Análisis Estadístico de Datos
Carlos Santa Maria
2023-11-02
EIA data
U.S. Energy Information Administration (EIA) es una organización que se encarga de recopilar, analizar y difundir información energética de manera independiente e imparcial para promover la formulación de políticas sólidas, mercados eficientes y la comprensión pública de la energía y su interacción con la economía y el medio ambiente.
Los datos que trabajaremos a continuación corresponden a la extracción de diferentes variables relacionadas con energías renovables y combustibles fósiles, las UE son 111 países de todos los continentes del mundo, seleccionados para fines académicos por ser aquellos países que presentan mayor cantidad de información de análisis.
Adicionalmente, se han incluido variables relacionadas al Producto interno Bruto de cada país para el año 2014 (GDP_USD y GDP_per_capita), así como la población de cada país a final de ese año.
El objetivo de este análisis es encontrar estructuras de correlación de tipo lineal entre variables de combustibles fósiles y energías renovables con el PIB de cada país, entendiendo que nuestras variables explicativas solamente son una parte del total del PIB.
Datos <- read.csv2("datos_taller_03.csv")
Datos<-as.data.frame(Datos)
columnas_a_convertir <- names(Datos)[-1]
Datos[columnas_a_convertir] <- lapply(Datos[columnas_a_convertir], as.numeric)
# Filtrar el dataframe Datos para excluir los países específicos
paises_excluidos <- c("UnitedStates", "China", "SaudiArabia", "Russia")
Datos_filtrados <- Datos[!Datos$Country %in% paises_excluidos, ]
str(Datos)## 'data.frame': 108 obs. of 61 variables:
## $ Country : chr "Albania" "Algeria" "Angola" "Argentina" ...
## $ GDP_USD : num 1.32e+10 2.14e+11 1.37e+11 5.26e+11 1.47e+12 ...
## $ Population : num 2889104 38923688 26941773 42669500 23475686 ...
## $ GDP_per_capita : num 4579 5493 5094 12335 62512 ...
## $ Bunker_fuel_consumption_TBPD : num 0.6 14 12 48 14 0 9.1 9.9 8.8 2.4 ...
## $ Bunker_residual_fuel_oil_consumption_TBPD : num 0 3.8 6.8 26 13 0 0 1.5 1.8 0 ...
## $ Crude_oil_including_lease_condensate_exports_TBPD : num 19 581 1632 49 224 ...
## $ Crude_oil_including_lease_condensate_imports_TBPD : num 0.9 6.4 0 9.5 441 152 0 211 27 450 ...
## $ Crude_oil_including_lease_condensate_production_TBPD : num 21 1420 1742 532 353 ...
## $ Crude_oil_including_lease_condensate_reserves_BB : num 0.2 12 9.1 2.8 1.4 0 7 0.1 0 0.2 ...
## $ Distillate_fuel_oil_consumption_TBPD : num 16 205 83 232 433 152 27 6 66 64 ...
## $ Distillate_fuel_oil_production_TBPD : num 1.8 184 11 173 213 81 60 81 7.4 169 ...
## $ Jet_fuel_consumption_TBPD : num 0.2 12 10 33 139 14 11 9 7 2.9 ...
## $ Jet_fuel_production_TBPD : num 0 43 8.5 29 82 13 15 63 0 7.3 ...
## $ Kerosene_consumption_TBPD : num 0 0 0.8 0.5 0.6 0 0.1 1 6.1 0 ...
## $ Kerosene_production_TBPD : num 0 0 1.5 0.3 0.1 0.4 0 0.5 4.9 0.3 ...
## $ Liquefied_petroleum_gases_.LPG._consumption_TBPD : num 3.9 63 7.2 56 61 3.4 5 2 0.6 6 ...
## $ Liquefied_petroleum_gases_.LPG._production_TBPD : num 0 26 1 39 16 2.2 6 1.9 0.4 19 ...
## $ Motor_gasoline_consumption_TBPD : num 2.8 97 25 122 320 38 32 17 3.9 27 ...
## $ Motor_gasoline_production_TBPD : num 0 70 0.6 123 241 43 29 18 1.4 92 ...
## $ Natural_gas_plant_liquids_production_TBPD : num 0 300 15 104 58 1 1 11 0.2 0 ...
## $ Other_liquids_production_TBPD : num 0 0 0 65 7 8.9 0 0 0 0.6 ...
## $ Other_refined_products_consumption_TBPD : num 5.4 35 9.8 221 148 41 22 21 2.9 54 ...
## $ Other_refined_products_production_TBPD : num 4.7 213 6.7 204 42 39 26 69 5.8 57 ...
## $ Petroleum_and_other_liquids_CO2_emissions_MMTCD : num 3.7 53 21 101 150 35 13 8.1 17 21 ...
## $ Petroleum_and_other_liquids_consumption_TBPD : num 28 416 159 764 1126 ...
## $ Petroleum_and_other_liquids_production_TBPD : num 21 1722 1756 713 442 ...
## $ Refined_petroleum_products_consumption_TBPD : num 28 416 159 764 1126 ...
## $ Refined_petroleum_products_production_TBPD : num 6.6 658 47 661 607 196 142 272 26 457 ...
## $ Refinery_processing_gain_TBPD : num 0 1.8 -0.7 12 23 3.7 5 2.9 0 2.1 ...
## $ Residual_fuel_oil_consumption_TBPD : num 0.1 4 23 99 23 9.4 2.2 2 24 15 ...
## $ Residual_fuel_oil_production_TBPD : num 0.1 120 17 93 12 17 5.6 39 5.8 113 ...
## $ Biomass_and_waste_electricity_installed_capacity_MK : num 0 0 0 0.2 0.8 2.1 0 0 0 0 ...
## $ Biomass_and_waste_electricity_net_generation_BKWH : num 0 0 0 1 3.5 5.1 0.2 0 0 0.2 ...
## $ Electricity_distribution_losses_BKWH : num 2.8 11 1.1 18 12 3.4 3.4 1.1 6.8 3.2 ...
## $ Electricity_exports_BKWH : num 0.2 0.9 0 0.2 0 17 0.5 0.2 0 4.5 ...
## $ Electricity_imports_BKWH : num 3.3 0.7 0 10 0 27 0.1 0.2 2.3 7.8 ...
## $ Electricity_installed_capacity_MK : num 1.8 16 1.8 38 68 24 7.4 7 9.4 10 ...
## $ Electricity_net_consumption_BKWH : num 5 49 8.1 123 229 64 20 25 48 33 ...
## $ Electricity_net_generation_BKWH : num 4.7 60 9.2 131 242 58 23 26 53 33 ...
## $ Electricity_net_imports_BKWH : num 3.1 -0.2 0 9.9 0 9.3 -0.4 0 2.3 3.3 ...
## $ Fossil_fuels_electricity_installed_capacity_MK : num 0.1 16 0.8 25 50 5.8 6.3 7 9.1 10 ...
## $ Fossil_fuels_electricity_net_generation_BKWH : num 0 60 4.2 92 205 11 22 26 52 32 ...
## $ Geothermal_electricity_installed_capacity_MK : num 0 0 0 0 0 0 0 0 0 0 ...
## $ Geothermal_electricity_net_generation_BKWH : num 0 0 0 0 0 0 0 0 0 0 ...
## $ Hydroelectric_pumped_storage_electricity_installed_capacity_MK: num 0 0 0 1 2.6 5.2 0 0 0 0 ...
## $ Hydroelectric_pumped_storage_electricity_net_generation_BKWH : num 0 0 0 -0.2 0 -1.7 0 0 0 0 ...
## $ Hydroelectricity_installed_capacity_MK : num 1.7 0.3 1 10 5.7 8.3 1.1 0 0.2 0 ...
## $ Hydroelectricity_net_generation_BKWH : num 4.7 0.3 5 32 18 39 1.3 0 0.6 0.1 ...
## $ Non.hydro_renewable_electricity_installed_capacity_MK : num 0 0 0 0.5 9.9 5 0 0 0.1 0 ...
## $ Non.hydro_renewable_electricity_net_generation_BKWH : num 0 0 0 1.6 18 9.5 0.2 0 0.2 0.2 ...
## $ Nuclear_electricity_installed_capacity_MK : num 0 0 0 1.6 0 0 0 0 0 0 ...
## $ Nuclear_electricity_net_generation_BKWH : num 0 0 0 5.3 0 0 0 0 0 0 ...
## $ Renewable_electricity_installed_capacity_MK : num 1.7 0.3 1 11 16 13 1.1 0 0.4 0 ...
## $ Renewable_electricity_net_generation_BKWH : num 4.7 0.3 5 34 36 49 1.5 0 0.8 0.3 ...
## $ Solar_electricity_installed_capacity_MK : num 0 0 0 0 5.3 0.8 0 0 0.1 0 ...
## $ Solar_electricity_net_generation_BKWH : num 0 0 0 0 4 0.7 0 0 0.2 0 ...
## $ Tide_and_wave_electricity_installed_capacity_MK : num 0 0 0 0 0 0 0 0 0 0 ...
## $ Tide_and_wave_electricity_net_generation_BKWH : num 0 0 0 0 0 0 0 0 0 0 ...
## $ Wind_electricity_installed_capacity_MK : num 0 0 0 0.2 3.8 2.1 0 0 0 0 ...
## $ Wind_electricity_net_generation_BKWH : num 0 0 0 0.6 10 3.7 0 0 0 0 ...Pregunta 1. \(w_1 = 10\)
Para tratar de explicar el total de PIB (GDP_USD) a través de las
variables en la base, ajuste un modelo de regresión con todas las
variables explicativas e interprete la salida del mismo con la ayuda de
la función summary().
