CLIMA VOLCAN ANTISANA
UNIVERSIDAD CENTRAL DEL ECUADOR
ANÁLISIS ESTADÍSTICO DEL CLIMA EN EL VOLCAN ANTISANA
FECHA: 24/01/2026
#INTEGRANTES: JUAN ARTEAGA, RONALD CARRERA, ANDRE LABANDA, ALEXANDER SAILEMA
#INTRODUCCIÓN
#Planteamiento del problema:
#Las variaciones de las condiciones meteorológicas constituyen un fenómeno ambiental de gran importancia,
#ya que influyen directamente en los ecosistemas, los recursos hídricos y diversas actividades humanas.
#Con el paso del tiempo, factores como la temperatura, la precipitación, el viento y la radiación solar pueden presentar cambios significativos que afectan el equilibrio ambiental y climático.
#En este contexto, el uso de herramientas estadísticas permite analizar los datos meteorológicos registrados en la estación Antisana,
#identificando patrones y tendencias que contribuyen a comprender el comportamiento del clima y su impacto en el entorno natural durante el período de estudio.
#Mapa de Ubicación
library(magick)
library(cowplot)
img <- image_read("C:/Users/JOSUE/Downloads/ESTADISTICA/img/Mapa Antisana.jpeg")
ggdraw() + draw_image(img)
#Objetivo General
#Aplicar la estadística para el estudio de las variables meteorológicas registradas en la estación Antisana durante todo el año 2012, mediante el uso de herramientas para la medición, análisis e interpretación de datos climáticos.
#Objetivos Especificos
#Conocer el comportamiento de las variables meteorológicas registradas en la estación Antisana, identificando sus principales características mediante el uso de medidas estadísticas descriptivas.
#Emplear modelos de probabilidad para establecer conclusiones sobre la variabilidad de las condiciones meteorológicas a partir de los resultados obtenidos en la muestra analizada.
#Deducir relaciones entre las variables meteorológicas con el fin de realizar estimaciones y análisis que contribuyan a la interpretación del comportamiento climático en el período de estudio.
#Para esta base de datos las primeras variables no se ocupan ya que tienen valores constantes y se van a ocupar para hacer el mapa de ubicación
#así que se va a trabajar con las demás Variables para realizar el análisis estadístico.
#ESTADÍSTICA DESCRIPTIVA
#Poblacion
#Todos los días del año en la estación meteorológica Antisana.
#P={x∣x ∈ dias de registro meteorologico ∧ Estacion(x)="Antisana"}
#Individuo
#Cada día de registro meteorológico en la estación Antisana.
#Individuo: xi,i=1,2,3,…,n
#Muestra
#Los datos disponibles corresponden a una muestra de días registrados en la estación meteorológica Antisana durante el período observado.
#M={x∣x∈dıas de registro meteorologico ∧ Estacioˊn(x)="Antisana" ∧ Año(x)=2012}
#Tabla de variables
Tabla_de_variables<-read.csv("tabla_variables_Antisana.csv",header = TRUE,dec = ".",
sep = ";")
Tabla_de_variablesdatos<-read.csv("weatherdataANTISANA.csv",header = TRUE,dec = ".",
sep = ",")
#Variables Cuantitativas continuas
