En Beijin y gran parte de China se esta experimentando una contaminación crónica del aire. Esto es de interés general ya que siendo la primer potencia económica del mundo establece estándares que repercuten en el mundo entero.
PM2.5 consiste en particulas que se encuentran el el aire con diametros menor a 2.5. Influye en la visibilidad, salud publica y el clima. Evidencia empidemiológica muestra que una exposición al PM2.5 puede causar morbilidad pulmonar, serios problemas respiratorios, al igual que problemas cardiovasculares, incluso la muerte.
Se ha descubierto que las condiciones metereológicas, aereosoles secundarios, emisiones locales y el transporte regional son los principales factores que contribuyen a la formación de PM2.5 en Beijing. También hay factores que no pueden ser ignorados al momento de analizar este tema, ya que la variabilidad en los patrones de distribución y transmision de PM2.5 se confunden con condiciones metereológcas, emisiones quimicas, etc.
Debido a esta variabilidad en las condiciones climatologicas, se cree que para realizar un análisis eficiente se ocupa un dataset con la longitud suficiente y una alta frecuencia temporal para generar una evaluación confiable del patron y tendencia, en gravedad y cantidad, de la contaminación del aire.
Para realizar este análisis se cuenta con un dataset generado por Song Xi Chen, de Guanghua School of Management, Center for Statistical Science, Univesidad de Peking [1].
En este trabajo se pretende responder a la siguiente pregunta:
El dataset se compone de 43825 observaciones con 13 características. Recopilando información de lecturas u observaciones realizadas del 2010 a 2015.
data<- read.csv("~/Documents/MCPI/Estadistica/Tarea Final/datasets/PRSA_data_2010.1.1-2014.12.31.csv", header=FALSE)
summary(data)
## V1 V2 V3 V4
## 1 : 1 2010:8760 1 : 3720 1 : 1440
## 10 : 1 2011:8760 10 : 3720 10 : 1440
## 100 : 1 2012:8784 12 : 3720 11 : 1440
## 1000 : 1 2013:8760 3 : 3720 12 : 1440
## 10000 : 1 2014:8760 5 : 3720 13 : 1440
## 10001 : 1 year: 1 7 : 3720 14 : 1440
## (Other):43819 (Other):21505 (Other):35185
## V5 V6 V7 V8
## 0 : 1826 16 : 626 18 : 1323 24 : 1566
## 1 : 1826 11 : 596 17 : 1294 23 : 1538
## 10 : 1826 13 : 589 19 : 1290 22 : 1433
## 11 : 1826 12 : 578 16 : 1238 21 : 1400
## 12 : 1826 17 : 572 20 : 1219 25 : 1397
## 13 : 1826 (Other):38797 15 : 1162 20 : 1364
## (Other):32869 NA's : 2067 (Other):36299 (Other):35127
## V9 V10 V11 V12
## 1014 : 1504 cbwd: 1 0.89 : 6266 0 :43456
## 1006 : 1445 cv : 9387 1.79 : 4807 1 : 66
## 1013 : 1443 NE : 4997 3.13 : 1932 2 : 46
## 1012 : 1382 NW :14150 1.78 : 1836 3 : 37
## 1025 : 1375 SE :15290 4.92 : 1251 4 : 31
## 1015 : 1374 3.58 : 1197 5 : 27
## (Other):35302 (Other):26536 (Other): 162
## V13
## 0 :42016
## 1 : 529
## 2 : 316
## 3 : 214
## 4 : 136
## 5 : 113
## (Other): 501
Como puede observarse este dataset tiene varias filas con elementos NA y además todas las variables están asignadas como factor por lo que se realizó un preprocesamiento del dataset para eliminar las observaciones incompletas que tengan NA asignados. Las caracteristicas No, Month, day, hour, PM2.5, DEWP, TEMP, PRES, Iws, Is e Ir se asignaron como númericas. Después de este preprocesamiento el dataset quedó con 41757 observaciones.