variables_explicativas <- setdiff(names(Datos_filtrados), c("Country", "GDP_per_capita"))
modelo <- lm(GDP_USD ~ ., data = Datos_filtrados[, variables_explicativas])
summary(modelo)##
## Call:
## lm(formula = GDP_USD ~ ., data = Datos_filtrados[, variables_explicativas])
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.704e+11 -3.084e+10 -1.200e+09 3.878e+10 1.787e+11
##
## Coefficients: (1 not defined because of singularities)
## Estimate
## (Intercept) 1.875e+10
## Population 1.076e+03
## Bunker_fuel_consumption_TBPD -4.536e+09
## Bunker_residual_fuel_oil_consumption_TBPD 6.222e+09
## Crude_oil_including_lease_condensate_exports_TBPD -1.257e+08
## Crude_oil_including_lease_condensate_imports_TBPD -4.988e+07
## Crude_oil_including_lease_condensate_production_TBPD 6.969e+10
## Crude_oil_including_lease_condensate_reserves_BB -1.295e+08
## Distillate_fuel_oil_consumption_TBPD -3.916e+10
## Distillate_fuel_oil_production_TBPD 6.524e+09
## Jet_fuel_consumption_TBPD -3.027e+10
## Jet_fuel_production_TBPD 5.883e+09
## Kerosene_consumption_TBPD -3.482e+10
## Kerosene_production_TBPD 8.235e+09
## Liquefied_petroleum_gases_.LPG._consumption_TBPD -3.761e+10
## Liquefied_petroleum_gases_.LPG._production_TBPD 8.580e+09
## Motor_gasoline_consumption_TBPD -3.805e+10
## Motor_gasoline_production_TBPD 7.204e+09
## Natural_gas_plant_liquids_production_TBPD 6.932e+10
## Other_liquids_production_TBPD 7.049e+10
## Other_refined_products_consumption_TBPD -3.933e+10
## Other_refined_products_production_TBPD 8.512e+09
## Petroleum_and_other_liquids_CO2_emissions_MMTCD -8.337e+09
## Petroleum_and_other_liquids_consumption_TBPD 3.961e+10
## Petroleum_and_other_liquids_production_TBPD -6.959e+10
## Refined_petroleum_products_consumption_TBPD NA
## Refined_petroleum_products_production_TBPD -8.090e+09
## Refinery_processing_gain_TBPD 8.067e+10
## Residual_fuel_oil_consumption_TBPD -3.933e+10
## Residual_fuel_oil_production_TBPD 1.187e+10
## Biomass_and_waste_electricity_installed_capacity_MK 1.797e+11
## Biomass_and_waste_electricity_net_generation_BKWH 2.025e+11
## Electricity_distribution_losses_BKWH 1.036e+11
## Electricity_exports_BKWH -1.001e+11
## Electricity_imports_BKWH 1.015e+11
## Electricity_installed_capacity_MK 5.338e+10
## Electricity_net_consumption_BKWH 1.156e+11
## Electricity_net_generation_BKWH -1.006e+11
## Electricity_net_imports_BKWH -2.140e+11
## Fossil_fuels_electricity_installed_capacity_MK -4.334e+10
## Fossil_fuels_electricity_net_generation_BKWH -1.476e+10
## Geothermal_electricity_installed_capacity_MK 4.741e+11
## Geothermal_electricity_net_generation_BKWH 1.602e+11
## Hydroelectric_pumped_storage_electricity_installed_capacity_MK -5.462e+10
## Hydroelectric_pumped_storage_electricity_net_generation_BKWH -1.181e+11
## Hydroelectricity_installed_capacity_MK -4.274e+11
## Hydroelectricity_net_generation_BKWH 1.570e+10
## Non.hydro_renewable_electricity_installed_capacity_MK -5.926e+11
## Non.hydro_renewable_electricity_net_generation_BKWH -1.873e+11
## Nuclear_electricity_installed_capacity_MK -4.569e+10
## Nuclear_electricity_net_generation_BKWH -1.867e+10
## Renewable_electricity_installed_capacity_MK 3.364e+11
## Renewable_electricity_net_generation_BKWH -1.914e+10
## Solar_electricity_installed_capacity_MK 4.221e+11
## Solar_electricity_net_generation_BKWH 2.630e+10
## Tide_and_wave_electricity_installed_capacity_MK -7.864e+12
## Tide_and_wave_electricity_net_generation_BKWH 3.243e+12
## Wind_electricity_installed_capacity_MK 4.660e+11
## Wind_electricity_net_generation_BKWH 1.075e+11
## Std. Error
## (Intercept) 1.830e+10
## Population 5.260e+02
## Bunker_fuel_consumption_TBPD 1.898e+09
## Bunker_residual_fuel_oil_consumption_TBPD 2.486e+09
## Crude_oil_including_lease_condensate_exports_TBPD 2.310e+08
## Crude_oil_including_lease_condensate_imports_TBPD 2.548e+08
## Crude_oil_including_lease_condensate_production_TBPD 3.805e+10
## Crude_oil_including_lease_condensate_reserves_BB 6.927e+08
## Distillate_fuel_oil_consumption_TBPD 2.323e+10
## Distillate_fuel_oil_production_TBPD 2.135e+10
## Jet_fuel_consumption_TBPD 2.328e+10
## Jet_fuel_production_TBPD 2.149e+10
## Kerosene_consumption_TBPD 2.351e+10
## Kerosene_production_TBPD 2.131e+10
## Liquefied_petroleum_gases_.LPG._consumption_TBPD 2.307e+10
## Liquefied_petroleum_gases_.LPG._production_TBPD 2.152e+10
## Motor_gasoline_consumption_TBPD 2.326e+10
## Motor_gasoline_production_TBPD 2.174e+10
## Natural_gas_plant_liquids_production_TBPD 3.817e+10
## Other_liquids_production_TBPD 3.823e+10
## Other_refined_products_consumption_TBPD 2.318e+10
## Other_refined_products_production_TBPD 2.177e+10
## Petroleum_and_other_liquids_CO2_emissions_MMTCD 9.060e+09
## Petroleum_and_other_liquids_consumption_TBPD 2.295e+10
## Petroleum_and_other_liquids_production_TBPD 3.808e+10
## Refined_petroleum_products_consumption_TBPD NA
## Refined_petroleum_products_production_TBPD 2.142e+10
## Refinery_processing_gain_TBPD 4.522e+10
## Residual_fuel_oil_consumption_TBPD 2.336e+10
## Residual_fuel_oil_production_TBPD 2.118e+10
## Biomass_and_waste_electricity_installed_capacity_MK 2.370e+11
## Biomass_and_waste_electricity_net_generation_BKWH 1.548e+11
## Electricity_distribution_losses_BKWH 4.339e+10
## Electricity_exports_BKWH 1.411e+11
## Electricity_imports_BKWH 1.396e+11
## Electricity_installed_capacity_MK 6.344e+10
## Electricity_net_consumption_BKWH 4.229e+10
## Electricity_net_generation_BKWH 4.542e+10
## Electricity_net_imports_BKWH 1.535e+11
## Fossil_fuels_electricity_installed_capacity_MK 6.363e+10
## Fossil_fuels_electricity_net_generation_BKWH 3.939e+10
## Geothermal_electricity_installed_capacity_MK 3.256e+11
## Geothermal_electricity_net_generation_BKWH 1.391e+11
## Hydroelectric_pumped_storage_electricity_installed_capacity_MK 7.041e+10
## Hydroelectric_pumped_storage_electricity_net_generation_BKWH 1.080e+11
## Hydroelectricity_installed_capacity_MK 1.706e+11
## Hydroelectricity_net_generation_BKWH 6.834e+10
## Non.hydro_renewable_electricity_installed_capacity_MK 2.292e+11
## Non.hydro_renewable_electricity_net_generation_BKWH 1.634e+11
## Nuclear_electricity_installed_capacity_MK 1.299e+11
## Nuclear_electricity_net_generation_BKWH 4.158e+10
## Renewable_electricity_installed_capacity_MK 1.563e+11
## Renewable_electricity_net_generation_BKWH 6.454e+10
## Solar_electricity_installed_capacity_MK 2.377e+11
## Solar_electricity_net_generation_BKWH 1.510e+11
## Tide_and_wave_electricity_installed_capacity_MK 2.171e+12
## Tide_and_wave_electricity_net_generation_BKWH 7.032e+11
## Wind_electricity_installed_capacity_MK 2.760e+11
## Wind_electricity_net_generation_BKWH 1.706e+11
## t value Pr(>|t|)
## (Intercept) 1.025 0.310749
## Population 2.045 0.046570
## Bunker_fuel_consumption_TBPD -2.390 0.021002
## Bunker_residual_fuel_oil_consumption_TBPD 2.503 0.015928
## Crude_oil_including_lease_condensate_exports_TBPD -0.544 0.589069
## Crude_oil_including_lease_condensate_imports_TBPD -0.196 0.845657
## Crude_oil_including_lease_condensate_production_TBPD 1.831 0.073523
## Crude_oil_including_lease_condensate_reserves_BB -0.187 0.852513
## Distillate_fuel_oil_consumption_TBPD -1.686 0.098652
## Distillate_fuel_oil_production_TBPD 0.306 0.761344
## Jet_fuel_consumption_TBPD -1.300 0.200049
## Jet_fuel_production_TBPD 0.274 0.785477
## Kerosene_consumption_TBPD -1.481 0.145441
## Kerosene_production_TBPD 0.387 0.700899
## Liquefied_petroleum_gases_.LPG._consumption_TBPD -1.630 0.109841
## Liquefied_petroleum_gases_.LPG._production_TBPD 0.399 0.691977
## Motor_gasoline_consumption_TBPD -1.636 0.108668
## Motor_gasoline_production_TBPD 0.331 0.741845
## Natural_gas_plant_liquids_production_TBPD 1.816 0.075916
## Other_liquids_production_TBPD 1.844 0.071660
## Other_refined_products_consumption_TBPD -1.697 0.096518
## Other_refined_products_production_TBPD 0.391 0.697548
## Petroleum_and_other_liquids_CO2_emissions_MMTCD -0.920 0.362246
## Petroleum_and_other_liquids_consumption_TBPD 1.726 0.091024
## Petroleum_and_other_liquids_production_TBPD -1.827 0.074140
## Refined_petroleum_products_consumption_TBPD NA NA
## Refined_petroleum_products_production_TBPD -0.378 0.707344
## Refinery_processing_gain_TBPD 1.784 0.081010
## Residual_fuel_oil_consumption_TBPD -1.684 0.098985
## Residual_fuel_oil_production_TBPD 0.561 0.577786
## Biomass_and_waste_electricity_installed_capacity_MK 0.758 0.452208
## Biomass_and_waste_electricity_net_generation_BKWH 1.308 0.197426
## Electricity_distribution_losses_BKWH 2.387 0.021144
## Electricity_exports_BKWH -0.709 0.481936
## Electricity_imports_BKWH 0.727 0.470770
## Electricity_installed_capacity_MK 0.841 0.404425
## Electricity_net_consumption_BKWH 2.734 0.008853
## Electricity_net_generation_BKWH -2.216 0.031701
## Electricity_net_imports_BKWH -1.394 0.169909
## Fossil_fuels_electricity_installed_capacity_MK -0.681 0.499223
## Fossil_fuels_electricity_net_generation_BKWH -0.375 0.709510
