Introducción

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:

  1. ¿Cómo influeyen las condiciones metereológicas en la concentración de particulas contaminantes PM2.5?
  2. ¿Se puede determinar una relación o aproximación de la concentración de PM2.5 respecto a las condiciones metereológicas con un modelo de regresión lineal?

Descripción de dataset

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

Características

A continuación se describen las 13 características:

  1. No: número de obsrvación. Cuantitativas, numericas, variable discreta.
  2. year: año que se tomó la observación. Cualitativa.
  3. month: mes que se tomó la observación. Cuantitativas, numericas, variable discreta.
  4. day: día que se tomó la observación. Cuantitativas, numericas, variable discreta.
  5. hour: hora que se tomó la observación. Cuantitativas, numericas, variable discreta.
  6. pm2.5: Concentración de PM2.5 (ug/m^3). Cuantitativas, numericas, variable continua.
  7. DEWP: Temperatura del punto de rocío. Cuantitativas, numericas, variable continua.
  8. TEMP: Temperatura. Cuantitativas, numericas, variable continua.
  9. PRES: Presión (hPa). Cuantitativas, numericas, variable continua.
  10. cbwd: Dirección combinada del viento. Cualitativa.
  11. Iws: Velocidad acumulada del viento (m/s). Cuantitativas, numericas, variable continua.
  12. Is: Horas acumuladas de nieve. Cuantitativas, numericas, variable discreta.
  13. Ir: Horas acumuladas de lluvia. Cuantitativas, numericas, variable discreta.

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.

Descripción de dataset usando medidas de tendencia central

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.

Correlación de características

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.

Correlación de variables más correlacionadas

## 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.

Modelo

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.

Evaluación del modelo

  • 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.

Regresión lineal usando la caracteristica DEWP (la más correlacionada)