# Temperatura Máxima
#Extracción Variable Cuantitativa Continua
Temp_max<- datos$Max.Temperature
min <-min(Temp_max)
max <-max(Temp_max)
R <-max-min
K <- floor(1+3.33*log10(length(Temp_max)))
A <-R/K
Li <-round(seq(from=min,to=max-A,by=A),2)
Ls <-round(seq(from=min+A,to=max,by=A),2)
Mc <-(Li+Ls)/2
ni<-c()
for (i in 1:K) {
if (i < K) {
ni[i] <- length(subset(Temp_max, Temp_max >= Li[i] & Temp_max < Ls[i]))
} else {
ni[i] <- length(subset(Temp_max, Temp_max >= Li[i] & Temp_max <= Ls[i]))
}
}
sum(ni)## [1] 366hi <-ni/sum(ni)*100
Ni_asc<-cumsum(ni)
Hi_asc<-cumsum(hi)
Ni_desc<-rev(cumsum(rev(ni)))
Hi_desc<-rev(cumsum(rev(hi)))
TDF_Temp_max <- data.frame(
Li, Ls, Mc, ni, round(hi, 2), Ni_asc, Ni_desc, round(Hi_asc, 2), round(Hi_desc, 2)
)
colnames(TDF_Temp_max) <- c("Li","Ls","Mc","ni","hi","Ni_asc","Ni_desc","Hi_asc(%)","Hi_desc(%)")
#Crear fila de totales
totales<-c(
Li="TOTAL",
Ls="-",
Mc="-",
ni=sum(ni),
hi=sum(hi),
Ni_asc="-",
Ni_desc="-",
Hi_asc="-",
Hi_desc="-")
TDF_Temp_max_final <-rbind(TDF_Temp_max,totales)
library(dplyr)
library(gt)
TDF_Temp_max_final %>%
gt() %>%
tab_header(
title = md("Tabla Nro. 1"),
subtitle = md("*Tabla de distribución de la Temperatura Máxima (°C)*")
) %>%
tab_source_note(
source_note = md("Autor: Grupo 3")
) %>%
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 | ||||||||
| Tabla de distribución de la Temperatura Máxima (°C) | ||||||||
| Li | Ls | Mc | ni | hi | Ni_asc | Ni_desc | Hi_asc(%) | Hi_desc(%) |
|---|---|---|---|---|---|---|---|---|
| 10.32 | 11.82 | 11.07 | 26 | 7.1 | 26 | 366 | 7.1 | 100 |
| 11.82 | 13.31 | 12.565 | 60 | 16.39 | 86 | 340 | 23.5 | 92.9 |
| 13.31 | 14.81 | 14.06 | 71 | 19.4 | 157 | 280 | 42.9 | 76.5 |
| 14.81 | 16.31 | 15.56 | 60 | 16.39 | 217 | 209 | 59.29 | 57.1 |
| 16.31 | 17.8 | 17.055 | 62 | 16.94 | 279 | 149 | 76.23 | 40.71 |
| 17.8 | 19.3 | 18.55 | 44 | 12.02 | 323 | 87 | 88.25 | 23.77 |
| 19.3 | 20.8 | 20.05 | 23 | 6.28 | 346 | 43 | 94.54 | 11.75 |
| 20.8 | 22.29 | 21.545 | 14 | 3.83 | 360 | 20 | 98.36 | 5.46 |
| 22.29 | 23.79 | 23.04 | 6 | 1.64 | 366 | 6 | 100 | 1.64 |
| TOTAL | - | - | 366 | 100 | - | - | - | - |
| Autor: Grupo 3 | ||||||||
# Histograma
histoT <- hist(
Temp_max,
main = "Gráfica Nº1: Distribución de la Temperatura Máxima",
xlab = "Temperatura Máxima(°C)",
ylab = "Cantidad",
col = "blue"
)
#Simplificación con el histograma
Hist_Temp_Max<-hist(Temp_max,breaks = 8,plot = F)
k<-length(Hist_Temp_Max$breaks)
Li<-Hist_Temp_Max$breaks[1:(length(Hist_Temp_Max$breaks)-1)]
Ls<-Hist_Temp_Max$breaks[2:length(Hist_Temp_Max$breaks)]
ni<-Hist_Temp_Max$counts
sum(ni)## [1] 366Mc<-Hist_Temp_Max$mids
hi<-(ni/sum(ni))
sum(hi)## [1] 1Ni_asc<-cumsum(ni)
Hi_asc<-cumsum(hi)
Ni_desc<-rev(cumsum(rev(ni)))
Hi_desc<-rev(cumsum(rev(hi)))
TDF_Temp_Maxima<-data.frame(Li=round(Li,2),
Ls=round(Ls,2),
Mc=round(Mc,2),
ni=ni,
hi=round(hi*100,2),
Ni_asc=Ni_asc,
Ni_desc=Ni_desc,
Hi_asc=round(Hi_asc*100,2),
Hi_desc=round(Hi_desc*100,2))