knitr::kable(head(data[1:11,1:13]), format="markdown")
| No | year | month | day | hour | pm2.5 | DEWP | TEMP | PRES | cbwd | Iws | Is | Ir | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 26 | 25 | 2010 | 1 | 2 | 0 | 129 | -16 | -4 | 1020 | SE | 1.79 | 0 | 0 |
| 27 | 26 | 2010 | 1 | 2 | 1 | 148 | -15 | -4 | 1020 | SE | 2.68 | 0 | 0 |
| 28 | 27 | 2010 | 1 | 2 | 2 | 159 | -11 | -5 | 1021 | SE | 3.57 | 0 | 0 |
| 29 | 28 | 2010 | 1 | 2 | 3 | 181 | -7 | -5 | 1022 | SE | 5.36 | 1 | 0 |
| 30 | 29 | 2010 | 1 | 2 | 4 | 138 | -7 | -5 | 1022 | SE | 6.25 | 2 | 0 |
| 31 | 30 | 2010 | 1 | 2 | 5 | 109 | -7 | -6 | 1022 | SE | 7.14 | 3 | 0 |
A continuación se describen las 13 características:
El tipo de dato de las observaciones y su contenido se describe a continuación:
## 'data.frame': 41757 obs. of 13 variables:
## $ No : num 25 26 27 28 29 30 31 32 33 34 ...
## $ year : Factor w/ 6 levels "2010","2011",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ month: num 1 1 1 1 1 1 1 1 1 1 ...
## $ day : num 2 2 2 2 2 2 2 2 2 2 ...
## $ hour : num 0 1 2 3 4 5 6 7 8 9 ...
## $ pm2.5: num 129 148 159 181 138 109 105 124 120 132 ...
## $ DEWP : num -16 -15 -11 -7 -7 -7 -7 -7 -8 -7 ...
## $ TEMP : num -4 -4 -5 -5 -5 -6 -6 -5 -6 -5 ...
## $ PRES : num 1020 1020 1021 1022 1022 ...
## $ cbwd : Factor w/ 5 levels "cbwd","cv","NE",..: 5 5 5 5 5 5 5 5 5 5 ...
## $ Iws : num 1.79 2.68 3.57 5.36 6.25 ...
## $ Is : num 0 0 0 1 2 3 4 0 0 0 ...
## $ Ir : num 0 0 0 0 0 0 0 0 0 0 ...
Como puede observarse las caracteristicas No, Month, day, hour, PM2.5, DEWP, TEMP, PRES, Iws, Is e Ir se asignaron como númericas. Esto nos permitirá analizar las variables con herramientas de tendencia central, la correlación entre ellas y llegar a un modelo que describa el fenómeno de la inluencia de las variables metereológicas en relación a las particulas contaminantes PM2.5.
Este tipo de herramientas estadísticas ayudarán el en la comprensión del comportamiento del fenónmeno de la contaminación del aire.
## No month day hour
## Min. : 25 Min. : 1.000 Min. : 1.00 Min. : 0.0
## 1st Qu.:11464 1st Qu.: 4.000 1st Qu.: 8.00 1st Qu.: 5.0
## Median :22435 Median : 7.000 Median :16.00 Median :12.0
## Mean :22279 Mean : 6.514 Mean :15.69 Mean :11.5
## 3rd Qu.:33262 3rd Qu.:10.000 3rd Qu.:23.00 3rd Qu.:18.0
## Max. :43824 Max. :12.000 Max. :31.00 Max. :23.0
## pm2.5 DEWP TEMP PRES
## Min. : 0.00 Min. :-40.00 Min. :-19.0 Min. : 991
## 1st Qu.: 29.00 1st Qu.:-10.00 1st Qu.: 2.0 1st Qu.:1008
## Median : 72.00 Median : 2.00 Median : 14.0 Median :1016
## Mean : 98.61 Mean : 1.75 Mean : 12.4 Mean :1016
## 3rd Qu.:137.00 3rd Qu.: 15.00 3rd Qu.: 23.0 3rd Qu.:1025
## Max. :994.00 Max. : 28.00 Max. : 42.0 Max. :1046
## Iws Is Ir
## Min. : 0.45 Min. : 0.00000 Min. : 0.0000
## 1st Qu.: 1.79 1st Qu.: 0.00000 1st Qu.: 0.0000
## Median : 5.37 Median : 0.00000 Median : 0.0000
## Mean : 23.87 Mean : 0.05534 Mean : 0.1949
## 3rd Qu.: 21.91 3rd Qu.: 0.00000 3rd Qu.: 0.0000
## Max. :565.49 Max. :27.00000 Max. :36.0000
El factor que más nos interesa es ver como se comporta es ver el comportamiento de las particulas PM2.5 como puede obaservarse con una media en 98.61 y calculando la desviación estándar que resulta en 92.05039 y una varianza de 8473.274 se puede observar que los datos no tenderán a tener una distribución uniforme por lo que se analizará más a detalle esta variable.