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
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##   23    0   0   0   0   0   0   0   0   0   0   1   1   0   3   6   5   8
##   24    0   0   0   0   0   0   0   0   0   0   0   0   1   0   4   3  10
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##   495   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   496   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   498   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   499   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   500   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   501   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   502   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   503   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   504   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   505   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   506   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   507   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   508   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   510   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   512   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   513   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   514   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   515   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   516   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   517   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   519   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   521   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   522   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   523   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   524   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   525   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   526   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   527   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   528   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   529   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   532   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   534   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   535   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   539   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   540   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   541   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   542   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   545   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   548   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   551   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   557   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   558   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   559   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   562   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   563   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   567   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   569   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   570   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   573   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   577   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   579   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   580   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   584   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   587   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   595   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   599   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   603   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   607   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   611   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   615   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   618   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   623   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   648   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   649   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   651   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   659   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   671   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   673   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   684   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   700   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   722   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   731   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   744   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   761   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   776   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   784   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   802   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   805   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   810   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   824   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   845   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   852   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   858   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   886   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   972   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1
##   980   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   994   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1
##      DEWP
## pm2.5 -23 -22 -21 -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6
##   0     0   0   0   0   0   0   0   0   0   0   0   0   0   1  0  0  0  0
##   1     0   0   0   0   0   0   0   0   0   0   0   0   0   0  1  1  0  0
##   2     0   0   0   0   0   0   0   1   1   0   0   0   0   1  0  1  0  1
##   3     1   0   1   0   2   0   0   2   1   1   0   0   2   0  1  2  1  0
##   4     0   1   1   2   5   2   1   0   2   1   3   0   0   3  0  2  3  1
##   5     2   3   0   5   1   1   2   2   6   1   2   2   1   0  0  1  4  6
##   6     0   8  12  11   5   9   3  10   4   3   5   4  11   4  4  6  6  2
##   7     4   7  13  10   9  16  10  10   5   7   8  13  10   2  3  3  9  2
##   8    11  21  13  20  12  18  15  10   9  18   6  15  11   4  8 11  7  4
##   9    20  26  23  17  17  10  18  22  21  14  13  12  11  10 12 11  7  5
##   10   18  24  20  17  11  20  15  22  16  19  14  19  15  11 11 22  4  6
##   11   17  31  26  31  20  25  18  24  25  20  14  21  17  13  8  8 10  7
##   12   20  29  26  25  29  27  26  21  20  18  16  12  13   8  7  9  8  6
##   13   29  29  28  33  25  18  24  28  21  12  20  17  11   8  9  6  7  3
##   14   11  23  21  26  26  30  24  24  17  12  11   9  14  15  2  5  8  4
##   15   18  24  11  21  21  23  17  21  20  19  12  11  15   6  7  9 10  9
##   16   31  27  26  28  31  27  32  29  22  15  19  13   6   8 11 14  6  5
##   17   28  20  17  29  31  29  26  29  21  17  10  13  14   7  7  8  7  7
##   18   20  13  26  30  31  17  17  18  15  14  13  10  12   3  4  6  6  7
##   19   19  22  19  16  18  27  12  14  17  11  14   5   9   9  3  8  3  2
##   20   17  13  20  17  16  20  20  12  18   8  13  10   5   5  1  7  6  3
##   21   12  17  23  16  19  15  11  18   8   5  13  11   5  10  2  7  2  7
##   22   10  16  12   9  17  18  12   5  16  16   8  16   9   4  4  6  4  4
##   23    6  10  14  18  16  15  11   9  15   8   4   8   6   4  4  7  6  4
##   24   12   8  12  12  11  13   9  13   9   8   7   7   8   7  4  3  3  4
##   25    7  15   7   8  10  14  13   7   8   8   6   5   3   7  4  8  7  5
##   26    5  16  12   6   8  12  14  11   6   8   5   8   6   5  4  6  5  6
##   27    9  19   7  14  14   7  13  14  13  11  11  17   9   7  2  8  9  6
##   28    1   6   6   4  11   6   3   5   7   8   7   5   3   5  4  5  2  5
##   29    5   6   8   6   7   6  11   9   5   1   9   7   3   8  3 10  2 10
##   30    3   3  10  10   8   9   4   6   3   7   5  10   2   5  4  0  2  1
##   31    3   4   5   4   7   8   7   6   5   6   2   4   6   9  9  5  4  4
##   32    5   4   6   4   3   9   8   3   7   5   6   9   8   4  2  7  5  4
##   33    4   5   8  10   8   4   3  12   6   7   4   5   4   2  4  2  4  3
##   34    5   4   7   1   6   6   5   7   9   3   3   5   4   5  7  7  4  4
##   35    1   4   2   2   2   6   5   7   8   4   6   4   8   2  5  5  8  1
##   36    4  11   8   2   8   6   8   7   4   2   5   4   7   4  4  1  6  3
##   37    3   8   7   3   4   5  12   3   7   2   6   5   7   5  3  5  1  1
##   38    0   3   3   3   4   6   5   6   6  10   5   7   5   5  3  4  8  5
##   39    2   5   5   3   5   9   3   8   1   7   3   3   7   4  4  5  5  9
##   40    2   5   5   5   5   9   8   4   4   9   5   3   4   7  4  6  6  4
##   41    3   4   6   3   7   6   5   5   4   6   5   6   5   5  3  6  3  6
##   42    1   5   3   4   6   6   3   5   6   5   4   4   5   3  3  6  2  2
##   43    3   4   8   3   6   8   5   5   2   2   6   7   6   3  3  6  5  5
##   