colnames(TDF_Temp_Maxima)<-c("Lim inf","Lim sup","MC","ni","hi(%)","Ni asc","Ni desc","Hi asc(%)","Hi desc(%)")
#Crear fila de totales
totales<-c(Li="TOTAL",
Ls="-",
Mc="-",
ni = sum(as.numeric(TDF_Temp_Maxima$ni)),
hi = sum(as.numeric(TDF_Temp_Maxima$hi)),
Ni_asc="-",
Ni_desc="-",
Hi_asc="-",
Hi_desc="-")
TDF_Temp_Maxima_final<-rbind(TDF_Temp_Maxima,totales)
library(dplyr)
library(gt)
TDF_Temp_Maxima_final %>%
gt() %>%
tab_header(
title = md("Tabla Nro. 2"),
subtitle = md("*Tabla Simplificada de distribución de la Temperatura Máxima en el volcan Antisana*")
) %>%
tab_source_note(
source_note = md("Autor: Grupo 3")
) %>%
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. 2 | ||||||||
| Tabla Simplificada de distribución de la Temperatura Máxima en el volcan Antisana | ||||||||
| Lim inf | Lim sup | MC | ni | hi(%) | Ni asc | Ni desc | Hi asc(%) | Hi desc(%) |
|---|---|---|---|---|---|---|---|---|
| 10 | 12 | 11 | 30 | 8.2 | 30 | 366 | 8.2 | 100 |
| 12 | 14 | 13 | 94 | 25.68 | 124 | 336 | 33.88 | 91.8 |
| 14 | 16 | 15 | 78 | 21.31 | 202 | 242 | 55.19 | 66.12 |
| 16 | 18 | 17 | 82 | 22.4 | 284 | 164 | 77.6 | 44.81 |
| 18 | 20 | 19 | 50 | 13.66 | 334 | 82 | 91.26 | 22.4 |
| 20 | 22 | 21 | 25 | 6.83 | 359 | 32 | 98.09 | 8.74 |
| 22 | 24 | 23 | 7 | 1.91 | 366 | 7 | 100 | 1.91 |
| TOTAL | - | - | 366 | 99.99 | - | - | - | - |
| Autor: Grupo 3 | ||||||||
#Gráficas
hist(Temp_max, breaks = 10,
main = "Gráfica N°3 Distribución para la Temperatura Máxima en el Volcan Antisana ",
xlab = "Temperatura Máxima (°C)",
ylab = "Cantidad",
ylim = c(0,max(ni)),
col = "yellow",
cex.main = 0.9,
cex.lab = 1,
cex.axis = 0.9,
xaxt = "n")
axis(1, at = Hist_Temp_Max$breaks,
labels = Hist_Temp_Max$breaks, las = 1,
cex.axis = 0.9)
hist(Temp_max, breaks = 10,
main = "Gráfica N°4: Distribución de la Temperatura Máxima en el volcan Antisana ",
xlab = "Temperatura Máxima (°C)",
ylab = "Cantidad",
ylim = c(0, length(Temp_max)),
col = "green",
cex.main = 0.9,
cex.lab = 1,
cex.axis = 0.9,
xaxt = "n")
axis(1, at = Hist_Temp_Max$breaks,
labels = Hist_Temp_Max$breaks, las = 1,
cex.axis = 0.9)
TDF_Temp_Maxima_final$hi <- as.numeric(TDF_Temp_Maxima_final$hi)
datos_grafico <- subset(TDF_Temp_Maxima_final, !(MC %in% c("-", "TOTAL")))
barplot(datos_grafico$hi,
space = 0,
col = "blue",
main = "Gráfica N°5: Distribución porcentual de la Temperatura Máxima en el Volcan Antisana",
xlab = "Temperatura Máxima (°C)",
ylab = "Porcentaje (%)",
names.arg = datos_grafico$MC,
ylim = c(0, 30))
barplot(datos_grafico$hi,
space = 0,
col = "skyblue",
main = "Gráfica N°6: Distribución porcentual de la Temperatura Máxima en el Volcan Antisana",
xlab = "Temperatura °C",
ylab = "Porcentaje (%)",
names.arg = datos_grafico$MC,
ylim = c(0, 100))
# Boxplot
boxplot(
Temp_max,
horizontal = TRUE,
col = "pink",
main = "Gráfica Nº7: Distribución de la Temperatura Máxima",
xlab = "Temperatura Máxima (°C)",
outline = TRUE,
pch = 19
)
# Ojivas
plot(
Li, Ni_desc,