## Geothermal_electricity_installed_capacity_MK 1.456 0.152167
## Geothermal_electricity_net_generation_BKWH 1.152 0.255411
## Hydroelectric_pumped_storage_electricity_installed_capacity_MK -0.776 0.441855
## Hydroelectric_pumped_storage_electricity_net_generation_BKWH -1.094 0.279810
## Hydroelectricity_installed_capacity_MK -2.506 0.015817
## Hydroelectricity_net_generation_BKWH 0.230 0.819318
## Non.hydro_renewable_electricity_installed_capacity_MK -2.586 0.012946
## Non.hydro_renewable_electricity_net_generation_BKWH -1.146 0.257656
## Nuclear_electricity_installed_capacity_MK -0.352 0.726551
## Nuclear_electricity_net_generation_BKWH -0.449 0.655487
## Renewable_electricity_installed_capacity_MK 2.152 0.036696
## Renewable_electricity_net_generation_BKWH -0.297 0.768157
## Solar_electricity_installed_capacity_MK 1.776 0.082367
## Solar_electricity_net_generation_BKWH 0.174 0.862480
## Tide_and_wave_electricity_installed_capacity_MK -3.622 0.000727
## Tide_and_wave_electricity_net_generation_BKWH 4.612 3.19e-05
## Wind_electricity_installed_capacity_MK 1.688 0.098103
## Wind_electricity_net_generation_BKWH 0.630 0.531750
##
## (Intercept)
## Population *
## Bunker_fuel_consumption_TBPD *
## Bunker_residual_fuel_oil_consumption_TBPD *
## Crude_oil_including_lease_condensate_exports_TBPD
## Crude_oil_including_lease_condensate_imports_TBPD
## Crude_oil_including_lease_condensate_production_TBPD .
## Crude_oil_including_lease_condensate_reserves_BB
## Distillate_fuel_oil_consumption_TBPD .
## Distillate_fuel_oil_production_TBPD
## Jet_fuel_consumption_TBPD
## Jet_fuel_production_TBPD
## Kerosene_consumption_TBPD
## Kerosene_production_TBPD
## Liquefied_petroleum_gases_.LPG._consumption_TBPD
## Liquefied_petroleum_gases_.LPG._production_TBPD
## Motor_gasoline_consumption_TBPD
## Motor_gasoline_production_TBPD
## Natural_gas_plant_liquids_production_TBPD .
## Other_liquids_production_TBPD .
## Other_refined_products_consumption_TBPD .
## Other_refined_products_production_TBPD
## Petroleum_and_other_liquids_CO2_emissions_MMTCD
## Petroleum_and_other_liquids_consumption_TBPD .
## Petroleum_and_other_liquids_production_TBPD .
## Refined_petroleum_products_consumption_TBPD
## Refined_petroleum_products_production_TBPD
## Refinery_processing_gain_TBPD .
## Residual_fuel_oil_consumption_TBPD .
## Residual_fuel_oil_production_TBPD
## Biomass_and_waste_electricity_installed_capacity_MK
## Biomass_and_waste_electricity_net_generation_BKWH
## Electricity_distribution_losses_BKWH *
## Electricity_exports_BKWH
## Electricity_imports_BKWH
## Electricity_installed_capacity_MK
## Electricity_net_consumption_BKWH **
## Electricity_net_generation_BKWH *
## Electricity_net_imports_BKWH
## Fossil_fuels_electricity_installed_capacity_MK
## Fossil_fuels_electricity_net_generation_BKWH
## Geothermal_electricity_installed_capacity_MK
## Geothermal_electricity_net_generation_BKWH
## Hydroelectric_pumped_storage_electricity_installed_capacity_MK
## Hydroelectric_pumped_storage_electricity_net_generation_BKWH
## Hydroelectricity_installed_capacity_MK *
## Hydroelectricity_net_generation_BKWH
## Non.hydro_renewable_electricity_installed_capacity_MK *
## Non.hydro_renewable_electricity_net_generation_BKWH
## Nuclear_electricity_installed_capacity_MK
## Nuclear_electricity_net_generation_BKWH
## Renewable_electricity_installed_capacity_MK *
## Renewable_electricity_net_generation_BKWH
## Solar_electricity_installed_capacity_MK .
## Solar_electricity_net_generation_BKWH
## Tide_and_wave_electricity_installed_capacity_MK ***
## Tide_and_wave_electricity_net_generation_BKWH ***
## Wind_electricity_installed_capacity_MK .
## Wind_electricity_net_generation_BKWH
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 8.101e+10 on 46 degrees of freedom
## Multiple R-squared: 0.9957, Adjusted R-squared: 0.9903
## F-statistic: 184.9 on 57 and 46 DF, p-value: < 2.2e-16El modelo resulta bastante ajustado, con un R-cuadrado ajustado de 0.9903, lo que sugiere que alrededor del 99.03% de la variabilidad en el PIB se explica por las variables independientes incluidas en el modelo. El p-valor general del modelo es muy bajo (p-valor: < 2.2e-16), lo que sugiere que al menos una de las variables explicativas está relacionada con el PIB.
Podemos interpretar lo siguiente a partir del primer resultado del modelo:
Population: Tiene una significancia moderada (p-valor: 0.046570). Un aumento en la población podría estar relacionado positivamente con el PIB.
Bunker_fuel_consumption_TBPD: Significancia moderada (p-valor: 0.021002). Una disminución en el consumo de combustible bunker podría tener una relación negativa con el PIB.
Tide_and_wave_electricity_installed_capacity_MK El coeficiente de -7.864e+12 indicaría que, manteniendo todas las demás variables constantes, un aumento de 1 unidad en la capacidad instalada de generación de electricidad a partir de las mareas y las olas, se asocia con una disminución estimada de $7.864 billones en el PIB. Esto sugiere que un aumento significativo en la capacidad instalada de generación de energía de mareas y olas está relacionado con una disminución en el PIB.
Tide_and_wave_electricity_net_generation_BKWH: El coeficiente de 3.243e+12 indicaría que un aumento de 1 unidad en la generación neta de electricidad a partir de mareas y olas (medido en miles de millones de kilovatios-hora, BKWH) se asocia con un aumento estimado de $3.243 billones en el PIB. Esto sugiere que un incremento en la generación neta de electricidad a partir de estas fuentes renovables está relacionado con un aumento en el PIB.
Pregunta 2. \(w_2 = 10\)
Analice el ANOVA del modelo para determinar si el modelo en conjunto, con todas sus variables, logran explicar en general el PIB.
modelo2 <- lm(GDP_USD ~ 1, data = Datos_filtrados[, variables_explicativas])
anova_result <- anova(modelo,modelo2)
anova_result## Analysis of Variance Table
##
## Model 1: GDP_USD ~ Population + Bunker_fuel_consumption_TBPD + Bunker_residual_fuel_oil_consumption_TBPD +
## Crude_oil_including_lease_condensate_exports_TBPD + Crude_oil_including_lease_condensate_imports_TBPD +
## Crude_oil_including_lease_condensate_production_TBPD + Crude_oil_including_lease_condensate_reserves_BB +
## Distillate_fuel_oil_consumption_TBPD + Distillate_fuel_oil_production_TBPD +
## Jet_fuel_consumption_TBPD + Jet_fuel_production_TBPD + Kerosene_consumption_TBPD +
## Kerosene_production_TBPD + Liquefied_petroleum_gases_.LPG._consumption_TBPD +
## Liquefied_petroleum_gases_.LPG._production_TBPD + Motor_gasoline_consumption_TBPD +
## Motor_gasoline_production_TBPD + Natural_gas_plant_liquids_production_TBPD +
## Other_liquids_production_TBPD + Other_refined_products_consumption_TBPD +
## Other_refined_products_production_TBPD + Petroleum_and_other_liquids_CO2_emissions_MMTCD +
## Petroleum_and_other_liquids_consumption_TBPD + Petroleum_and_other_liquids_production_TBPD +
## Refined_petroleum_products_consumption_TBPD + Refined_petroleum_products_production_TBPD +
## Refinery_processing_gain_TBPD + Residual_fuel_oil_consumption_TBPD +
## Residual_fuel_oil_production_TBPD + Biomass_and_waste_electricity_installed_capacity_MK +
## Biomass_and_waste_electricity_net_generation_BKWH + Electricity_distribution_losses_BKWH +
## Electricity_exports_BKWH + Electricity_imports_BKWH + Electricity_installed_capacity_MK +
## Electricity_net_consumption_BKWH + Electricity_net_generation_BKWH +
## Electricity_net_imports_BKWH + Fossil_fuels_electricity_installed_capacity_MK +
## Fossil_fuels_electricity_net_generation_BKWH + Geothermal_electricity_installed_capacity_MK +
## Geothermal_electricity_net_generation_BKWH + Hydroelectric_pumped_storage_electricity_installed_capacity_MK +
## Hydroelectric_pumped_storage_electricity_net_generation_BKWH +
## Hydroelectricity_installed_capacity_MK + Hydroelectricity_net_generation_BKWH +
## Non.hydro_renewable_electricity_installed_capacity_MK + Non.hydro_renewable_electricity_net_generation_BKWH +
## Nuclear_electricity_installed_capacity_MK + Nuclear_electricity_net_generation_BKWH +
## Renewable_electricity_installed_capacity_MK + Renewable_electricity_net_generation_BKWH +
## Solar_electricity_installed_capacity_MK + Solar_electricity_net_generation_BKWH +
## Tide_and_wave_electricity_installed_capacity_MK + Tide_and_wave_electricity_net_generation_BKWH +
## Wind_electricity_installed_capacity_MK + Wind_electricity_net_generation_BKWH
## Model 2: GDP_USD ~ 1
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 46 3.0186e+23
## 2 103 6.9450e+25 -57 -6.9148e+25 184.87 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Los valores significativos en la tabla ANOVA se pueden interpretar a partir del valor p (Pr(>F)). Las variables con valores de p bajos son las más relevantes para explicar las variaciones en el PIB. Las variables con valores de p altos podrían no ser relevantes para predecir el PIB y podrían ser consideradas para ser eliminadas del modelo.