44    0   1   1   5   7   4   5   4   3   4   3   3   3   5  2  6  4  6
##   45    1   5   6   3   4   4   4   2   4   2   3   6   8   4  4  3  3 11
##   46    0   2   0   3   8   7   8   6   5   6   3   4   7   8  4  4  5  5
##   47    2   5   2   3   6   8   5   6   6   2   2   4   7   2  9  3  4  5
##   48    1   5   2   3   5   6   3   7   7   3   5   2   1   2  6  8  3  6
##   49    0   9   3   4   4   5  11   2   3   7   4   7   3   6  8  4  5  5
##   50    1   5   4   1   6   1   3   7   4   6   4   2   2   7  5  6  7  2
##   51    1   4   4   3   6   4   4   3   2   4   4   5   7   5  7  1  1  2
##   52    4   3   1   9   3   2   3   3   3   5   4   5   3   2  5  8  7 11
##   53    0   1   1   4   4   3   4  10   4   4   3   4   5   3  6  9  2  4
##   54    2   0   0   4   6   2   5   0   3   5   3   8   6   2  4  7  4  1
##   55    1   0   3   3   5   6   4   2   2   3   4   3   4   7  6  5  8  9
##   56    2   2   2   3   5   6   1   3   1   4   3   6   4   1  4  3  2  5
##   57    1   2   1   1   2   2   2   5   3   6   3   3   2   6  3  6  4  2
##   58    2   2   0   1   4   6   3   2   5   4   2   3   4   4  4  3  2  3
##   59    3   3   2   4   5   1   0   3   3   3   3   4   4   5  3  6  7  7
##   60    3   3   2   1   2   4   1   6   0   5   3   4   5   2  3  4  4  7
##   61    4   0   3   1   5   2   5   5   3   4   3   2   4   5  3  6  0  4
##   62    0   1   3   0   2   2   4   1   2   6   2   2   2   9  2  4 11  3
##   63    1   2   0   1   3   2   1   1   8   8   3   7   6   6  6  4  5  5
##   64    2   1   2   4   3   3   2   3   4   4   4   6   2   5  1  6  4  3
##   65    0   0   1   1   2   8   1   5   4   4   2   3   6   5  4  7  3  2
##   66    2   5   0   5   2   2  10   3   7   3   3   4   2   2  3  6  6  7
##   67    2   0   1   4   2   9   1   1   5   5   5   2   4   3  7  1  2  5
##   68    2   0   0   1   1   4   2   4   3   5   6   4   1   4  4  5  2  5
##   69    3   0   2   3   8   2   2   7   3   3   8  10   6   7  2  7  3  3
##   70    0   1   2   4   3   5   1   4   5   5   1   7   5   6  3  3  6  4
##   71    0   1   2   3   2   7   1   6   5   4   3   6   4   7  6  4  5  3
##   72    1   0   0   3   4   4   3   2   4   3   7   4   6   8  5  4  6  4
##   73    0   2   3   3   3   2   3   5   3   7   5   4   5  12  1  3  1  4
##   74    0   1   2   0   5   7   0   1   2   3   5   2   6   4  3  5  3  4
##   75    1   1   1   2   1   4   4   1   2   6   1   6   2   5  7  2  4  4
##   76    1   0   0   1   4   1   1   5   4   0   3   5   5   4  9  1  2  5
##   77    0   0   0   3   3   4   3   2   3   2   6   4   7   4  3  2  3  5
##   78    0   0   1   1   6   3   2   3   4   7   3   6   6   4  2  2  4  5
##   79    2   2   2   0   6   1   2   7   2   2   5   4   4   9  5  2  7  3
##   80    1   1   1   2   3   1   2   2   3   2   5   6   5   3  4  4  3  4
##   81    0   1   1   1   1   2   1   4   2   2   6   6   1   5  3  2  5  4
##   82    1   2   1   1   3   0   4   0   2   1   3  11   3   2  6  3  5  3
##   83    0   0   1   2   2   0   3   2   4   2   1   1   4   1  7  6  2  2
##   84    0   2   0   1   2   6   3   2   3   5   3   7   1   6  1  5  0  5
##   85    1   2   1   0   2   5   1   0   3   5   2   5   3   2  1  6  2  4
##   86    0   0   0   1   2   0   4   3   1   3   1   1   4   6  1  2  6  4
##   87    0   0   0   5   2   5   5   4   3   3   2   4   6   2  5  1  4  6
##   88    3   1   1   1   2   2   4   2   4   1   1   4   5   3  2  2  3  5
##   89    0   1   2   1   1   3   4   1   3   3   4   2   3   5  2  4  6  4
##   90    0   0   0   0   2   2   2   1   5   3   6   7   3   2  5  2  9  8
##   91    0   1   0   3   5   1   3   1   2   1   4   4   3   5  3  0  5  3
##   92    1   0   0   1   2   2   1   5   1   3   2   4   4   4  1  3  2  3
##   93    0   1   1   0   2   1   3   3   2   2   4   2   6   3  2  6  7  4
##   94    0   1   1   0   1   2   1   2   2   4   1   2   4   2  1  0  5  3
##   95    0   0   2   3   7   6   2   0   3   3   4   3   4   2  2  2  5  2
##   96    1   2   0   2   2   1   3   5   1   4   2   1   6   2  4  4  6  5
##   97    1   0   1   1   4   1   0   2   0   0   7   2   2   5  3  4  6  0
##   98    0   0   1   0   1   0   1   2   2   2   1   2   1   4  6  4  4  5
##   99    0   0   1   0   1   2   1   4   0   4   1   4   3   4  9  1  2  6
##   100   0   0   2   3   1   5   0   2   1   3   4   2   5   6  3  6  6  8
##   101   0   0   0   2   1   1   0   0   1   2   3   2   3   1  3  2  4  2
##   102   0   0   1   1   1   0   3   2   3   4   5   1   1   0  2  3  5  2
##   103   1   1   1   0   2   0   1   2   2   4   2   0   0   