main = "Gráfica Nº8: Distribución Ascendente y Descendente de la Temperatura Máxima",
xlab = "Temperatura Máxima(°C)",
ylab = "Cantidad",
xlim = c(0, 100),
col = "red",
type = "o",
lwd = 3
)
lines(
Ls, Ni_asc,
col = "green",
type = "o",
lwd = 3
)
# Ojiva Porcentual
plot(
Li, Hi_desc,
main = "Gráfica Nº9: Distribución Ascendente y Descendente de la Temperatura Máxima",
xlab = "Temperatura Máxima (°C)",
ylab = "Porcentaje (%)",
xlim = c(0, 100),
col = "red",
type = "o",
lwd = 2
)
lines(
Ls, Hi_asc,
col = "blue",
type = "o",
lwd = 3
)
# INDICADORES ESTADISTICOS
# Indicadores de Tendencia Central
# Media aritmética
media <- round(mean(Temp_max), 0)
media## [1] 16# Moda
# Moda
max_frecuencia <- max(TDF_Temp_Maxima_final$ni)
moda <- TDF_Temp_Maxima_final$MC[TDF_Temp_Maxima_final$ni == max_frecuencia]
moda## [1] "13"# Mediana
mediana <- median(Temp_max)
mediana## [1] 15.51# INDICADORES DE DISPERSIÓN #
# Desviación Estándar
# Varianza
varianza <- var(Temp_max)
varianza## [1] 8.222732sd <- sd(Temp_max)
sd## [1] 2.867531# Coeficiente de Variación
cv <- round((sd / media) * 100, 2)
cv## [1] 17.92# INDICADORES DE FORMA #
# Coeficiente deAsimetría
library("e1071")
asimetria <- skewness(Temp_max, type = 2)
asimetria## [1] 0.3905542#Curtosis
curtosis <- kurtosis(Temp_max)
curtosis## [1] -0.5581832# TABLA RESUMEN FINAL
tabla_indicadores <- data.frame(
"Variable" = c("Temperatura Máxima"),
"Rango" = c(paste0("[", min(Temp_max), " ; ", max(Temp_max), "]")),
"X" = c(round(media, 0)),
"Me" = c(round(mediana, 0)),
"Mo" = c(paste(moda, collapse = ", ")),
"V" = c(round(varianza,2)),
"Sd" = c(round(sd, 0)),
"Cv" = c(cv),
"As" = c(round(asimetria, 2)),
"K" = c(round(curtosis, 2)),
"Valores Atípicos" = "-"
)
library(gt)
tabla_indicadores_gt <- tabla_indicadores %>%
gt() %>%
tab_header(
title = md("Tabla N°2.1"),
subtitle = md("*Indicadores estadísticos de la variable Temperatura Máxima*")
) %>%
tab_source_note(
source_note = md("Autor: Grupo 3")
) %>%
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",
table_body.hlines.color = "gray",
table_body.border.bottom.color = "black",
row.striping.include_table_body = TRUE,
heading.border.bottom.color = "black"
) %>%
tab_style(
style = cell_text(weight = "bold"),
locations = cells_body(
rows = Variable == "Temperatura Máxiima"
)
)
tabla_indicadores_gt| Tabla N°2.1 | ||||||||||
| Indicadores estadísticos de la variable Temperatura Máxima | ||||||||||
| Variable | Rango | X | Me | Mo | V | Sd | Cv | As | K | Valores.Atípicos |
|---|---|---|---|---|---|---|---|---|---|---|
| Temperatura Máxima | [10.32 ; 23.79] | 16 | 16 | 13 | 8.22 | 3 | 17.92 | 0.39 | -0.56 | - |
| Autor: Grupo 3 | ||||||||||
#CONCLUSIÓN
#La variable temperatura max, fluctúa entre 10.32 y 23.79,
#y sus valores giran entorno a 16 con una desviación estandar de 3, siendo un conjunto de datos homogéneo,
#los valores se acumulan de manera parcialmente debil en la parte baja de la variable,
#sin presencia de valores atípicos.