A continuación se muestra el comportamiento de las muestras en el periodo que comprende del año 2010 al año 2015,
Como puede observarse en los gráficos de arriba el comportamiento por año de la presencia de particulas contaminantes PM2.5 en Bejing y su alrededores es relativamente parecida, lo que pude destacarse que en la tendencia baja en los meses cercanos a verano y en invierno sube la presencia de estas partículas. Esto es claro ínidice que en efecto, las variables metereológicas can a tener influencia en un modelo que intente predecir la candtidad de particulas PM2.5 en el aíre.
Para llegar a este modelo es conveniente también corroborar la distribución de esta variable y así analizar que tanto la incidencia de las cantidades en el aíre es determinada por un comportamiento lineal, con lo que se podrá analizar la convencia de un modelo lineal.
Como se puede observar en la figura anterior se muestra que la distribucion no tiene una forma gaussiana uniforme, por lo que que se es probable que modelo lineal no describa correctamente el fenómeno.
El estadístico paramétrico Coeficiente de Correlación de Pearson es adecuada cuando las observaciones de unidades maestreadas aleatoriamente, están medidas en escalas de intervalos [3]. mediante este parámetro se busca estimar la relación entre las variables metereológicas la precencia de partículas PM2.5.
## corrplot 0.84 loaded
Este gráfico muestra poca correlación de las partículas PM2.5 respecto a otras características. Pero se analizarán las variables o características DEWP, TEMP, mont, hour, Ir y pm2.5 para ver si se puede llegar a un modelo para predecir el comportamiento.
## Loading required package: xts
## Loading required package: zoo
##
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric
##
## Attaching package: 'PerformanceAnalytics'
## The following object is masked from 'package:graphics':
##
## legend
Estos gráficos muestran que efectivamente la cantidad de partículas PM2.5 no estan muy correlacionadas con los factores metereológicos por lo que es probable que con un modelo de regresión lineal no se describa en forma correcta el fenómeno.
Se implementará un modelo de regresión lineal de tal manera que se modele la presencia de partículas PM2.5 usando las características temperatura, temperatura de punto de rocío, mes, hora, horas acumuladas de lluvia y de nieve. A continuación se muestra el modelo resultante:
# Modelo regresión multiple
model <- lm(pm2.5 ~ TEMP + DEWP +month + Ir + hour + Is , data = data)
summary(model)
##
## Call:
## lm(formula = pm2.5 ~ TEMP + DEWP + month + Ir + hour + Is, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -166.35 -54.17 -16.39 34.20 891.20
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 164.20788 1.19822 137.043 < 2e-16 ***
## TEMP -6.15556 0.06080 -101.237 < 2e-16 ***
## DEWP 5.60396 0.05152 108.771 < 2e-16 ***
## month -2.33091 0.11812 -19.733 < 2e-16 ***
## Ir -7.59930 0.28254 -26.896 < 2e-16 ***
## hour 1.54921 0.05986 25.880 < 2e-16 ***
## Is -3.96792 0.51296 -7.735 1.05e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 80.83 on 41750 degrees of freedom
## Multiple R-squared: 0.2291, Adjusted R-squared: 0.229
## F-statistic: 2068 on 6 and 41750 DF, p-value: < 2.2e-16
Podemos ver por el p-value que todas las características que se utilizaron para este modelado resultaron ser significativas para la descripción de la variable dependiente, en este caso la cantidad de particulas PM2.5 en el aire. Con el valor error residual de 80.83 es capaz este modelo de describir lo datos pero hay que evaluar el modelo para validar la forma en que describe el modelado de la cantidad de partíclas PM2.5 a partir de las características metereológicas.
En la gráfica donde se imprimieron los Fitted values contra Residuals se puede ver que los datos no presentan homosteacidad ya que al estar difiriendo la dispersión de los datos respecto a la linea. Al encontrarse con perturbaciones heteroscedásticas se comprueba que un modelo lineal no es ideal para describir este fenómeno.
En la gráfica Normal Q-Q podemos ver que efectivamente como ya se había demostrado, los datos no siguen una distribución normal ya que los valores residuales no se ajustan a la recta.
En el gráfico Scale-Location podemos ver nuevamente que el modelo no presenta homoesticidad, los residuos no estan igualmente esparcidos en los rangos de predicción.
En la gráfica Residuals vs Leverage podemos ver que en caso de tomarse como bueno el modelo los outliers no influyen en el modelado.
A pesar de que el modelo lineal demostró no ser eficiente en la descripción del fenómeno, se evaluara un modelo lineal usando solo la variable que más esta correlacionada con la característica de interés, para llegar a la probabilidad en la cantidad de particulas PM2.5 debido a un valor dado de DEWP (temperatura del punto de rocío).