Variables significativas: Population, Bunker_residual_fuel_oil_consumption_TBPD, Crude_oil_including_lease_condensate_imports_TBPD y Distillate_fuel_oil_consumption_TBPD entre otras, muestran valores de p muy bajos (<<0.05), lo que sugiere una fuerte relación con el PIB.
Variables menos significativas: Liquefied_petroleum_gases_.LPG._consumption_TBPD, Liquefied_petroleum_gases_.LPG._production_TBPD, Fossil_fuels_electricity_installed_capacity_MK y Geothermal_electricity_net_generation_BKWH tienen valores de p altos (>0.05), lo que sugiere que podrían no estar contribuyendo significativamente al modelo.
Por otra parte, para el modelo con solo el término de intercepto, un valor alto del estadístico F junto con un valor p extremadamente pequeño indicaría que el modelo con el término de intercepto es significativamente mejor que un modelo sin variables predictoras para explicar la variabilidad en los datos.
Pregunta 3. \(w_3 = 10\)
A través de los gráficos asociados al modelo, realice un diagnóstico del mismo verificando los supuestos del modelo de regresión lineal. ¿Cumple el modelo todos los supuestos?
# Gráfico de dispersión de residuos vs valores ajustados para verificar homocedasticidad
plot(modelo, which = 1)
# Gráfico Q-Q de los residuos para verificar normalidad
plot(modelo, which = 2)
# Gráfico de dispersión de residuos vs variables explicativas para verificar linealidad
plot(modelo, which = 3)
Se evidencia ausencia de homocedasticidad, hay una mayor dispersión en el extremo izquierdo del gráfico. De igual forma, no existe normalidad en los residuos por que existen puntos muy alejados a la diagonalen los extremos. Finalmente, no hay linealidad entre los residuos y las variables explicativas.Es decir, no se cumplen todos los supuestos del modelo.
Pregunta 4. \(w_4 = 10\)
Estime ahora un modelo de regresión lineal múltiple, pero esta vez
realice una transformación de logaritmo sobre la variable de respuesta
log(GDP_USD). ¿Qué pasa ahora con el modelo cuando
realizamos esta transformación? ¿Cambió el cumplimiento de los supuestos
del modelo con respecto al estimado en los pasos anteriores? ¿Con cuál
modelo se quedaría?
# Aplicar la transformación logarítmica a la variable de respuesta
Datos_filtrados$log_GDP_USD <- log(Datos_filtrados$GDP_USD)
# Estimar el modelo de regresión lineal múltiple con la variable transformada
modelo_log <- lm(Datos_filtrados$log_GDP_USD~ ., data = Datos_filtrados[, variables_explicativas])
summary(modelo_log)##
## Call:
## lm(formula = Datos_filtrados$log_GDP_USD ~ ., data = Datos_filtrados[,
## variables_explicativas])
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.51594 -0.26504 -0.01037 0.22497 1.74785
##
## Coefficients: (1 not defined because of singularities)
## Estimate
## (Intercept) 2.391e+01
## GDP_USD 3.040e-12
## Population 7.974e-09
## Bunker_fuel_consumption_TBPD 3.322e-02
## Bunker_residual_fuel_oil_consumption_TBPD -3.492e-02
## Crude_oil_including_lease_condensate_exports_TBPD -1.516e-03
## Crude_oil_including_lease_condensate_imports_TBPD 2.139e-03
## Crude_oil_including_lease_condensate_production_TBPD 1.845e-01
## Crude_oil_including_lease_condensate_reserves_BB 1.012e-02
## Distillate_fuel_oil_consumption_TBPD -1.769e-01
## Distillate_fuel_oil_production_TBPD -7.038e-03
## Jet_fuel_consumption_TBPD -1.898e-01
## Jet_fuel_production_TBPD -2.508e-02
## Kerosene_consumption_TBPD -2.060e-01
## Kerosene_production_TBPD -3.281e-02
## Liquefied_petroleum_gases_.LPG._consumption_TBPD -1.698e-01
## Liquefied_petroleum_gases_.LPG._production_TBPD -1.801e-02
## Motor_gasoline_consumption_TBPD -1.835e-01
## Motor_gasoline_production_TBPD -2.708e-02
## Natural_gas_plant_liquids_production_TBPD 1.773e-01
## Other_liquids_production_TBPD 1.776e-01
## Other_refined_products_consumption_TBPD -1.747e-01
## Other_refined_products_production_TBPD 2.866e-03
## Petroleum_and_other_liquids_CO2_emissions_MMTCD 1.271e-01
## Petroleum_and_other_liquids_consumption_TBPD 1.598e-01
## Petroleum_and_other_liquids_production_TBPD -1.824e-01
## Refined_petroleum_products_consumption_TBPD NA
## Refined_petroleum_products_production_TBPD 4.619e-03
## Refinery_processing_gain_TBPD 4.100e-01
## Residual_fuel_oil_consumption_TBPD -1.822e-01
## Residual_fuel_oil_production_TBPD 1.296e-02
## Biomass_and_waste_electricity_installed_capacity_MK -3.029e+00
## Biomass_and_waste_electricity_net_generation_BKWH 2.187e-01
## Electricity_distribution_losses_BKWH 9.617e-03
## Electricity_exports_BKWH -1.824e+00
## Electricity_imports_BKWH 1.842e+00
## Electricity_installed_capacity_MK 6.223e-01
## Electricity_net_consumption_BKWH 9.323e-02
## Electricity_net_generation_BKWH 3.169e-01
## Electricity_net_imports_BKWH -1.949e+00
## Fossil_fuels_electricity_installed_capacity_MK -5.563e-01
## Fossil_fuels_electricity_net_generation_BKWH -4.085e-01
## Geothermal_electricity_installed_capacity_MK -2.878e+00
## Geothermal_electricity_net_generation_BKWH 1.917e-01
## Hydroelectric_pumped_storage_electricity_installed_capacity_MK -9.076e-01
## Hydroelectric_pumped_storage_electricity_net_generation_BKWH -1.959e+00
## Hydroelectricity_installed_capacity_MK -5.433e-01
## Hydroelectricity_net_generation_BKWH -4.069e-01
## Non.hydro_renewable_electricity_installed_capacity_MK 2.378e+00
## Non.hydro_renewable_electricity_net_generation_BKWH -5.921e-01
## Nuclear_electricity_installed_capacity_MK -2.234e+00
## Nuclear_electricity_net_generation_BKWH -1.760e-01
## Renewable_electricity_installed_capacity_MK -6.417e-02
## Renewable_electricity_net_generation_BKWH 6.458e-03
## Solar_electricity_installed_capacity_MK -2.911e+00
## Solar_electricity_net_generation_BKWH 3.067e-01
## Tide_and_wave_electricity_installed_capacity_MK -1.104e+01
## Tide_and_wave_electricity_net_generation_BKWH 1.746e+00
## Wind_electricity_installed_capacity_MK -5.261e+00
## Wind_electricity_net_generation_BKWH 1.131e+00
## Std. Error
## (Intercept) 1.538e-01
## GDP_USD 1.226e-12
## Population 4.567e-09
## Bunker_fuel_consumption_TBPD 1.673e-02
## Bunker_residual_fuel_oil_consumption_TBPD 2.203e-02
## Crude_oil_including_lease_condensate_exports_TBPD 1.927e-03
## Crude_oil_including_lease_condensate_imports_TBPD 2.119e-03
## Crude_oil_including_lease_condensate_production_TBPD 3.277e-01
## Crude_oil_including_lease_condensate_reserves_BB 5.761e-03
## Distillate_fuel_oil_consumption_TBPD 1.990e-01
## Distillate_fuel_oil_production_TBPD 1.777e-01
## Jet_fuel_consumption_TBPD 1.971e-01
## Jet_fuel_production_TBPD 1.788e-01
## Kerosene_consumption_TBPD 2.001e-01
## Kerosene_production_TBPD 1.774e-01
## Liquefied_petroleum_gases_.LPG._consumption_TBPD 1.972e-01
## Liquefied_petroleum_gases_.LPG._production_TBPD 1.792e-01
## Motor_gasoline_consumption_TBPD 1.989e-01
## Motor_gasoline_production_TBPD 1.809e-01
## Natural_gas_plant_liquids_production_TBPD 3.285e-01
## Other_liquids_production_TBPD 3.294e-01
## Other_refined_products_consumption_TBPD 1.986e-01
## Other_refined_products_production_TBPD 1.812e-01
## Petroleum_and_other_liquids_CO2_emissions_MMTCD 7.600e-02
## Petroleum_and_other_liquids_consumption_TBPD 1.968e-01
## Petroleum_and_other_liquids_production_TBPD 3.279e-01
## Refined_petroleum_products_consumption_TBPD NA
## Refined_petroleum_products_production_TBPD 1.783e-01
## Refinery_processing_gain_TBPD 3.887e-01
## Residual_fuel_oil_consumption_TBPD 2.001e-01
## Residual_fuel_oil_production_TBPD 1.767e-01
## Biomass_and_waste_electricity_installed_capacity_MK 1.982e+00
## Biomass_and_waste_electricity_net_generation_BKWH 1.311e+00
## Electricity_distribution_losses_BKWH 3.824e-01
## Electricity_exports_BKWH 1.180e+00
## Electricity_imports_BKWH 1.167e+00
## Electricity_installed_capacity_MK 5.314e-01
## Electricity_net_consumption_BKWH 3.791e-01
## Electricity_net_generation_BKWH 3.972e-01
## Electricity_net_imports_BKWH 1.302e+00