#Temperatura Mínima
Temp_min<- datos$Min.Temperature
min2 <-min(Temp_min)
max2 <-max(Temp_min)
R2 <-max2-min2
K2 <- floor(1+3.33*log10(length(Temp_min)))
A2 <-R2/K2
Li2 <-round(seq(from=min2,to=max2-A2,by=A2),2)
Ls2 <-round(seq(from=min2+A2,to=max2,by=A2),2)
Mc2 <-(Li2+Ls2)/2
ni2<-c()
for (i in 1:K2) {
if (i < K2) {
ni2[i] <- length(subset(Temp_min, Temp_min >= Li2[i] & Temp_min < Ls2[i]))
} else {
ni2[i] <- length(subset(Temp_min, Temp_min >= Li2[i] & Temp_min <= Ls2[i]))
}
}
sum(ni2)## [1] 366hi2 <-ni2/sum(ni2)*100
Ni_asc2<-cumsum(ni2)
Hi_asc2<-cumsum(hi2)
Ni_desc2<-rev(cumsum(rev(ni2)))
Hi_desc2<-rev(cumsum(rev(hi2)))
TDF_Temp_min <- data.frame(
Li2, Ls2, Mc2, ni2, round(hi2, 2), Ni_asc2, Ni_desc2, round(Hi_asc2, 2), round(Hi_desc2, 2)
)
colnames(TDF_Temp_min) <- c("Li","Ls","Mc","ni","hi","Ni_asc","Ni_desc","Hi_asc(%)","Hi_desc(%)")
#Crear fila de totales
totales<-c(
Li="TOTAL",
Ls="-",
Mc="-",
ni=sum(ni2),
hi=sum(hi2),
Ni_asc="-",
Ni_desc="-",
Hi_asc="-",
Hi_desc="-")
TDF_Temp_min_final <-rbind(TDF_Temp_min,totales)
library(dplyr)
library(gt)
TDF_Temp_min_final %>%
gt() %>%
tab_header(
title = md("Tabla Nro. 3"),
subtitle = md("*Tabla de distribución de la Temperatura Mínima en el Volcan Antisana (°C)*")
) %>%
tab_source_note(
source_note = md("Autor: Grupo 3")
) %>%
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. 3 | ||||||||
| Tabla de distribución de la Temperatura Mínima en el Volcan Antisana (°C) | ||||||||
| Li | Ls | Mc | ni | hi | Ni_asc | Ni_desc | Hi_asc(%) | Hi_desc(%) |
|---|---|---|---|---|---|---|---|---|
| 2.65 | 3.56 | 3.105 | 1 | 0.27 | 1 | 366 | 0.27 | 100 |
| 3.56 | 4.47 | 4.015 | 4 | 1.09 | 5 | 365 | 1.37 | 99.73 |
| 4.47 | 5.38 | 4.925 | 6 | 1.64 | 11 | 361 | 3.01 | 98.63 |
| 5.38 | 6.29 | 5.835 | 21 | 5.74 | 32 | 355 | 8.74 | 96.99 |
| 6.29 | 7.21 | 6.75 | 55 | 15.03 | 87 | 334 | 23.77 | 91.26 |
| 7.21 | 8.12 | 7.665 | 108 | 29.51 | 195 | 279 | 53.28 | 76.23 |
| 8.12 | 9.03 | 8.575 | 80 | 21.86 | 275 | 171 | 75.14 | 46.72 |
| 9.03 | 9.94 | 9.485 | 60 | 16.39 | 335 | 91 | 91.53 | 24.86 |
| 9.94 | 10.85 | 10.395 | 31 | 8.47 | 366 | 31 | 100 | 8.47 |
| TOTAL | - | - | 366 | 100 | - | - | - | - |
| Autor: Grupo 3 | ||||||||
# Histograma
histoT <- hist(
Temp_min,
main = "Gráfica Nº10: Distribución de la Temperatura Mínima",
xlab = "Temperatura Mínima(°C)",
ylab = "Cantidad",
col = "blue"
)
#Simplificación con el histograma
