - `ord 2` - `ord 12` - `ord 9` - `ord 6` -
## `num 1` - `num 13` - `ord 3` + Lag, data = finalData[, -c(1,
## 2)])
##
## Residuals:
## Min 1Q Median 3Q Max
## -1135.15 -2.85 0.16 3.08 1051.83
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.573e+03 3.560e+00 -441.77 <2e-16 ***
## `num 2` -3.886e+00 1.974e-02 -196.86 <2e-16 ***
## `num 3` 6.667e-01 2.858e-03 233.29 <2e-16 ***
## `num 4` 4.806e-01 7.054e-03 68.13 <2e-16 ***
## `num 5` -2.151e+00 1.232e-02 -174.60 <2e-16 ***
## `num 6` 3.298e-01 6.675e-03 49.40 <2e-16 ***
## `num 7` 3.442e-01 3.683e-03 93.47 <2e-16 ***
## `num 8` -2.322e-01 2.093e-03 -110.95 <2e-16 ***
## `num 9` 4.983e-01 2.068e-03 240.97 <2e-16 ***
## `num 10` 1.734e+03 2.336e+00 741.95 <2e-16 ***
## `num 11` 1.569e+02 7.328e-01 214.09 <2e-16 ***
## `ord 1` 1 2.504e+00 1.438e-01 17.42 <2e-16 ***
## `ord 4` 1 9.078e+00 3.564e-01 25.48 <2e-16 ***
## `ord 5` 1 -3.307e+01 4.450e-01 -74.32 <2e-16 ***
## `ord 7` 1 1.259e+01 2.005e-01 62.79 <2e-16 ***
## `ord 8` 1 2.032e+00 1.496e-01 13.58 <2e-16 ***
## `ord 10` 1 3.543e+00 2.766e-01 12.81 <2e-16 ***
## `ord 11` 1 1.984e+01 3.097e-01 64.06 <2e-16 ***
## Lag 9.769e-01 6.873e-04 1421.38 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 15.67 on 98363 degrees of freedom
## (1 observation deleted due to missingness)
## Multiple R-squared: 0.9729, Adjusted R-squared: 0.9729
## F-statistic: 1.962e+05 on 18 and 98363 DF, p-value: < 2.2e-166. Causalidade
## Granger causality test
##
## Model 1: num 12 ~ Lags(num 12, 1:1) + Lags(num 3, 1:1)
## Model 2: num 12 ~ Lags(num 12, 1:1)
## Res.Df Df F Pr(>F)
## 1 98379
## 2 98380 -1 36.274 1.72e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Granger causality test
##
## Model 1: num 12 ~ Lags(num 12, 1:1) + Lags(num 10, 1:1)
## Model 2: num 12 ~ Lags(num 12, 1:1)
## Res.Df Df F Pr(>F)
## 1 98379
## 2 98380 -1 56.815 4.83e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1