## Fossil_fuels_electricity_installed_capacity_MK 5.316e-01
## Fossil_fuels_electricity_net_generation_BKWH 3.279e-01
## Geothermal_electricity_installed_capacity_MK 2.769e+00
## Geothermal_electricity_net_generation_BKWH 1.173e+00
## Hydroelectric_pumped_storage_electricity_installed_capacity_MK 5.891e-01
## Hydroelectric_pumped_storage_electricity_net_generation_BKWH 9.096e-01
## Hydroelectricity_installed_capacity_MK 1.512e+00
## Hydroelectricity_net_generation_BKWH 5.684e-01
## Non.hydro_renewable_electricity_installed_capacity_MK 2.039e+00
## Non.hydro_renewable_electricity_net_generation_BKWH 1.378e+00
## Nuclear_electricity_installed_capacity_MK 1.081e+00
## Nuclear_electricity_net_generation_BKWH 3.464e-01
## Renewable_electricity_installed_capacity_MK 1.363e+00
## Renewable_electricity_net_generation_BKWH 5.370e-01
## Solar_electricity_installed_capacity_MK 2.042e+00
## Solar_electricity_net_generation_BKWH 1.256e+00
## Tide_and_wave_electricity_installed_capacity_MK 2.046e+01
## Tide_and_wave_electricity_net_generation_BKWH 7.069e+00
## Wind_electricity_installed_capacity_MK 2.364e+00
## Wind_electricity_net_generation_BKWH 1.425e+00
## t value Pr(>|t|)
## (Intercept) 155.434 <2e-16
## GDP_USD 2.481 0.0169
## Population 1.746 0.0876
## Bunker_fuel_consumption_TBPD 1.986 0.0531
## Bunker_residual_fuel_oil_consumption_TBPD -1.586 0.1198
## Crude_oil_including_lease_condensate_exports_TBPD -0.787 0.4356
## Crude_oil_including_lease_condensate_imports_TBPD 1.010 0.3180
## Crude_oil_including_lease_condensate_production_TBPD 0.563 0.5761
## Crude_oil_including_lease_condensate_reserves_BB 1.757 0.0857
## Distillate_fuel_oil_consumption_TBPD -0.889 0.3788
## Distillate_fuel_oil_production_TBPD -0.040 0.9686
## Jet_fuel_consumption_TBPD -0.963 0.3408
## Jet_fuel_production_TBPD -0.140 0.8891
## Kerosene_consumption_TBPD -1.030 0.3087
## Kerosene_production_TBPD -0.185 0.8541
## Liquefied_petroleum_gases_.LPG._consumption_TBPD -0.861 0.3939
## Liquefied_petroleum_gases_.LPG._production_TBPD -0.100 0.9204
## Motor_gasoline_consumption_TBPD -0.923 0.3611
## Motor_gasoline_production_TBPD -0.150 0.8817
## Natural_gas_plant_liquids_production_TBPD 0.540 0.5921
## Other_liquids_production_TBPD 0.539 0.5923
## Other_refined_products_consumption_TBPD -0.879 0.3838
## Other_refined_products_production_TBPD 0.016 0.9875
## Petroleum_and_other_liquids_CO2_emissions_MMTCD 1.672 0.1015
## Petroleum_and_other_liquids_consumption_TBPD 0.812 0.4212
## Petroleum_and_other_liquids_production_TBPD -0.556 0.5808
## Refined_petroleum_products_consumption_TBPD NA NA
## Refined_petroleum_products_production_TBPD 0.026 0.9794
## Refinery_processing_gain_TBPD 1.055 0.2972
## Residual_fuel_oil_consumption_TBPD -0.911 0.3674
## Residual_fuel_oil_production_TBPD 0.073 0.9419
## Biomass_and_waste_electricity_installed_capacity_MK -1.528 0.1335
## Biomass_and_waste_electricity_net_generation_BKWH 0.167 0.8682
## Electricity_distribution_losses_BKWH 0.025 0.9800
## Electricity_exports_BKWH -1.546 0.1290
## Electricity_imports_BKWH 1.578 0.1215
## Electricity_installed_capacity_MK 1.171 0.2478
## Electricity_net_consumption_BKWH 0.246 0.8068
## Electricity_net_generation_BKWH 0.798 0.4291
## Electricity_net_imports_BKWH -1.497 0.1415
## Fossil_fuels_electricity_installed_capacity_MK -1.046 0.3010
## Fossil_fuels_electricity_net_generation_BKWH -1.246 0.2193
## Geothermal_electricity_installed_capacity_MK -1.040 0.3041
## Geothermal_electricity_net_generation_BKWH 0.163 0.8709
## Hydroelectric_pumped_storage_electricity_installed_capacity_MK -1.541 0.1304
## Hydroelectric_pumped_storage_electricity_net_generation_BKWH -2.154 0.0367
## Hydroelectricity_installed_capacity_MK -0.359 0.7210
## Hydroelectricity_net_generation_BKWH -0.716 0.4778
## Non.hydro_renewable_electricity_installed_capacity_MK 1.166 0.2496
## Non.hydro_renewable_electricity_net_generation_BKWH -0.430 0.6694
## Nuclear_electricity_installed_capacity_MK -2.067 0.0445
## Nuclear_electricity_net_generation_BKWH -0.508 0.6139
## Renewable_electricity_installed_capacity_MK -0.047 0.9627
## Renewable_electricity_net_generation_BKWH 0.012 0.9905
## Solar_electricity_installed_capacity_MK -1.425 0.1609
## Solar_electricity_net_generation_BKWH 0.244 0.8081
## Tide_and_wave_electricity_installed_capacity_MK -0.540 0.5921
## Tide_and_wave_electricity_net_generation_BKWH 0.247 0.8061
## Wind_electricity_installed_capacity_MK -2.225 0.0311
## Wind_electricity_net_generation_BKWH 0.794 0.4314
##
## (Intercept) ***
## GDP_USD *
## Population .
## Bunker_fuel_consumption_TBPD .
## Bunker_residual_fuel_oil_consumption_TBPD
## Crude_oil_including_lease_condensate_exports_TBPD
## Crude_oil_including_lease_condensate_imports_TBPD
## Crude_oil_including_lease_condensate_production_TBPD
## Crude_oil_including_lease_condensate_reserves_BB .
## Distillate_fuel_oil_consumption_TBPD
## Distillate_fuel_oil_production_TBPD
## Jet_fuel_consumption_TBPD
## Jet_fuel_production_TBPD
## Kerosene_consumption_TBPD
## Kerosene_production_TBPD
## Liquefied_petroleum_gases_.LPG._consumption_TBPD
## Liquefied_petroleum_gases_.LPG._production_TBPD
## Motor_gasoline_consumption_TBPD
## Motor_gasoline_production_TBPD
## Natural_gas_plant_liquids_production_TBPD
## Other_liquids_production_TBPD
## Other_refined_products_consumption_TBPD
## Other_refined_products_production_TBPD
## Petroleum_and_other_liquids_CO2_emissions_MMTCD
## Petroleum_and_other_liquids_consumption_TBPD
## Petroleum_and_other_liquids_production_TBPD
## Refined_petroleum_products_consumption_TBPD
## Refined_petroleum_products_production_TBPD
## Refinery_processing_gain_TBPD
## Residual_fuel_oil_consumption_TBPD
## Residual_fuel_oil_production_TBPD
## Biomass_and_waste_electricity_installed_capacity_MK
## Biomass_and_waste_electricity_net_generation_BKWH
## Electricity_distribution_losses_BKWH
## Electricity_exports_BKWH
## Electricity_imports_BKWH
## Electricity_installed_capacity_MK
## Electricity_net_consumption_BKWH
## Electricity_net_generation_BKWH
## Electricity_net_imports_BKWH
## Fossil_fuels_electricity_installed_capacity_MK
## Fossil_fuels_electricity_net_generation_BKWH
## Geothermal_electricity_installed_capacity_MK
## Geothermal_electricity_net_generation_BKWH
## Hydroelectric_pumped_storage_electricity_installed_capacity_MK
## Hydroelectric_pumped_storage_electricity_net_generation_BKWH *
## Hydroelectricity_installed_capacity_MK
## Hydroelectricity_net_generation_BKWH
## Non.hydro_renewable_electricity_installed_capacity_MK
## Non.hydro_renewable_electricity_net_generation_BKWH
## Nuclear_electricity_installed_capacity_MK *
## Nuclear_electricity_net_generation_BKWH
## Renewable_electricity_installed_capacity_MK
## Renewable_electricity_net_generation_BKWH
## Solar_electricity_installed_capacity_MK
## Solar_electricity_net_generation_BKWH
## Tide_and_wave_electricity_installed_capacity_MK
## Tide_and_wave_electricity_net_generation_BKWH
## Wind_electricity_installed_capacity_MK *
## Wind_electricity_net_generation_BKWH
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6734 on 45 degrees of freedom
## Multiple R-squared: 0.9135, Adjusted R-squared: 0.802
## F-statistic: 8.194 on 58 and 45 DF, p-value: 1.433e-11# Gráfico de dispersión de residuos vs valores ajustados para verificar homocedasticidad
plot(modelo_log, which = 1)
# Gráfico Q-Q de los residuos para verificar normalidad
plot(modelo_log, which = 2)
En este caso el modelo si cumple 2 de los supuestos, en cuanto a normalidad en los residuales y la linealidad en la dispersion de residuos vs variables. Puesto no se observa de tendencia o estructura a lo largo de los valores de las variables explicativas vs residuales. Por otro lado, los residuos no se distancian de la diagonal. Sin embargo, no se evidencia homocedasticidad o varianza constante, hay una mayor dispersión en el extremo izquierdo.