5  3  3  4  2
##   104   0   2   1   1   1   0   0   1   1   2   2   3   3   3  4  4  2  3
##   105   0   1   1   2   2   1   2   1   1   4   3   3   1   2  3  2  8  3
##   106   0   0   0   1   6   1   0   2   1   2   2   1   1   1  5  5  4  4
##   107   0   0   0   1   0   5   3   1   0   2   2   3   3   2  4  1  4  3
##   108   0   0   0   1   2   2   3   2   0   4   1   4   2   2  2  4  4  3
##   109   0   0   0   1   1   2   0   2   3   4   4   5   3   1  3  4  2  5
##   110   0   0   0   0   1   2   0   1   1   1   1   1   2   1  3  5  1  1
##   111   0   2   1   2   2   0   4   6   1   3   1   2   3   2  4  5  3  3
##   112   0   0   0   0   1   1   2   1   5   2   1   3   6   1  5  3  5  2
##   113   0   0   0   1   3   2   1   0   2   4   2   0   3   2  5  9  0  2
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##   513   0   0   0   0   0   0   0   0   0   0   0   0   1   0  1  1  0  0
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##   515   0   0   0   0   0   0   0   0   0   0   0   0   0   0  0  0  0  2
##   516   0   0   0   0   0   0   0   0   0   0   0   0   0   0  0  0  0  0
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##   524   0   0   0   0   0   0   0   0   0   0   0   0   0   1  0  0  0  0
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##   528   0   0   0   0   0   0   0   0   0   0   0   0   1   0  0  0  0  1
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##   539   0   0   0   0   0   0   0   0   0   0   0   0   1   0  0  0  0  0
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##   584   0   0   0   0   0   0   0   0   0   0   0   0   0   0  0  0  0  1
##   587   0   0   0   0   0   0   0   0   0   0   0   0   0   0  0  1  0  0
##   595   0   0   0   0   0   0   0   0   0   0   0   0   0   0  0  0  0  0
##   599   0   0   0   0   0   0   0   0   0   1   0   0   0   0  0  0  0  0
##   603   0   0   0   0   0   0   0   0   0   0   0   0   1   0  0  0  0  0
##   607   0   0   0   0   0   0   0   0   0   0   0   0   0   0  0  0  0  1
##   611   0   0   0   0   0   0   0   0   0   0   0   0   0   0  0  0  0  1
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##   618   0   0   0   0   0   0   0   0   0   0   0   0   0   0  0  0  1  0
##   623   0   0   0   0   0   0   0   0   0   0   0   0   0   0  0  0  1  0
##   648   0   0   0   0   0   0   0   0   0   0   0   0   0   0  1  0  0  0
##   649   0   0   0   0   0   0   0   0   0   0   0   0   0   0  0  1  0  0
##   651   0   0   0   0   0   0   0   0   0   0   0   0   0   0  0  1  0  1
##   659   0   0   0   0   0   0   0   0   0   0   0   0   0   0  1  0  0  0
##   671   0   0   0   0   0   0   0   0   0   0   0   0   0   0  0  0  1  0
##   673   0   0   0   0   0   0   0   0   0   0   0   0   0   0  0  0  0  1
##   684   0   0   0   0   0   0   0   0   0   0   0   0   0   0  0  0  0  1
##   700   0   0   0   0   0   0   0   0   0   0   0   0   0   0  0  0  0  0
##   722   0   0   0   0   0   0   0   0   0   0   0   0   0   0  0  0  0  1
##   731   0   0   0   0   0   0   0   0   0   0   0   0   0   0  0  1  0  0
##   744   0   0   0   0   0   0   0   0   0   0   0   0   0   0  1  0  0  0
##   761   0   0   0   0   0   0   0   0   0   0   0   0   0   1  0  0  0  0
##   776   0   0   0   0   0   0   0   0   0   0   0   0   0   0  0  1  0  0
##   784   0   0   0   0   0   0   0   0   0   0   0   0   0   0  0  1  0  0
##   802   0   0   0   0   0   0   0   0   0   0   0   0   0   0  0  0  1  0
##   805   0   0   0   0   0   0   0   0   0   0   0   0   0   1  0  0  0  0
##   810   0   0   0   0   0   0   0   0   0   0   0   0   0   0  0  0  1  0
##   824   0   0   0   0   0   0   0   0   0   0   0   0   0   0  0  1  0  0
##   845   0   0   0   0   0   0   0   0   0   0   0   0   0   0  0  0  1  0
##   852   0   0   0   0   0   0   0   0   0   0   0   0   0   0  1  0  0  0
##   858   0   0   0   0   0   0   0   0   0   0   0   0   0   1  0  0  0  0
##   886   0   0   0   0   0   0   0   0   0   0   0   0   0   0  0  1  0  0
##   972   0   0   0   0   0   0   0   0   0   0   0   0   0   0  0  0  0  0
##   980   0   0   0   0   0   0   0   0   0   1   0   0   0   0  0  0  0  0
##   994   0   0   0   0   0   0   0   0   0   0   0   0   0   0  0  0  0  0
##      DEWP
## pm2.5 -5 -4 -3 -2 -1  0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17
##   0    1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
##   1    0  0  0  1  0  0  0  0  0  0  0  1  0  0  0  0  0  0  1  0  0  0  0
##   2    0  0  2  1  3  0  2  0  0  0  1  1  0  1  0  2  0  0  0  0  0  1  0
##   3    2  2  2  1  0  2  2  2  1  0  0  3  2  5  