title: “ESTUDIO ESTADÍSTICO DE LA CALIDAD DEL AIRE EN INDIA” output: html_notebook — # UNIVERSIDAD CENTRAL DEL ECUADOR ### PROYECTO:ESTUDIO ESTADÍSTICO DE LA CALIDAD DEL AIRE EN INDIA ### FECHA: 11/02/2026
# ===== LIBRERÍAS NECESARIAS =====
library(dplyr)
library(gt)
library(magrittr)
# Carga de datos
datos <- read.csv("~/ariana tercer semestre/Estadistica/city_day.csv",
header = TRUE, dec = ".", sep = ",", na.strings = "-")
datos <- na.omit(datos)
# 1. seleccionar dos variables
datos_prom <- aggregate(NO2 ~ AQI, data = datos, mean)
Y <- datos_prom$AQI # efecto
X <- datos_prom$NO2 # causa
#La concentración de monóxido de carbono (CO) es la causa porque corresponde a un contaminante gaseoso primario de alta toxicidad que se acumula en la atmósfera,
#especialmente en zonas urbanas con alta actividad vehicular e industrial, y el Índice de Calidad del Aire (AQI) es el efecto, ya que varía en respuesta a
#los incrementos en la concentración de CO para sintetizar el nivel de riesgo para la salud humana, mostrando un comportamiento de tipo exponencial.
# 2. Tabla pares de valores (TVP)
TVP_NO2_AQI <- data.frame(X,Y)
TVP_NO2_AQI %>%
gt() %>%
fmt_number(
columns = everything(), # Aplica a todas las columnas
decimals = 2 # Define 2 decimales
) %>%
fmt_number(
columns = everything(), # Aplica a todas las columnas
decimals = 2 # Define 2 decimales
) %>%
tab_header(
title = md("Tabla Nro. 1"),
subtitle = md("*Pares de valores de NO2 y AQI, estudio de la calidad del aire en la India *")
) %>%
tab_source_note(
source_note = md("Autor: Grupo2")
) %>%
tab_options(
table.border.top.color = "black",
table.border.bottom.color = "black",
table.border.top.style = "solid",
table.border.bottom.style = "solid",
column_labels.border.top.color = "black",
column_labels.border.bottom.color = "black",
column_labels.border.bottom.width = px(2),
row.striping.include_table_body = TRUE,
heading.border.bottom.color = "black",
heading.border.bottom.width = px(2),
table_body.hlines.color = "gray",
table_body.border.bottom.color = "black"
)| Tabla Nro. 1 | |
| *Pares de valores de NO2 y AQI, estudio de la calidad del aire en la India * | |
| X | Y |
|---|---|
| 12.21 | 23.00 |
| 14.05 | 26.00 |
| 15.57 | 29.00 |
| 12.63 | 30.00 |
| 17.28 | 31.00 |
| 11.61 | 32.00 |
| 16.29 | 33.00 |
| 15.56 | 34.00 |
| 12.77 | 35.00 |
| 14.16 | 36.00 |
| 14.77 | 37.00 |
| 13.91 | 38.00 |
| 13.01 | 39.00 |
| 14.82 | 40.00 |
| 18.55 | 41.00 |
| 15.99 | 42.00 |
| 16.34 | 43.00 |
| 15.60 | 44.00 |
| 13.18 | 45.00 |
| 15.69 | 46.00 |
| 16.81 | 47.00 |
| 17.66 | 48.00 |
| 18.94 | 49.00 |
| 16.28 | 50.00 |
| 17.56 | 51.00 |
| 20.71 | 52.00 |
| 21.25 | 53.00 |
| 20.30 | 54.00 |
| 21.08 | 55.00 |
| 18.05 | 56.00 |
| 14.11 | 57.00 |
| 17.29 | 58.00 |