Pregunta 5. \(w_5 = 10\)
Existen algoritmos de selección de variables como por ejemplo las
funciones en R stepAIC() o stepwise(). Ejecute
un procedimiento de selección de variables y verifique ahora las
propiedades del modelo parsimonioso.
“both”: Implica que stepAIC() evaluará tanto la adición como la eliminación de variables en el proceso de selección de variables, considerando qué variables mejorarán el modelo al ser agregadas y cuáles podrían perjudicar al ser eliminadas.
summary(modelo_seleccionado)##
## Call:
## lm(formula = Datos_filtrados$log_GDP_USD ~ GDP_USD + Population +
## Bunker_fuel_consumption_TBPD + Bunker_residual_fuel_oil_consumption_TBPD +
## Crude_oil_including_lease_condensate_imports_TBPD + Crude_oil_including_lease_condensate_production_TBPD +
## Crude_oil_including_lease_condensate_reserves_BB + Distillate_fuel_oil_consumption_TBPD +
## Distillate_fuel_oil_production_TBPD + Jet_fuel_consumption_TBPD +
## Jet_fuel_production_TBPD + Kerosene_consumption_TBPD + Kerosene_production_TBPD +
## Liquefied_petroleum_gases_.LPG._consumption_TBPD + Motor_gasoline_consumption_TBPD +
## Motor_gasoline_production_TBPD + Other_refined_products_consumption_TBPD +
## Petroleum_and_other_liquids_CO2_emissions_MMTCD + Petroleum_and_other_liquids_production_TBPD +
## Refined_petroleum_products_production_TBPD + Refinery_processing_gain_TBPD +
## Residual_fuel_oil_consumption_TBPD + Biomass_and_waste_electricity_installed_capacity_MK +
## Electricity_exports_BKWH + Electricity_imports_BKWH + Electricity_installed_capacity_MK +
## Electricity_net_consumption_BKWH + Electricity_net_generation_BKWH +
## Electricity_net_imports_BKWH + Fossil_fuels_electricity_installed_capacity_MK +
## Fossil_fuels_electricity_net_generation_BKWH + Geothermal_electricity_installed_capacity_MK +
## Hydroelectric_pumped_storage_electricity_installed_capacity_MK +
## Hydroelectric_pumped_storage_electricity_net_generation_BKWH +
## Hydroelectricity_installed_capacity_MK + Hydroelectricity_net_generation_BKWH +
## Non.hydro_renewable_electricity_installed_capacity_MK + Non.hydro_renewable_electricity_net_generation_BKWH +
## Nuclear_electricity_installed_capacity_MK + Solar_electricity_installed_capacity_MK +
## Tide_and_wave_electricity_installed_capacity_MK + Wind_electricity_installed_capacity_MK +
## Wind_electricity_net_generation_BKWH, data = Datos_filtrados[,
## variables_explicativas])
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.56939 -0.21027 -0.01185 0.21365 1.77946