2  0  1  0  1  0  0  0  0
##   4    0  3  2  3  2  3  0  1  2  0  1  2  3  2  1  2  2  1  0  0  0  2  3
##   5    2  1  4  7  0  8  1  3  1  0  3  4  2  3  3  6  4  4  1  1  0  0  1
##   6    1  4  4  5  4  4  2  8  3  2  6  6  4  6  2  9 10  6  3  1  3  4  3
##   7    3  8  6  8  8  3  5  8  3  6  8  9  4  8  4  1  7  3  2  0  4  3  2
##   8    4  7  5  4  4 13  5  9  6  7  6  7 11  4  7  6  6  6  4  1  4  2  6
##   9    2  5  7  9  4 10  6  6 14  9  8 12  4  8  7  4  5  7  3  9  6 10  5
##   10   3  8  4  9  8  7  8  8  9 11  8 10 11  4  6  8 14 12  5  7  4  6  2
##   11   7  9 12  9  8  7 11 12 10  6  5  8 10  4  9 10  8  7 14  7  5  5  7
##   12   6  5  8 10 10 12  9  8  9  5  7  6  8 10  7 12  9 12 13  5  3  5  6
##   13   2  6 12  5  4  7 12  8 12  6  5  7 10  6  6  7  9  8 12 12  9  7  5
##   14   7  7  7  4  8  6  4 10  4  3  4  5  2  5  8  6  6  7  6 12  7  7  3
##   15   2  8  9  7 15  3  4  8  3  4  6  3  5  7 10  5 11  9  8  9  8  9  5
##   16  12  9  3 12  9  8  6  9 10  6  5  4  6  9 15 10  5 12 15 10 11 10  9
##   17  11  3  3  4  7  6  9  6  2  7  6  6  6  7  4 12  9 16  9 18 10 11 11
##   18   8  7 11  9 10  4  4  5  7  7  3  1  4  4  6  6  4  8  8 12 14 10 10
##   19   6  6  8  8 10  4  3  7  6  5  5  2  3  6  3  3  6  8  9 10  9 13  7
##   20   8  6  8  5  7  6  7  6  8  4  2  1  6  6  6  5  4 11  3  9 11  7  8
##   21   5  5  5 10  4  3  5  5  2  1  6  9  7  2  4  7  5  7 10 12  8  6  7
##   22   8  5  6  9 10 13  8  4  4  5  5 10  5  2  4  8  2  8 10 12  8 13  8
##   23   7  5  7  5  8  5  5  7  3  3  9 11  3  6  5  3  0  8  8  9  5 15 13
##   24   9  8  4 10  8  3  3  3  1  5  7  4  6  7  4  5  4  8 12 11  3  8 11
##   25   7  6  7  7  2  9  6  2  3  2  1  6  1  7  3  6  4  7  6 12 10 11  8
##   26   2  5 10  4  7  6  6  4  2  5  5  7  7  4  4  6  3  5 10 11 11  5 10
##   27   4  5  8 15  6  7  9  6  2  7  7  6  8  8 11  2  3  6 10 13  4 11 17
##   28   7  7  9  5  8  4  4  4  8  6  7  7  7  4  4  7  3  7  5  9 10  8  9
##   29   3  3  4  3  4  4  3  4  5  3  4  5  8  1  6  5  8  3  9 12  7 13  6
##   30   6  2  2 10  6  6  1  4  3  5  4  3  5  3  1  8  4  5  9  6 11  7  6
##   31   6  4  2  3  5  7  4  1  7  6  2  4  5  1  2  4  7  9  9 10  8  8 16
##   32   6  5  6  3  3  7  1  7  6  4  2  6  7  4  3  4  4 11  8  3  7  5 15
##   33   5  3  3  5  6  5  1  4  5  3  5  7  5  5  4  1  5  7  9  9 12  3  8
##   34   9  7  7  5  4  8  4  4  1  3  5  6  6  3  3  5  2  8  3  4 11  8  9
##   35   8  8  5  0  3  3  6  7  3  4  4  2  3  2  3  3  6  5 12  7  9 11 12
##   36   6  6 12  7  2  9  7  2  3  4  1  7  1  1  1  1  4  7  7  6 11 13  9
##   37   9  5  2  5 10  8  1  4  1  3  5  8  4  4  8  3  5  6  6  7  6  7 10
##   38   7 15 16  8  5  4  4  1  1  4  0  9  2  5  8  5  3  4 11  6  4 14 11
##   39   6  5  9  9  1  4  4  6  1  6  7  6  3  5  5  4  6  3  9  5 11  7 12
##   40   4  3  7  4  5  4  4  1  5  3 10  6  2  2  7  5  3  7  6  5  8 12 10
##   41   6  6  8  9  8  2  4  4  3  1  5  6  5  4  2  5  3  4  6  5  9  9  6
##   42   9  4  4  4  2  6  3  2  4  4  7  6  7  2  3  9  2  7  5  4  8 14  7
##   43   7  2  3  2  6  3  5  2  3  4  5 10  5  4  6  5  4  5  8  8  5  8  9
##   44   3  6  4  7  3  4  9  5  2  5  5  4  2  4  6  3  3  4  6  4  9  4 11
##   45   7  3  2  1  3  5  8  5  6  5  3  8  4  3  4  4  3  5  9  5  9  8  6
##   46   4  8  3  3  4  2  5  4  3  4 10  3  8  2  1  4  4  6  5  7 12  7  6
##   47   3  5  2  1  4  7  8  4  8  4  3  8  5  4  2  4  3  7  8  6  9 11  8
##   48   9  5  5  5  3  8  6  6  3  7  8  7  2  4  8  4  7  6 10  7 14 11 13
##   49   6  1  2  2  2  4  4  1  5  2  4  7  5  4  7  5  4  6  7  5  8  5 15
##   50   8  2  8  0  5  3  4  5  2  6  5  8  4  4  5  5  4  5  5  8  9 14 16
##   51   6  5  7  4  7  9  5  7  6  4  0  6  4  4  4  3  3  2  5  6  7  9 12
##   52   4  3  7  3  6  9  5  4  4  3  2  4  0  3  4  3  5  2  8  6  8  6 13
##   53   4  3  2  6  3  5  4  6  1  6  6  3  1  7  4  7  0  2  5  4  8  7  7
##   54   2  6  9  3  2  5  3  5  2  3  6  2  0  5  7  2  2  9  7  5  6 10 13
##   55   3  1  2  4  6  6  0  3  3  5  6  8  8  4  2  6  5  8  9 11  7  4  5
##   56   3  3  6  3  3  6  7  7  5  2  3  2  5  5  2  3  4 10  7  2 11  3 11
##   57   3  5  5  4  4  7  6  0  5  5  4  6  7  2  9  4  5  5  3  4  5 13 11
##   58   5  3  5  1  4  2  1  6  2  6  3  3  5  1  2  8  7  5  5  9  5  9 11
##   59   5  2  6  2  5  6  4  4  2  6  7  3  7  7  2  8  4  6  8 12  7 13 13
##   60   3  3  2  0  5  6  3  7  2  6  6  3  6  4  4  2  3 10  3  4  3 13 11
##   61   3  2  3  2  0  5  2  2  3  3  1  4  4  4  4  4  3  7  6  7 10  4 14
##   62   3  4  2  2  3  2  2  4  2  1  4  4  2  