Hist_Temp_Min<-hist(Temp_min,breaks = 8,plot = F)
k2<-length(Hist_Temp_Min$breaks)
Li2<-Hist_Temp_Min$breaks[1:(length(Hist_Temp_Min$breaks)-1)]
Ls2<-Hist_Temp_Min$breaks[2:length(Hist_Temp_Min$breaks)]
ni2<-Hist_Temp_Min$counts
sum(ni2)## [1] 366Mc2<-Hist_Temp_Min$mids
hi2<-(ni2/sum(ni2))
sum(hi2)## [1] 1Ni_asc2<-cumsum(ni2)
Hi_asc2<-cumsum(hi2)
Ni_desc2<-rev(cumsum(rev(ni2)))
Hi_desc2<-rev(cumsum(rev(hi2)))
TDF_Temp_Mínima<-data.frame(Li=round(Li2,2),
Ls=round(Ls2,2),
Mc=round(Mc2,2),
ni=ni2,
hi=round(hi2*100,2),
Ni_asc=Ni_asc2,
Ni_desc=Ni_desc2,
Hi_asc=round(Hi_asc2*100,2),
Hi_desc=round(Hi_desc2*100,2))
colnames(TDF_Temp_Mínima)<-c("Lim inf","Lim sup","MC","ni","hi(%)","Ni asc","Ni desc","Hi asc(%)","Hi desc(%)")
#Crear fila de totales
totales<- c(Li="TOTAL",
Ls="-",
Mc="-",
ni = sum(as.numeric(TDF_Temp_Mínima$ni)),
hi = sum(as.numeric(TDF_Temp_Mínima$hi)),
Ni_asc="-",
Ni_desc="-",
Hi_asc="-",
Hi_desc="-"
)
TDF_Temp_Mínima_final<-rbind(TDF_Temp_Mínima,totales)
library(dplyr)
library(gt)
TDF_Temp_Mínima_final %>%
gt() %>%
tab_header(
title = md("Tabla Nro. 4"),
subtitle = md("*Tabla Simplificada de distribución de la Temperatura Mínima en el volcan Antisana*")
) %>%
tab_source_note(
source_note = md("Autor: Grupo 3")
) %>%
tab_options(
table.border.top.color = "black",
table.border.bottom.color = "black",
table.border.top.style = "solid",
table.border.bottom.style = "solid",
column_labels.border.top.color = "black",
column_labels.border.bottom.color = "black",
column_labels.border.bottom.width = px(2),
row.striping.include_table_body = TRUE,
heading.border.bottom.color = "black",
heading.border.bottom.width = px(2),
table_body.hlines.color = "gray",
table_body.border.bottom.color = "black"
)| Tabla Nro. 4 | ||||||||
| Tabla Simplificada de distribución de la Temperatura Mínima en el volcan Antisana | ||||||||
| Lim inf | Lim sup | MC | ni | hi(%) | Ni asc | Ni desc | Hi asc(%) | Hi desc(%) |
|---|---|---|---|---|---|---|---|---|
| 2 | 3 | 2.5 | 1 | 0.27 | 1 | 366 | 0.27 | 100 |
| 3 | 4 | 3.5 | 2 | 0.55 | 3 | 365 | 0.82 | 99.73 |
| 4 | 5 | 4.5 | 7 | 1.91 | 10 | 363 | 2.73 | 99.18 |
| 5 | 6 | 5.5 | 16 | 4.37 | 26 | 356 | 7.1 | 97.27 |
| 6 | 7 | 6.5 | 48 | 13.11 | 74 | 340 | 20.22 | 92.9 |
| 7 | 8 | 7.5 | 109 | 29.78 | 183 | 292 | 50 | 79.78 |
| 8 | 9 | 8.5 | 90 | 24.59 | 273 | 183 | 74.59 | 50 |
| 9 | 10 | 9.5 | 66 | 18.03 | 339 | 93 | 92.62 | 25.41 |