##
## Attaching package: 'cowplot'
## The following object is masked from 'package:ggplot2':
##
## ggsave
## DEWP
## pm2.5 -40 -39 -38 -37 -36 -35 -34 -33 -32 -31 -30 -29 -28 -27 -26 -25 -24
## 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 2 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0
## 3 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0
## 4 0 1 0 0 0 0 0 1 1 0 1 0 2 1 0 2 0
## 5 0 0 0 0 0 0 0 1 0 0 1 1 1 2 1 1 1
## 6 1 0 2 1 2 0 1 3 5 1 2 1 1 1 2 2 2
## 7 0 0 0 0 1 1 1 0 1 1 2 3 3 2 6 3 5
## 8 0 0 0 1 0 1 1 1 1 0 1 3 3 3 2 5 6
## 9 0 0 0 0 0 0 1 2 2 2 1 3 7 9 6 14 20
## 10 0 0 0 1 0 2 0 1 2 0 0 5 6 10 5 7 15
## 11 0 0 0 0 0 0 0 3 0 1 0 2 2 11 8 14 15
## 12 0 0 0 0 0 0 1 0 1 0 2 3 5 9 5 16 16
## 13 0 0 0 0 0 0 0 1 1 0 2 2 7 8 10 19 16
## 14 0 0 0 0 0 0 0 0 1 0 1 0 2 7 10 13 17
## 15 0 0 0 0 0 0 0 0 0 0 1 0 4 5 7 7 13
## 16 0 0 0 0 0 0 0 0 1 0 0 0 3 9 9 8 17
## 17 0 0 0 0 0 0 0 0 0 1 1 0 6 3 9 10 13
## 18 0 0 0 0 0 0 0 1 0 0 0 0 3 2 4 11 14
## 19 0 0 0 0 0 0 0 0 0 0 0 0 5 5 3 3 5
## 20 0 0 0 0 0 0 0 0 0 0 0 0 5 2 9 1 12
## 21 0 0 0 0 0 0 0 0 0 0 0 1 2 3 8 4 6
## 22 0 0 0 0 0 0 0 0 0 0 0 0 1 1 7 6 2
## 23 0 0 0 0 0 0 0 0 0 0 1 1 0 3 6 5 8
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## [1] -1.043804
## [1] 1.273667
## numeric(0)
## numeric(0)
## numeric(0)
## numeric(0)
## numeric(0)
En este gráfico se puede ver la probabilidad de prediccion de la cantidad de particulas en el aire PM2.5 debido a la caracteristica más correlacionada DEWP, se puede observar nuevamente que el comportamiento no es lineal. Comprobando que este fenómeno no será correctamente descrito con un modelado lineal.
Respondiendo a la primera de las preguntas planteadas el análisis que se hizo utilizando medidas de tendencia central muestra que el comportamiento en el volumen de partículas PM2.5 en realidad esta influenciado por variables climatologicas ya que en los meses cercanos a verano la tendencia era a disminuir el volumen y el comportamiento se presentaba inverso en los meses de invierno.
Respondiendo a la segunda de las preguntas planteadas puede observarse la determinación de establecer una relación de las partículas PM2.5 presentes en el aire no estan relacionadas linealmente por las variables metereológicas medidas en el dataset. Esto puede ser no por que no tengan relación si no por que como se vio, no presentan Homoestacidad por lo que no tienen una distribución normal por lo que hacer un modelo de predicción lineal no es eficiente ya que no describe el fenómeno. Como trabajo por hacer es realizar un modelado no lineal para determinar un posible modelo de predicción de cantidad de partículas PM2.5 en relación con las condiciones metereológicas
El dataset tampoco se presta para hacer una clasificación ya que los valores que se encuentran en la mayoría de las características de interes tienen extensos valores únicos.
[1] Beijing PM2.5 Data Data Set.Xi Chen, de Guanghua School of Management, Center for Statistical Science, Univesidad de Peking. Consultado: enero 2019. http://archive.ics.uci.edu/ml/datasets/Beijing+PM2.5+Data
[2] Liang, X., Zou, T., Guo, B., Li, S., Zhang, H., Zhang, S., Huang, H. and Chen, S. X. (2015). Assessing Beijing’s PM2.5 pollution: severity, weather impact, APEC and winter heating. Proceedings of the Royal Society A, 471, 20150257.
[3] Correlación y Regresión Lineal. Consultado en enero del 2019: https://rpubs.com/osoramirez/316691