4  2  6  4  6  3  5  9 11 10
##   63   7  3  0  9  3  2 11  3  4  2  8  2  9  4  5  8  7  3  5  7  5  6  6
##   64   2  3  6  4  3  5  4  6  3  5  4  4  7  2  5  1  4  9  3  5  6  8 10
##   65   8  1  3  7  3  0  4  3  4  3  6  3  6  3  5  5  2  5  3  6 10  3  6
##   66   2  4  1  2  2  1  4  4  5  2  5  7  3  6  5  3  5  4  7  3  5  4  8
##   67   1  0  3  3  4  1  5  3  6  2  6  4  4  3  2  5  5  3  5  8  3  5 13
##   68   5  6  3  2  3  0  2  4  6  6  6  2  5  4  2  5  1  1  5  6  4  9  8
##   69   3  5  4  5  5 10  4  3  2  3  8  2  7  7  4  6  4  4  5 11  8  9 15
##   70   6  2  3  4  4  4  5  5  2  5  2  7  6  5  3  5  3  4  4  3  5 12  7
##   71   5  3  5  4  3  2  8  6  2  3  5  3  3  1  4  3  2  5  5  6  8  8  9
##   72   3  4  1  1  3  7  2  2  0  2  5  7  5  3  6  3  1  7  5  3  5 11  6
##   73   2  4  2  4  1  1  5  4  3  7  6  1  5  5  4  5  3  3  4  4  3  7 11
##   74   5  5  3  3  3  1  4  2  2  1  1  6  3  1  3  3  1  3  8  4  6  8 14
##   75   3  1  2  2  4  2  6  3  3  8 10  2  2  5  1  1  2  7  2  7  5 11  4
##   76   5  7  4  3  4  6  3  1  2  4  4  3  2  4  3  4  3  4  7  3  4 12  5
##   77   5  9  1  6  2  2  4  4  1  5  3  5  6  5  5  5  4  8  2  1  8  7  6
##   78   4  4  3  2  4  4  2  3  3  7  3  3  8  4  2  3  4  8  4  7  3  2  9
##   79   6  5  8  5  9  5  1  5  1  8  8  3  8  6  5  1  6  4  7  5  6  4 11
##   80   4  5  5  3  5  5  6  4  5  3  4  7 12  0  7  7  5  6  7  4  8  6 11
##   81   4  4  2  3  2  2  3  2  2  1  3  3  6  3  4  4  0  4 10  4  4  9 14
##   82   6  4  2  3  1  2  2  7  2  4  2  3  7  2  3  5  5  2  2  4  3  8  7
##   83   3  5  2  4  4  5  3  3  5  2  7  3 10  4  1  2  6  7  7  4  5  7  6
##   84   1  3  4  3  5  4  7  2  4  2  6  3  4  5  2  2  2  3  5  5  7  6  6
##   85   3  3  3  0  2  4  0  2  3  1  3  2  9  6  4  3  5  5  3  3  9  8  9
##   86   7  3  2  1  3  4  2  5  5  2  2  2  5  4  4  1  5  4  7  4  8 12  5
##   87   4  2  5  6  3  5  2  3  2  4  4  2  5  2  0  4  3  3  4  7  6  6  8
##   88   5  6  5  1  2  1  1  1  2  0  0  3  5  2  2  2  2  5  1  2  4  9 13
##   89   6  4  4  1  2  3  1  2  8  4  1  5  4  4  5  2  2  5  2  3  6 14  9
##   90   3 10  6  4  1  3  2  7  8  3  4  5  2  3  3  7  2  5  4  7  4 10  6
##   91   8  7  2  5  4  2  7  9  1  5  5  3  6  3  2  4  3  1  4  5  8  4  6
##   92   6  5  1  2  1  2  4  5  1  1  3  4  3  7  2  3  3  2  5  6  7  7  4
##   93   3  1  3  4  4  1  1  4  1  4  2  5  7  2  3  4  5  3  2  3  2 11  9
##   94   3  8  1  1  2  1  3  2  4  1  2  1  5  4  5  0  4  1  7  3  8 10  4
##   95   5  4  1  2  3  2  3  1  4  4  5  2  6  3  3  6  1  2  0  4  6  7  7
##   96   6  2  3  3  2  3  0  3  3  1  1  7  9  2  5  4  4  2  4  6  6 11 12
##   97   4  8  4  3  4  1  0  5  4  4  1  2  2  1  2  3  7  2  7  3  7  5  4
##   98   3  4  1  3  5  3  2  3  4  5  1  4  4  4  5  5  4  7  4  4 14  8  5
##   99   7  0  5  0  3  0  2  3  2  2  4  3  7  3  2  3  3  6  3  3  8  8  3
##   100  3  5  3  4  3  4  2  0  2  0  0  3  8  6  3  8  1  8  4  3  6  9  4
##   101  7  6  1  4  1  4  2  2  3  2  3  2  3  2  3  1  3  5  4  4  9 11  8
##   102  2  1  2  2  3  0  2  4  4  2  4  3  8  7  3  2  0  1  4  3  3  7  7
##   103  2  4  2  1  3  2  2  0  2  8  0  2  5  5  7  2  0  1  4  5  6  8  7
##   104  0  2  2  1  1  2  0  0  2  3  1  2  4  1  4  1  6  9  4  3  5  7  5
##   105  3  3  4  2  3  2  4  1  3  4  1  4  2  6  4  1  4  6  6  2  4  4  6
##   106  2  2  1  3  4  3  5  0  2  2  1  5  1  4  2  2  2  4  4  3  4  6  5
##   107  3  1  3  1  2  5  3  2  4  2  0  1  7  1  3  4  6  2  2  7  4  3  2
##   108  5  6  3  2  0  1  0  0  2  4  3  1  6  2  5  3  4  3  3  2  7  4 10
##   109  3  3  3  0  2  2  2  2  0  0  2  1  4  3  1  2  3  2  2  4  7  6  4
##   110  0  3  4  5  4  2  0  1  2  5  4  2  4  5  2  3  0  3  3  2  4  4  3
##   111  1  3  5  3  3  2  4  2  6  2  7  2  6  2  2  2  0  1  4  3  5  8  4
##   112  5  2  1  1  4  2  1  0  2  2  2  3  2  0  3  2  6  2  4  2  2  7  2
##   113  2  0  0  1  5  2  3  3  1  6  1  3  3  2  3  8  4  3  3  2  3  3  7
##   114  2  8  1  3  1  3  4  3  2  1  1  3  4  2  2  5  3  2  0  1  2  5  7
##   115  2  5  3  1  2  4  0  2  0  1  2  1  1  4  4  4  7  2  2  1 10  6  1
##   116  2  2  4  0  4  1  3  2  3  3  3  1  2  2  4  1  3  1  5  1  4  6  3
##   117  1  1  1  1  0  2  1  1  1  1  2  1  1  1  2  1  0  2  2  4  7  7  7
##   118  4  1  5  2  4  2  3  0  0  4  1  0  2  4  2  3  4  2  2  5  4  4  7
##   119  3  3  1  2  2  1  1  2  0  2  1  0  3  4  1  3  4  5  2  2  5  3  8
##   120  0  1  0  2  1  4  3  0  0  2  0  1  1  1  2  2  0  2  3  2  6  2  9
##   121  4  4  3  0  3  3  1  4  6  3  3  2  2  