| 18.08 | 59.00 |
| 16.84 | 60.00 |
| 18.44 | 61.00 |
| 20.48 | 62.00 |
| 19.71 | 63.00 |
| 20.87 | 64.00 |
| 21.98 | 65.00 |
| 24.36 | 66.00 |
| 21.62 | 67.00 |
| 22.90 | 68.00 |
| 22.80 | 69.00 |
| 23.96 | 70.00 |
| 22.93 | 71.00 |
| 22.42 | 72.00 |
| 22.88 | 73.00 |
| 23.81 | 74.00 |
| 24.58 | 75.00 |
| 25.74 | 76.00 |
| 22.33 | 77.00 |
| 29.57 | 78.00 |
| 26.62 | 79.00 |
| 27.04 | 80.00 |
| 32.59 | 81.00 |
| 26.76 | 82.00 |
| 28.76 | 83.00 |
| 28.84 | 84.00 |
| 26.66 | 85.00 |
| 25.98 | 86.00 |
| 28.91 | 87.00 |
| 27.30 | 88.00 |
| 29.43 | 89.00 |
| 33.25 | 90.00 |
| 30.69 | 91.00 |
| 30.10 | 92.00 |
| 30.69 | 93.00 |
| 24.98 | 94.00 |
| 27.15 | 95.00 |
| 31.89 | 96.00 |
| 34.26 | 97.00 |
| 29.97 | 98.00 |
| 28.26 | 99.00 |
| 31.74 | 100.00 |
| 30.38 | 101.00 |
| 28.46 | 102.00 |
| 35.02 | 103.00 |
| 36.42 | 104.00 |
| 33.60 | 105.00 |
| 33.50 | 106.00 |
| 32.57 | 107.00 |
| 36.29 | 108.00 |
| 31.30 | 109.00 |
| 33.74 | 110.00 |
| 31.69 | 111.00 |
| 33.50 | 112.00 |
| 29.75 | 113.00 |
| 39.15 | 114.00 |
| 37.00 | 115.00 |
| 37.45 | 116.00 |
| 34.70 | 117.00 |
| 34.27 | 118.00 |
| 34.44 | 119.00 |
| 34.84 | 120.00 |
| 27.57 | 121.00 |
| 34.65 | 122.00 |
| 33.76 | 123.00 |
| 37.28 | 124.00 |
| 40.20 | 125.00 |
| 38.42 | 126.00 |
| 34.88 | 127.00 |
| 32.78 | 128.00 |
| 35.66 | 129.00 |
| 34.39 | 130.00 |
| 35.58 | 131.00 |
| 37.77 | 132.00 |
| 43.83 | 133.00 |
| 30.80 | 134.00 |
| 33.41 | 135.00 |
| 40.24 | 136.00 |
| 32.83 | 137.00 |
| 32.14 | 138.00 |
| 34.25 | 139.00 |
| 33.30 | 140.00 |
| 34.32 | 141.00 |
| 36.76 | 142.00 |
| 36.04 | 143.00 |
| 37.61 | 144.00 |
| 32.40 | 145.00 |
| 44.40 | 146.00 |
| 29.67 | 147.00 |
| 31.97 | 148.00 |
| 29.64 | 149.00 |
| 41.31 | 150.00 |
| 40.71 | 151.00 |
| 29.33 | 152.00 |
| 37.87 | 153.00 |
| 35.43 | 154.00 |
| 37.16 | 155.00 |
| 42.96 | 156.00 |
| 31.87 | 157.00 |
| 40.25 | 158.00 |
| 40.46 | 159.00 |
| 39.69 | 160.00 |
| 34.79 | 161.00 |
| 42.16 | 162.00 |
| 46.05 | 163.00 |
| 43.81 | 164.00 |
| 37.25 | 165.00 |
| 32.63 | 166.00 |
| 41.96 | 167.00 |
| 44.24 | 168.00 |
| 39.12 | 169.00 |
| 32.61 | 170.00 |
| 33.44 | 171.00 |
| 37.00 | 172.00 |
| 39.16 | 173.00 |
| 34.08 | 174.00 |
| 39.37 | 175.00 |
| 33.36 | 176.00 |
| 39.89 | 177.00 |
| 45.18 | 178.00 |
| 38.55 | 179.00 |
| 42.42 | 180.00 |
| 39.33 | 181.00 |
| 45.71 | 182.00 |
| 34.73 | 183.00 |
| 50.48 | 184.00 |
| 43.02 | 185.00 |
| 37.00 | 186.00 |
| 34.85 | 187.00 |
| 27.97 | 188.00 |
| 38.87 | 189.00 |
| 38.00 | 190.00 |
| 35.86 | 191.00 |
| 50.45 | 192.00 |
| 38.54 | 193.00 |
| 47.53 | 194.00 |
| 46.70 | 195.00 |
| 44.59 | 196.00 |
| 50.95 | 197.00 |
| 42.98 | 198.00 |
| 41.16 | 199.00 |
| 41.08 | 200.00 |
| 46.33 | 201.00 |
| 37.48 | 202.00 |
| 47.06 | 203.00 |
| 25.82 | 204.00 |