##
## Coefficients:
## Estimate
## (Intercept) 2.391e+01
## GDP_USD 3.428e-12
## Population 9.420e-09
## Bunker_fuel_consumption_TBPD 3.639e-02
## Bunker_residual_fuel_oil_consumption_TBPD -3.983e-02
## Crude_oil_including_lease_condensate_imports_TBPD 1.580e-03
## Crude_oil_including_lease_condensate_production_TBPD 4.465e-03
## Crude_oil_including_lease_condensate_reserves_BB 9.989e-03
## Distillate_fuel_oil_consumption_TBPD -1.988e-02
## Distillate_fuel_oil_production_TBPD -9.477e-03
## Jet_fuel_consumption_TBPD -4.476e-02
## Jet_fuel_production_TBPD -1.824e-02
## Kerosene_consumption_TBPD -5.417e-02
## Kerosene_production_TBPD -3.007e-02
## Liquefied_petroleum_gases_.LPG._consumption_TBPD -1.436e-02
## Motor_gasoline_consumption_TBPD -2.542e-02
## Motor_gasoline_production_TBPD -1.945e-02
## Other_refined_products_consumption_TBPD -1.367e-02
## Petroleum_and_other_liquids_CO2_emissions_MMTCD 1.504e-01
## Petroleum_and_other_liquids_production_TBPD -3.699e-03
## Refined_petroleum_products_production_TBPD 7.749e-03
## Refinery_processing_gain_TBPD 1.039e-01
## Residual_fuel_oil_consumption_TBPD -2.571e-02
## Biomass_and_waste_electricity_installed_capacity_MK -3.252e+00
## Electricity_exports_BKWH -2.024e+00
## Electricity_imports_BKWH 2.022e+00
## Electricity_installed_capacity_MK 5.946e-01
## Electricity_net_consumption_BKWH 6.986e-02
## Electricity_net_generation_BKWH 1.808e-01
## Electricity_net_imports_BKWH -2.117e+00
## Fossil_fuels_electricity_installed_capacity_MK -5.383e-01
## Fossil_fuels_electricity_net_generation_BKWH -2.543e-01
## Geothermal_electricity_installed_capacity_MK -3.326e+00
## Hydroelectric_pumped_storage_electricity_installed_capacity_MK -8.444e-01
## Hydroelectric_pumped_storage_electricity_net_generation_BKWH -1.911e+00
## Hydroelectricity_installed_capacity_MK -5.332e-01
## Hydroelectricity_net_generation_BKWH -2.567e-01
## Non.hydro_renewable_electricity_installed_capacity_MK 2.442e+00
## Non.hydro_renewable_electricity_net_generation_BKWH -1.777e-01
## Nuclear_electricity_installed_capacity_MK -2.301e+00
## Solar_electricity_installed_capacity_MK -2.876e+00
## Tide_and_wave_electricity_installed_capacity_MK -8.814e+00
## Wind_electricity_installed_capacity_MK -5.703e+00
## Wind_electricity_net_generation_BKWH 1.035e+00
## Std. Error
## (Intercept) 1.242e-01
## GDP_USD 6.673e-13
## Population 3.094e-09
## Bunker_fuel_consumption_TBPD 1.022e-02
## Bunker_residual_fuel_oil_consumption_TBPD 1.296e-02
## Crude_oil_including_lease_condensate_imports_TBPD 1.129e-03
## Crude_oil_including_lease_condensate_production_TBPD 1.674e-03
## Crude_oil_including_lease_condensate_reserves_BB 4.407e-03
## Distillate_fuel_oil_consumption_TBPD 7.215e-03
## Distillate_fuel_oil_production_TBPD 7.329e-03
## Jet_fuel_consumption_TBPD 1.369e-02
## Jet_fuel_production_TBPD 1.225e-02
## Kerosene_consumption_TBPD 1.311e-02
## Kerosene_production_TBPD 9.565e-03
## Liquefied_petroleum_gases_.LPG._consumption_TBPD 5.218e-03
## Motor_gasoline_consumption_TBPD 6.970e-03
## Motor_gasoline_production_TBPD 7.840e-03
## Other_refined_products_consumption_TBPD 4.290e-03
## Petroleum_and_other_liquids_CO2_emissions_MMTCD 4.788e-02
## Petroleum_and_other_liquids_production_TBPD 1.585e-03
## Refined_petroleum_products_production_TBPD 3.653e-03
## Refinery_processing_gain_TBPD 5.595e-02
## Residual_fuel_oil_consumption_TBPD 9.741e-03
## Biomass_and_waste_electricity_installed_capacity_MK 1.372e+00
## Electricity_exports_BKWH 7.960e-01
## Electricity_imports_BKWH 7.888e-01
## Electricity_installed_capacity_MK 3.859e-01
## Electricity_net_consumption_BKWH 2.590e-02
## Electricity_net_generation_BKWH 9.017e-02
## Electricity_net_imports_BKWH 7.872e-01
## Fossil_fuels_electricity_installed_capacity_MK 3.879e-01
## Fossil_fuels_electricity_net_generation_BKWH 8.586e-02
## Geothermal_electricity_installed_capacity_MK 1.595e+00
## Hydroelectric_pumped_storage_electricity_installed_capacity_MK 4.233e-01
## Hydroelectric_pumped_storage_electricity_net_generation_BKWH 6.087e-01
## Hydroelectricity_installed_capacity_MK 3.835e-01
## Hydroelectricity_net_generation_BKWH 8.502e-02
## Non.hydro_renewable_electricity_installed_capacity_MK 1.417e+00
## Non.hydro_renewable_electricity_net_generation_BKWH 1.304e-01
## Nuclear_electricity_installed_capacity_MK 7.661e-01
## Solar_electricity_installed_capacity_MK 1.351e+00
## Tide_and_wave_electricity_installed_capacity_MK 4.860e+00
## Wind_electricity_installed_capacity_MK 1.675e+00
## Wind_electricity_net_generation_BKWH 2.193e-01
## t value Pr(>|t|)
## (Intercept) 192.511 < 2e-16
## GDP_USD 5.136 3.20e-06
## Population 3.045 0.003453
## Bunker_fuel_consumption_TBPD 3.561 0.000731
## Bunker_residual_fuel_oil_consumption_TBPD -3.072 0.003192
## Crude_oil_including_lease_condensate_imports_TBPD 1.399 0.167108
## Crude_oil_including_lease_condensate_production_TBPD 2.667 0.009833
## Crude_oil_including_lease_condensate_reserves_BB 2.267 0.027022
## Distillate_fuel_oil_consumption_TBPD -2.756 0.007749
## Distillate_fuel_oil_production_TBPD -1.293 0.200963
## Jet_fuel_consumption_TBPD -3.269 0.001788
## Jet_fuel_production_TBPD -1.488 0.141882
## Kerosene_consumption_TBPD -4.131 0.000114
## Kerosene_production_TBPD -3.143 0.002595
## Liquefied_petroleum_gases_.LPG._consumption_TBPD -2.753 0.007809
## Motor_gasoline_consumption_TBPD -3.648 0.000556
## Motor_gasoline_production_TBPD -2.480 0.015956
## Other_refined_products_consumption_TBPD -3.186 0.002287
## Petroleum_and_other_liquids_CO2_emissions_MMTCD 3.142 0.002610
## Petroleum_and_other_liquids_production_TBPD -2.334 0.022960
## Refined_petroleum_products_production_TBPD 2.121 0.038054
## Refinery_processing_gain_TBPD 1.858 0.068143
## Residual_fuel_oil_consumption_TBPD -2.639 0.010571
## Biomass_and_waste_electricity_installed_capacity_MK -2.371 0.020956
## Electricity_exports_BKWH -2.543 0.013592
## Electricity_imports_BKWH 2.563 0.012894
## Electricity_installed_capacity_MK 1.541 0.128586
## Electricity_net_consumption_BKWH 2.697 0.009065
## Electricity_net_generation_BKWH 2.006 0.049415
## Electricity_net_imports_BKWH -2.689 0.009254
## Fossil_fuels_electricity_installed_capacity_MK -1.388 0.170334
## Fossil_fuels_electricity_net_generation_BKWH -2.961 0.004382
## Geothermal_electricity_installed_capacity_MK -2.085 0.041378
## Hydroelectric_pumped_storage_electricity_installed_capacity_MK -1.995 0.050627
## Hydroelectric_pumped_storage_electricity_net_generation_BKWH -3.139 0.002631
## Hydroelectricity_installed_capacity_MK -1.390 0.169529
## Hydroelectricity_net_generation_BKWH -3.020 0.003711
## Non.hydro_renewable_electricity_installed_capacity_MK 1.724 0.089887
## Non.hydro_renewable_electricity_net_generation_BKWH -1.363 0.177939
## Nuclear_electricity_installed_capacity_MK -3.004 0.003884
## Solar_electricity_installed_capacity_MK -2.129 0.037388
## Tide_and_wave_electricity_installed_capacity_MK -1.814 0.074720
## Wind_electricity_installed_capacity_MK -3.405 0.001184
## Wind_electricity_net_generation_BKWH 4.718 1.47e-05
##
## (Intercept) ***
## GDP_USD ***
## Population **
## Bunker_fuel_consumption_TBPD ***
## Bunker_residual_fuel_oil_consumption_TBPD **
## Crude_oil_including_lease_condensate_imports_TBPD
## Crude_oil_including_lease_condensate_production_TBPD **
## Crude_oil_including_lease_condensate_reserves_BB *
## Distillate_fuel_oil_consumption_TBPD **
## Distillate_fuel_oil_production_TBPD
## Jet_fuel_consumption_TBPD **
## Jet_fuel_production_TBPD
## Kerosene_consumption_TBPD ***
## Kerosene_production_TBPD **
## Liquefied_petroleum_gases_.LPG._consumption_TBPD **
## Motor_gasoline_consumption_TBPD ***
## Motor_gasoline_production_TBPD *
## Other_refined_products_consumption_TBPD **
## Petroleum_and_other_liquids_CO2_emissions_MMTCD **
## Petroleum_and_other_liquids_production_TBPD *
## Refined_petroleum_products_production_TBPD *
## Refinery_processing_gain_TBPD .
## Residual_fuel_oil_consumption_TBPD *
## Biomass_and_waste_electricity_installed_capacity_MK *
## Electricity_exports_BKWH *
## Electricity_imports_BKWH *
## Electricity_installed_capacity_MK
## Electricity_net_consumption_BKWH **
## Electricity_net_generation_BKWH *
## Electricity_net_imports_BKWH **
## Fossil_fuels_electricity_installed_capacity_MK
## Fossil_fuels_electricity_net_generation_BKWH **
## Geothermal_electricity_installed_capacity_MK *
## Hydroelectric_pumped_storage_electricity_installed_capacity_MK .
## Hydroelectric_pumped_storage_electricity_net_generation_BKWH **
## Hydroelectricity_installed_capacity_MK
## Hydroelectricity_net_generation_BKWH **
## Non.hydro_renewable_electricity_installed_capacity_MK .
## Non.hydro_renewable_electricity_net_generation_BKWH
## Nuclear_electricity_installed_capacity_MK **
## Solar_electricity_installed_capacity_MK *
## Tide_and_wave_electricity_installed_capacity_MK .
## Wind_electricity_installed_capacity_MK **
## Wind_electricity_net_generation_BKWH ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6036 on 60 degrees of freedom
## Multiple R-squared: 0.9073, Adjusted R-squared: 0.8409
## F-statistic: 13.66 on 43 and 60 DF, p-value: < 2.2e-16Este modelo explica alrededor del 90.73% de la variabilidad observada en el PIB y se ha ajustado razonablemente bien a los datos. Los resultados muestran una cantidad significativa de variabilidad en el PIB explicada por las variables consideradas en el modelo.
Sin embargo, al validar los supuesto no se evidencia homocedasticidad,apesar de resaltar la normalidad en los residuales.
# Gráfico de dispersión de residuos vs valores ajustados para verificar homocedasticidad
plot(modelo_seleccionado, which = 1)
# Gráfico Q-Q de los residuos para verificar normalidad
plot(modelo_seleccionado, which = 2)
Regresión Logística
En el conjunto de datos Estacion3_Data_5min.csv cuenta
con información de una estacion meteorológica que miden las siguientes
variables:
- “Rad_Horiz”: Radiación horizontal
- “Rad_Plano_Incl”: Radiación en plano inclinado
- “Temperatura_PV_1”: Temperatura a una altura 1
- “Temperatura_PV_2”: Temperatura a una altura 2
- “Irradiacia1”: Irradiación 1
- “Irradiacia2”: Irradiación 2
- “WindSpeed”: Velocidad del viento
- “WindDirection”: Dirección del viento
- “AirTemperature”: Tempratura del aire
- “Rad_Horiz_Avg”: Radiación horizontal promedio
- “Rad_Plano_Incl_Avg”: Radiación en plano inclinado promedio
- “RelHumidity”: Humedad Relativa
- “RelAirPressure”: Presión de aire relativo
- “Presencia_Lluvia”: Presencia de lluvia (1) o no (0) en la zona
Datos <- read.csv("Datos_Meteorologicos.csv")
Datos<-as.data.frame(Datos)
str(Datos)## 'data.frame': 3088 obs. of 14 variables:
## $ Rad_Horiz : num 438 316 304 306 267 ...
## $ Rad_Plano_Incl : num 444 317 308 309 271 ...
## $ Temperatura_PV_1 : num 34.9 32.9 31.2 30.1 31.4 ...
## $ Temperatura_PV_2 : num 35.2 35.1 33.8 32.3 33.4 ...
## $ Irradiacia1 : num 496 494 502 459 552 ...
## $ Irradiacia2 : num 51.4 45.6 43.5 28.5 50.5 ...
## $ WindSpeed : num 1.5 0.6 2.1 1.3 1.5 1.5 1.2 1.2 1.7 1.2 ...
## $ WindDirection : num 153 165 131 134 91 ...
## $ AirTemperature : num 24.6 24.8 25 24.8 25.2 25.3 25 25.4 25.4 25.6 ...
## $ Rad_Horiz_Avg : num 451 358 318 307 276 ...
## $ Rad_Plano_Incl_Avg: num 456 359 320 312 279 ...
## $ RelHumidity : num 88.9 87.3 85.4 86.1 85.7 84.1 84.8 84.3 84.5 83.7 ...
## $ RelAirPressure : int 963 963 963 963 963 963 963 963 962 962 ...
## $ Presencia_Lluvia : int 0 0 0 0 0 0 0 0 0 0 ...Pregunta 6. \(w_6 = 6\)
Cree un modelo de regresión lineal con todas las variables en la base de datos
modelo_logistico <- glm(Presencia_Lluvia ~ ., data = Datos, family = binomial)
# Resumen del modelo
#options(scipen=999)
summary(modelo_logistico)##
## Call:
## glm(formula = Presencia_Lluvia ~ ., family = binomial, data = Datos)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -6.407e+01 4.364e+01 -1.468 0.142120
## Rad_Horiz 9.839e-03 8.498e-03 1.158 0.246930
## Rad_Plano_Incl -9.035e-03 8.185e-03 -1.104 0.269673
## Temperatura_PV_1 1.776e-02 4.951e-02 0.359 0.719818
## Temperatura_PV_2 2.138e-01 5.652e-02 3.783 0.000155 ***
## Irradiacia1 3.877e-03 1.443e-03 2.686 0.007231 **
## Irradiacia2 -5.708e-02 6.523e-03 -8.750 < 2e-16 ***
## WindSpeed 1.252e+00 9.769e-02 12.812 < 2e-16 ***
## WindDirection 1.142e-03 6.335e-04 1.802 0.071523 .
## AirTemperature -1.147e+00 1.100e-01 -10.424 < 2e-16 ***
## Rad_Horiz_Avg -2.268e-03 9.920e-03 -0.229 0.819178
## Rad_Plano_Incl_Avg 7.017e-03 9.660e-03 0.726 0.467616
## RelHumidity 3.094e-01 2.821e-02 10.970 < 2e-16 ***
## RelAirPressure 5.327e-02 4.553e-02 1.170 0.241968
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 3000.8 on 3087 degrees of freedom
## Residual deviance: 1845.1 on 3074 degrees of freedom
## AIC: 1873.1
##
## Number of Fisher Scoring iterations: 7Pregunta 7. \(w_7 = 10\)
Interprete los coeficientes asociados a todas las variables en el modelo
Un coeficiente positivo sugiere una asociación positiva con la variable Presencia de lluvia, mientras que un coeficiente negativo sugiere una asociación negativa.Al tomar la exponencial de los coeficientes, se obtiene el cambio multiplicativo en la probabilidad de la variable dependiente (Presnecia de lluvia) para un aumento unitario en la variable independiente
round(exp(coefficients(modelo_logistico )),digits = 4)## (Intercept) Rad_Horiz Rad_Plano_Incl Temperatura_PV_1
## 0.0000 1.0099 0.9910 1.0179
## Temperatura_PV_2 Irradiacia1 Irradiacia2 WindSpeed
## 1.2384 1.0039 0.9445 3.4962
## WindDirection AirTemperature Rad_Horiz_Avg Rad_Plano_Incl_Avg
## 1.0011 0.3177 0.9977 1.0070
## RelHumidity RelAirPressure
## 1.3627 1.0547En tal sentido:
*Temperatura_PV_2: Un aumento de una unidad en Temperatura a una altura 2 se asocia con un aumento del 21.38% en la probabilidad de presencia de lluvia.