1  0  2  2  6  3  1  6  5  8
##   122  2  3  1  1  4  0  2  2  1  5  5  0  2  1  3  1  2  6  2  4  2  6  3
##   123  5  4  3  2  2  2  2  3  1  3  2  2  2  4  0  4  4  1  2  3  5  7  4
##   124  2  4  2  2  2  4  1  2  2  2  0  2  2  2  0  2  2  4  3  6  4  2  5
##   125  1  1  2  1  1  0  0  1  1  2  2  2  2  3  5  2  2  4  1  3  5  6  4
##   126  6  5  3  0  5  5  0  2  1  2  1  2  1  3  1  2  4  3  0  2  3  3  3
##   127  2  2  2  3  1  2  6  2  2  4  1  2  1  3  3  4  0  3  4  4  3  4  6
##   128  4  1  7  3  0  1  3  2  4  2  2  2  0  2  2  1  3  0  1  8  5  4  4
##   129  3  2  1  2  3  1  2  1  2  2  5  0  1  2  4  1  1  6  3  2  8  1  2
##   130  3  1  0  4  2  1  4  5  0  4  1  0  2  2  1  2  2  2  3  5  4  2  1
##   131  2  2  2  2  1  0  3  2  1  1  0  1  2  2  2  2  2  3  1  2  3  7  5
##   132  2  4  1  2  2  2  1  4  2  1  1  1  3  1  4  2  1  4  0  6  8  7  1
##   133  1  4  2  0  0  1  0  1  1  0  3  3  1  2  0  1  2  2  5  3  3  4  4
##   134  2  1  1  3  0  1  2  0  4  4  3  3  3  2  1  0  0  0  3  5  1  4  6
##   135  4  5  4  2  3  2  3  1  2  1  0  3  1  3  2  4  1  2  2  2  1  4  4
##   136  6  3  2  3  2  1  2  2  2  3  4  2  2  2  3  0  4  3  2  3  6  2  5
##   137  1  0  0  1  2  2  1  0  2  1  0  4  2  2  2  3  1  2  4  4  3  6  4
##   138  4  4  2  1  2  1  1  2  1  4  3  1  1  2  1  3  1  1  4  1  4  1  5
##   139  1  4  0  0  1  2  2  2  4  0  1  1  0  1  3  4  6  4  2  5  2  1  1
##   140  1  3  1  1  1  1  1  0  0  1  2  1  3  2  1  2  6  4  1  2  2  8  4
##   141  3  2  1  1  4  1  0  5  0  2  1  5  2  0  2  1  1  3  2  2  1  7  4
##   142  1  4  1  1  2  2  2  3  0  2  1  4  1  1  1  2  1  4  0  1  4  4  4
##   143  3  4  4  2  3  2  3  2  1  3  1  3  3  5  2  4  3  1  5  3  7  3  5
##   144  3  5  3  1  3  2  2  3  0  3  1  1  1  3  1  5  3  3  2  1  2  6  6
##   145  2  1  0  0  2  3  1  1  1  0  0  3  2  0  3  1  2  2  1  1  2  3  4
##   146  2  0  3  1  2  1  1  1  1  0  2  4  2  2  2  2  1  1  2  4  5  3  5
##   147  1  3  2  0  4  0  2  2  3  1  2  0  1  0  2  2  2  4  0  1  2  4  5
##   148  2  5  3  2  1  2  1  0  2  1  2  1  2  1  2  2  5  2  2  4  1  1  3
##   149  4  0  1  0  2  1  3  2  0  3  2  4  2  1  0  0  3  5  2  2  2  8  5
##   150  6  4  0  0  2  1  2  0  1  1  1  2  3  0  1  2  1  1  2  2  4  5  2
##   151  2  1  2  1  0  2  1  3  1  3  1  1  2  2  1  3  6  2  0  2  2  3  7
##   152  3  6  1  2  1  1  1  2  0  2  0  2  1  2  2  4  1  3  5  4  6  3  6
##   153  6  2  2  6  2  3  4  0  2  1  1  0  1  1  2  0  4  3  3  0  5  4  7
##   154  2  0  3  1  2  1  1  1  1  3  4  2  1  4  3  1  0  1  1  0  3  4  3
##   155  2  2  3  2  2  1  1  2  0  0  1  0  1  2  2  1  3  3  2  0  1  3  4
##   156  3  4  0  2  0  2  1  2  2  1  1  1  1  1  2  3  3  2  2  1  1  1  3
##   157  3  0  1  1  3  0  0  2  3  2  2  1  2  0  0  4  1  2  2  4  1  2  4
##   158  2  1  1  1  2  2  0  3  3  1  1  1  4  2  1  5  2  0  2  0  2  2  0
##   159  2  4  1  3  2  4  0  4  3  2  0  0  1  2  3  1  2  0  1  2  4  4  3
##   160  2  3  0  1  3  0  1  1  1  2  3  0  1  1  0  3  1  1  2  3  0  4  8
##   161  1  1  2  1  0  3  0  2  0  1  1  2  2  1  1  2  2  3  2  4  1  2  2
##   162  2  1  1  1  0  1  1  2  1  1  0  3  1  1  2  2  4  3  4  2  1  0  1
##   163  1  0  2  2  2  2  1  4  0  2  1  3  0  3  0  3  2  2  3  0  0  3  1
##   164  3  2  8  4  3  2  1  4  1  1  1  0  2  1  2  7  1  4  2  2  4  3  6
##   165  1  1  4  2  3  1  3  2  3  0  1  1  0  3  2  2  1  1  3  0  3  2  1
##   166  3  2  1  3  0  2  0  4  3  0  3  3  1  0  0  3  2  2  3  1  4  1  5
##   167  4  2  2  1  0  1  0  2  3  1  1  1  1  2  2  2  6  0  0  2  0  1  3
##   168  0  1  0  3  2  0  1  2  1  1  2  0  2  1  0  3  2  5  1  3  4  3  3
##   169  2  1  1  2  0  0  3  2  1  0  1  0  0  0  0  2  3  0  2  0  2  0  3
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##   172  4  2  1  3  2  1  1  0  0  2  0  1  1  2  0  2  1  4  4  0  1  2  1
##   173  1  0  4  0  1  3  1  1  2  0  1  1  0  0  0  1  2  2  0  1  2  1  4
##   174  2  1  2  3  4  1  1  3  1  2  1  2  0  2  1  2  1  3  2  1  2  4  0
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##   183  2  3  3  3  1  3  1  1  3  1  0  0  5  1  0  0  0  5  0  2  2  1  2
##   184  3  2  0  2  2  4  3  2  3  0  2  3  2  2  2  2  1  1  0  0  0  1  3
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##   980  0  0  0  0  0  0  0  0  0  0  0
##   994  0  0  0  0  0  0  0  0  0  0  0
## [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.

Conclusiones

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.

Fuentes

[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