| 43.28 | 205.00 |
| 34.38 | 206.00 |
| 49.01 | 207.00 |
| 44.25 | 208.00 |
| 49.29 | 209.00 |
| 22.50 | 210.00 |
| 34.34 | 211.00 |
| 19.65 | 212.00 |
| 23.55 | 213.00 |
| 41.62 | 214.00 |
| 44.66 | 215.00 |
| 31.22 | 216.00 |
| 41.25 | 217.00 |
| 40.56 | 218.00 |
| 47.72 | 219.00 |
| 43.23 | 220.00 |
| 44.93 | 221.00 |
| 47.54 | 222.00 |
| 40.96 | 223.00 |
| 46.93 | 224.00 |
| 58.95 | 225.00 |
| 45.87 | 226.00 |
| 38.89 | 227.00 |
| 48.34 | 228.00 |
| 48.65 | 229.00 |
| 49.43 | 230.00 |
| 43.08 | 231.00 |
| 50.44 | 232.00 |
| 43.17 | 233.00 |
| 44.67 | 234.00 |
| 41.21 | 235.00 |
| 48.51 | 236.00 |
| 55.18 | 237.00 |
| 34.69 | 238.00 |
| 47.27 | 239.00 |
| 53.38 | 240.00 |
| 55.91 | 241.00 |
| 56.01 | 242.00 |
| 44.49 | 243.00 |
| 43.64 | 244.00 |
| 36.99 | 245.00 |
| 44.84 | 246.00 |
| 48.53 | 247.00 |
| 47.39 | 248.00 |
| 40.19 | 249.00 |
| 50.26 | 251.00 |
| 40.70 | 252.00 |
| 41.94 | 253.00 |
| 53.43 | 254.00 |
| 49.45 | 255.00 |
| 28.89 | 256.00 |
| 47.07 | 257.00 |
| 46.74 | 258.00 |
| 43.23 | 259.00 |
| 57.92 | 260.00 |
| 39.22 | 261.00 |
| 42.01 | 262.00 |
| 46.40 | 263.00 |
| 45.50 | 264.00 |
| 44.30 | 265.00 |
| 41.88 | 266.00 |
| 55.63 | 267.00 |
| 36.91 | 268.00 |
| 47.42 | 269.00 |
| 34.14 | 270.00 |
| 44.17 | 271.00 |
| 40.94 | 272.00 |
| 43.46 | 273.00 |
| 50.00 | 274.00 |
| 38.79 | 275.00 |
| 56.83 | 276.00 |
| 55.62 | 277.00 |
| 66.51 | 278.00 |
| 46.24 | 279.00 |
| 42.91 | 280.00 |
| 47.55 | 281.00 |
| 42.08 | 282.00 |
| 37.85 | 283.00 |
| 48.00 | 284.00 |
| 47.13 | 285.00 |
| 51.97 | 286.00 |
| 52.55 | 287.00 |
| 42.52 | 288.00 |
| 50.64 | 289.00 |
| 43.60 | 290.00 |
| 65.89 | 291.00 |
| 44.26 | 292.00 |
| 53.22 | 293.00 |
| 26.97 | 294.00 |
| 49.29 | 295.00 |
| 61.96 | 296.00 |
| 42.51 | 297.00 |
| 50.64 | 298.00 |
| 48.69 | 299.00 |
| 49.44 | 300.00 |
| 50.99 | 301.00 |
| 49.73 | 302.00 |
| 58.88 | 303.00 |
| 57.01 | 304.00 |
| 60.99 | 305.00 |
| 59.33 | 306.00 |
| 56.61 | 307.00 |
| 34.72 | 308.00 |
| 53.40 | 309.00 |
| 50.49 | 310.00 |
| 36.23 | 311.00 |
| 48.73 | 312.00 |
| 56.86 | 313.00 |
| 46.18 | 314.00 |
| 52.04 | 315.00 |
| 40.40 | 316.00 |
| 47.65 | 317.00 |
| 46.52 | 318.00 |
| 53.00 | 319.00 |
| 56.00 | 320.00 |
| 51.27 | 321.00 |
| 24.71 | 322.00 |
| 39.29 | 323.00 |
| 31.23 | 324.00 |
| 45.34 | 325.00 |
| 79.29 | 326.00 |
| 42.66 | 327.00 |
| 63.72 | 328.00 |
| 61.18 | 329.00 |
| 58.40 | 330.00 |
| 51.38 | 331.00 |
| 46.92 | 332.00 |
| 40.71 | 333.00 |
| 49.40 | 334.00 |
| 51.37 | 335.00 |
| 49.88 | 336.00 |
| 53.35 | 338.00 |
| 50.35 | 339.00 |
| 44.19 | 340.00 |
| 49.68 | 341.00 |
| 53.22 | 342.00 |
| 54.36 | 343.00 |
| 51.41 | 344.00 |
| 50.38 | 345.00 |
| 44.69 | 346.00 |
| 70.78 | 347.00 |
| 59.40 | 348.00 |
| 47.33 | 349.00 |
| 54.47 | 350.00 |