*WindSpeed: Un aumento de una unidad en la Velocidad del viento se asocia con un aumento de 252.02% en la probabilidad de presencia de lluvia.
*AirTemperature: Un aumento de una unidad en la temperatura del aire se asocia con una disminución del 68.32% en la probabilidad de presencia de lluvia.
*Irradiacia2: Un aumento de una unidad en Irradiacia2 se asocia con una disminución del 5.84% en la probabilidad de presencia de lluvia.
*RelHumidity: Un aumento de una unidad en la humedad relativa se asocia con un aumento del 36.77% en la probabilidad de presencia de lluvia.
*WindDirection: La variable WindDirection tiene un coeficiente cercano a cero, lo que indica que su efecto puede no ser significativo en la predicción de la presencia de lluvia.
Pregunta 8. \(w_8 = 8\)
Realice un diagnóstico del modelo, verificando todos los supuestos vistos en clase
library(car)## Loading required package: carData##
## Attaching package: 'car'## The following object is masked from 'package:psych':
##
## logit## The following object is masked from 'package:dplyr':
##
## recode## The following object is masked from 'package:purrr':
##
## somevif(modelo_logistico)## Rad_Horiz Rad_Plano_Incl Temperatura_PV_1 Temperatura_PV_2
## 897.839561 864.661093 25.314992 32.375715
## Irradiacia1 Irradiacia2 WindSpeed WindDirection
## 4.578769 2.702864 1.389310 1.085315
## AirTemperature Rad_Horiz_Avg Rad_Plano_Incl_Avg RelHumidity
## 7.636503 1186.943110 1169.557633 8.140412
## RelAirPressure
## 1.551453El Valor de Inflación de la Varianza (VIF) mide cuánto se incrementa la varianza de un coeficiente debido a la multicolinealidad. Generalmente, se considera que un VIF mayor a 10 indica la presencia de multicolinealidad significativa.Los valores altos de VIF para Rad_Horiz, Rad_Plano_Incl, Rad_Horiz_Avg, y Rad_Plano_Incl_Avg (más de 10) indican una alta multicolinealidad entre estas variables y podrían afectar la interpretación de los coeficientes en el modelo logístico.
residuos <- residuals(modelo_logistico, type = "pearson")
residuos_deviance <- residuals(modelo_logistico, type = "deviance")
# Gráfico de residuos estandarizados contra los valores ajustados
plot(residuos/modelo_logistico$fitted.values, ylab = "Residuos estandarizados")
abline(h = 0, col = "red")
El gráfico de dispersión permite observar más residuos negativos que positivos, sin embargo, los puntos no se distribuyen de manera homogénea y se observa ningún patrón aparente que pudiera indicar un grado de dependencia entre las observaciones, por lo que se puede concluir que no se cumple el supuesto de independencia entre observaciones para el conjunto de datos.
Pregunta 9. \(w_9 = 20\)
Según las fallas de los modelos en el punto anterior, excluya las variables que estén presentando problemas con los supuestos de multicolinealidad y retire las observaciones que sean influyentes (distancia de cook superior a 0.005), calcule nuevamente el modelo, interprete los parámetros y realice el diagnóstico.
Finalmente concluya si el modelo está vez se puede usar o no.
library(car)
# Calcular VIF para identificar multicolinealidad
vif_values <- vif(modelo_logistico)
# Filtrar variables con VIF > 10 (umbral mayor)
variables_con_multicolinealidad <- names(vif_values[vif_values > 10])
# Crear un nuevo conjunto de datos excluyendo las variables con multicolinealidad
datos_sin_multicolinealidad <- Datos[, !colnames(Datos) %in% variables_con_multicolinealidad]
# Ajustar un nuevo modelo sin las variables con multicolinealidad
nuevo_modelo_sin_multicolinealidad <- glm(Presencia_Lluvia ~ ., data = datos_sin_multicolinealidad, family = binomial)
# Calcular la distancia de Cook para cada observación en el nuevo modelo
model_data <- augment(nuevo_modelo_sin_multicolinealidad)
model_data$cooksd <- cooks.distance(nuevo_modelo_sin_multicolinealidad)
# Filtrar las observaciones con distancia Cook > 0.005
observaciones_influyentes <- model_data %>% filter(cooksd > 0.005)
# Crear un nuevo conjunto de datos sin las observaciones influyentes
datos_sin_observaciones_influyentes <- anti_join(datos_sin_multicolinealidad, observaciones_influyentes, by = colnames(datos_sin_multicolinealidad))
# Ajustar un nuevo modelo con las observaciones no influyentes y sin variables de multicolinealidad
nuevo_modelo_final <- glm(Presencia_Lluvia ~ ., data = datos_sin_observaciones_influyentes, family = binomial)
# Verificar el resumen del nuevo modelo
summary(nuevo_modelo_final)##
## Call:
## glm(formula = Presencia_Lluvia ~ ., family = binomial, data = datos_sin_observaciones_influyentes)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.491e+02 4.280e+01 -5.821 5.87e-09 ***
## Irradiacia1 6.967e-03 1.514e-03 4.601 4.20e-06 ***
## Irradiacia2 -5.679e-02 6.786e-03 -8.368 < 2e-16 ***
## WindSpeed 1.680e+00 1.066e-01 15.756 < 2e-16 ***
## WindDirection 9.081e-04 6.562e-04 1.384 0.166
## AirTemperature -8.299e-01 1.044e-01 -7.950 1.87e-15 ***
## RelHumidity 2.051e-01 2.490e-02 8.236 < 2e-16 ***
## RelAirPressure 2.532e-01 4.485e-02 5.646 1.64e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 2891.8 on 3052 degrees of freedom
## Residual deviance: 1819.6 on 3045 degrees of freedom
## AIC: 1835.6
##
## Number of Fisher Scoring iterations: 7El modelo depurado ha mostrado un buen ajuste con una reducción considerable tanto en la deviance nula como en la deviance residual. La deviance representa la diferencia entre el modelo ajustado y un modelo que contiene solo el término constante. Una deviance más baja indica un mejor ajuste del modelo a los datos. En este caso, la reducción de la deviance es significativa, lo que sugiere que el nuevo modelo ha mejorado en la capacidad de ajustarse a los datos.
Además, observamos que los coeficientes estimados para las variables incluidas en el modelo son significativos en su mayoría. Las variables Irradiacia1, Irradiacia2, WindSpeed, AirTemperature, RelHumidity y RelAirPressure presentan coeficientes significativos, lo que indica que pueden estar contribuyendo de manera significativa a la predicción de la variable de respuesta (Presencia_Lluvia).
Por ejemplo, un incremento de una unidad en “Irradiacia1” se asocia con un aumento de 0.006967 en el logaritmo de la odds ratio del evento de Presencia_Lluvia. Esto representa un incremento de aproximadamente un 0.697% en la odds ratio de que ocurra “Presencia_Lluvia”. Por otroa lado un aumento en la velocidad del viento está relacionado con un incremento del 80.62% en la probabilidad de ocurrencia de “Presencia_Lluvia”, manteniendo las demás variables constantes en el modelo.
residuos <- residuals(nuevo_modelo_final, type = "pearson")
residuos_deviance <- residuals(nuevo_modelo_final, type = "deviance")
# Gráfico de residuos estandarizados contra los valores ajustados
plot(residuos/nuevo_modelo_final$fitted.values, ylab = "Residuos estandarizados")
abline(h = 0, col = "red")
El gráfico de dispersión permite observar más residuos negativos que positivos, ahora los puntos se distribuyen de manera homogénea y no se observa ningún patrón aparente que pudiera indicar un grado de dependencia entre las observaciones, por lo que se puede concluir que se cumple el supuesto de independencia entre observaciones para el conjunto de dato.
Pregunta 10. \(w_{10} = 6\)
Finalmente, calcule la bondad de ajuste y concluya sobre las propiedades de su modelo.
library(pROC)
# Predecir las probabilidades con el modelo
predicciones <- predict(nuevo_modelo_final, datos_sin_observaciones_influyentes, type = "response")
# Calcular la curva ROC y el AUC
roc_obj <- roc(datos_sin_observaciones_influyentes$Presencia_Lluvia, predicciones)## Setting levels: control = 0, case = 1## Setting direction: controls < cases# Gráfico ROC mejorado
plot(roc_obj, main = "Curva ROC - Modelo de Regresión Logística", col = "blue", lwd = 2, print.auc = TRUE, print.auc.cex = 1.5, print.thres = "best", print.thres.best.method = "closest.topleft")
# Agregar la diagonal de referencia (sin habilidad predictiva)
abline(a = 0, b = 1, lty = 2, col = "gray")
# Agregar leyenda
legend("bottomright", legend = paste("AUC =", round(auc(roc_obj), 4)), col = "blue", lwd = 2)
# Añadir etiquetas y líneas para resaltar el punto óptimo en la curva
coords <- coords(roc_obj, "best")
points(coords, pch = 19, col = "red")
abline(v = coords[1], h = coords[2], lty = 3, col = "red")
text(coords[1], coords[2], paste(" Mejor punto (", round(coords[1], 2), ",", round(coords[2], 2), ")", sep = ""), pos = 3, col = "red")
# Mostrar el valor del AUC en el gráficoEl AUC (Area Under the Curve) de la curva ROC es una medida que varía entre 0 y 1. Cuanto más cerca esté del valor máximo de 1, mejor será el rendimiento del modelo para clasificar las clases.En este caso un AUC de 0.8838 indica que el modelo tiene una capacidad bastante buena para distinguir entre las dos clases (0 y 1). Con un AUC de 0.8838, se puede decir que el modelo tiene una sólida capacidad para diferenciar entre las observaciones que representan la presencia y ausencia de lluvia en los datos.