| 48.21 | 351.00 |
| 48.40 | 352.00 |
| 42.90 | 353.00 |
| 55.68 | 354.00 |
| 57.81 | 356.00 |
| 66.95 | 357.00 |
| 45.14 | 358.00 |
| 61.78 | 359.00 |
| 49.81 | 360.00 |
| 59.36 | 361.00 |
| 51.04 | 362.00 |
| 69.60 | 363.00 |
| 36.72 | 364.00 |
| 62.99 | 365.00 |
| 59.54 | 366.00 |
| 68.82 | 367.00 |
| 54.86 | 368.00 |
| 68.62 | 369.00 |
| 58.58 | 370.00 |
| 60.11 | 371.00 |
| 54.38 | 372.00 |
| 66.19 | 373.00 |
| 61.17 | 374.00 |
| 64.06 | 375.00 |
| 54.13 | 376.00 |
| 63.12 | 377.00 |
| 66.32 | 378.00 |
| 65.78 | 379.00 |
| 50.55 | 380.00 |
| 55.04 | 381.00 |
| 67.67 | 382.00 |
| 71.50 | 383.00 |
| 47.66 | 384.00 |
| 58.03 | 385.00 |
| 29.49 | 387.00 |
| 50.03 | 388.00 |
| 75.41 | 389.00 |
| 51.13 | 390.00 |
| 58.28 | 391.00 |
| 72.90 | 392.00 |
| 69.93 | 394.00 |
| 73.34 | 396.00 |
| 63.96 | 397.00 |
| 64.97 | 398.00 |
| 59.70 | 399.00 |
| 83.03 | 400.00 |
| 76.71 | 401.00 |
| 58.39 | 403.00 |
| 61.11 | 404.00 |
| 58.72 | 405.00 |
| 67.99 | 406.00 |
| 82.74 | 407.00 |
| 60.46 | 411.00 |
| 61.81 | 413.00 |
| 62.83 | 415.00 |
| 47.98 | 417.00 |
| 60.03 | 419.00 |
| 66.69 | 420.00 |
| 57.55 | 421.00 |
| 67.03 | 422.00 |
| 69.35 | 423.00 |
| 48.25 | 424.00 |
| 67.23 | 425.00 |
| 55.65 | 426.00 |
| 74.62 | 428.00 |
| 82.53 | 430.00 |
| 75.86 | 431.00 |
| 57.53 | 432.00 |
| 72.28 | 433.00 |
| 70.23 | 437.00 |
| 42.35 | 438.00 |
| 69.31 | 439.00 |
| 74.55 | 440.00 |
| 50.24 | 441.00 |
| 19.14 | 442.00 |
| 55.10 | 443.00 |
| 43.73 | 444.00 |
| 42.92 | 449.00 |
| 78.91 | 450.00 |
| 64.13 | 451.00 |
| 63.01 | 452.00 |
| 25.75 | 453.00 |
| 65.45 | 454.00 |
| 79.60 | 455.00 |
| 70.46 | 456.00 |
| 78.43 | 458.00 |
| 71.37 | 460.00 |
| 63.92 | 462.00 |
| 94.04 | 463.00 |
| 67.49 | 464.00 |
| 61.63 | 467.00 |
| 78.71 | 468.00 |
| 71.48 | 471.00 |
| 36.39 | 472.00 |
| 54.10 | 473.00 |
| 65.59 | 475.00 |
| 92.32 | 478.00 |
| 106.04 | 480.00 |
| 85.14 | 482.00 |
| 86.59 | 483.00 |
| 76.89 | 484.00 |
| 64.80 | 485.00 |
| 34.44 | 487.00 |
| 64.18 | 492.00 |
| 54.76 | 497.00 |
| 75.06 | 501.00 |
| 0.65 | 502.00 |
| 55.61 | 506.00 |
| 70.54 | 509.00 |
| 16.83 | 510.00 |
| 84.74 | 515.00 |
| 25.37 | 522.00 |
| 25.00 | 531.00 |
| 61.10 | 532.00 |
| 74.41 | 537.00 |
| 77.63 | 557.00 |
| 65.77 | 561.00 |
| 75.26 | 577.00 |
| 73.61 | 591.00 |
| 24.61 | 593.00 |
| 59.35 | 595.00 |
| 80.73 | 597.00 |
| 70.10 | 613.00 |
| 49.67 | 659.00 |
| 77.51 | 675.00 |
| 81.67 | 677.00 |
| Autor: Grupo2 | |
# 3. grafica de dispercion
plot(X, Y,
main = "Grafica No1:Diagrama de dispersion entre NO2 y AQI
en el estudio de la calidad del aire en la India",
xlab = "NO2 (µg/m³)", # Nombre eje X
ylab = "AQI (Indice)", # Nombre eje Y
col = "skyblue", # Color de los puntos
pch = 16, # Tipo de punto sólido
cex = 1.2, # Tamaño de los puntos
cex.main = 1, # Tamaño del título
cex.lab = 1, # Tamaño de los ejes
cex.axis = 0.9,
xlim = c(0, max(X)*1.05),
ylim = c(0, max(Y)*1.05)) 
# 4. Conjetura
#La distribución de los puntos en el gráfico muestra una curva ascendente,
#lo que sugiere un modelo exponencial. El AQI aumenta de forma acelerada a medida
#que se incrementa la concentración de CO, indicando una relación no lineal y un
#impacto creciente del contaminante sobre la calidad del aire.
Y1<-log(Y)
regresionexponencial<- lm(Y1~X)
# Ver los coeficientes (a,b)
beta0<- regresionexponencial$coefficients[1]
beta1<- regresionexponencial$coefficients[2]
b<- beta1
b## X
## 0.03310434a<-exp(beta0)
a## (Intercept)
## 47.92617# 6. Grafica de dispercion modelo-realidad
plot(X, Y,
main = " Grafica No2: Regresion lineal entre NO2 y AQI
en el estudio de la calidad del aire en la India ",
xlab = "NO2 (µg/m³)", # Nombre eje X
ylab = "AQI (Indice)", # Nombre eje Y
col = "blue", # Color de los puntos
pch = 16, # Tipo de punto sólido
cex = 1.2, # Tamaño de los puntos
cex.main = 1, # Tamaño del título
cex.lab = 1, # Tamaño de los ejes
cex.axis = 0.9,
xlim = c(0, max(X)*1.05),
ylim = c(0, max(Y)*1.05))
curve(a*exp(b*x), from = 0,to=100,col="red",add = TRUE)
# 7. Test de bondad
#Test de Pearson, coeficiente de correlación (relacion inversa)
r<- cor(X,Y1)*100
r## [1] 79.74544# 8. Coeficiente de determinación muestral
r2<- r^2/100
r2## [1] 63.59335# 9. Restricciones
# Dominio [x]: D = {R+^0}
# Dominio [y]: D = {R+^0}
# ¿Existe algún valor en el dominio de x que sustituido en el modelo matemático
# genere un valor en y fuera de su dominio?
# No existen restricciones para el uso del modelo exponencial, ya que la
# concentración de dióxido de nitrógeno (NO2) toma valores no negativos y el
# modelo genera siempre valores positivos del Índice de Calidad del Aire (AQI).
# Además, al ser un modelo exponencial creciente, el AQI aumenta conforme se
# incrementa la concentración de NO2, sin salirse de su dominio físico.
# 10. Aplicaciones del modelo
# AQI esperado cuando la concentración de NO2 es de 40 µg/m³
AQI_esperado <- 47.92617 * exp(0.03310434 * 40)
AQI_esperado## [1] 180.1582# 11. Conclusión
# Entre la concentración de dióxido de nitrógeno (NO2) y el Índice de Calidad del Aire (AQI)
#existe una relación de tipo exponencial, cuyo modelo es y = 47.92617 * e^(0.03310434x),
#donde x representa la concentración de NO2 y y el AQI. El modelo indica que el AQI aumenta
#de forma acelerada a medida que se incrementa la concentración de NO2, evidenciando que
#este contaminante influye de manera significativa en la calidad del aire, mientras que el
#porcentaje restante de variación se debe a otros factores ambientales no considerados
#en el modelo.