| 10 | 11 | 10.5 | 27 | 7.38 | 366 | 27 | 100 | 7.38 |
| TOTAL | - | - | 366 | 99.99 | - | - | - | - |
| Autor: Grupo 3 | ||||||||
#Gráficas
hist(Temp_min, breaks = 10,
main = "Gráfica N°11 Distribución para la Temperatura Mínima en el Volcan Antisana ",
xlab = "Temperatura Mínima (°C)",
ylab = "Cantidad",
ylim = c(0,max(ni2)),
col = "yellow",
cex.main = 0.9,
cex.lab = 1,
cex.axis = 0.9,
xaxt = "n")
axis(1, at = Hist_Temp_Min$breaks,
labels = Hist_Temp_Min$breaks, las = 1,
cex.axis = 0.9)
hist(Temp_min, breaks = 10,
main = "Gráfica N°12: Distribución de la Temperatura Mínima en el volcan Antisana ",
xlab = "Temperatura Mínima (°C)",
ylab = "Cantidad",
ylim = c(0, length(Temp_min)),
col = "green",
cex.main = 0.9,
cex.lab = 1,
cex.axis = 0.9,
xaxt = "n")
axis(1, at = Hist_Temp_Min$breaks,
labels = Hist_Temp_Min$breaks, las = 1,
cex.axis = 0.9)
df <- TDF_Temp_min_final
df$hi <- as.numeric(df$hi)
datos_grafico <- df[1:(nrow(df)-1), ]
barplot(
datos_grafico$hi,
space = 0,
col = "blue",
main = "Gráfica N°13: Distribución porcentual de la Temperatura Mínima en el Volcán Antisana",
xlab = "Temperatura Mínima (°C)",
ylab = "Porcentaje (%)",
names.arg = datos_grafico$Mc, # si tu columna se llama MC, cámbialo por datos_grafico$MC
ylim = c(0, max(datos_grafico$hi, na.rm = TRUE) + 5)
)
datos_grafico$hi <- as.numeric(datos_grafico$hi)
sum(datos_grafico$hi)## [1] 100barplot(
datos_grafico$hi,
space = 0,
col = "skyblue",
main = "Gráfica N°14: Distribución porcentual de la Temperatura Mínima en el Volcán Antisana",
xlab = "Temperatura Mínima (°C)",
ylab = "Porcentaje (%)",
names.arg = datos_grafico$MC,
ylim = c(0, 100)
)
# Boxplot
boxplot(
Temp_min,
horizontal = TRUE,
col = "pink",
main = "Gráfica Nº15: Distribución de la Temperatura Mínima",
xlab = "Temperatura Mínima (°C)",
outline = TRUE,
pch = 19
)
# Ojivas
plot(
Li2, Ni_desc2,
main = "Gráfica Nº16: Distribución Ascendente y Descendente de la Temperatura Mínima",
xlab = "Temperatura Mínima(°C)",
ylab = "Cantidad",
xlim = c(0, 100),
col = "red",
type = "o",
lwd = 3
)
lines(
Ls2, Ni_asc2,
col = "green",
type = "o",
lwd = 3
)
# Ojiva Porcentual
plot(
Li2, Hi_desc2,
main = "Gráfica Nº17: Distribución Ascendente y Descendente de la Temperatura Mínima",
xlab = "Temperatura Mínima (°C)",
ylab = "Porcentaje (%)",
xlim = c(0, 100),
col = "red",
type = "o",
lwd = 2
)
lines(
Ls2, Hi_asc2,
col = "blue",
type = "o",
lwd = 3
)
# INDICADORES ESTADISTICOS
# Indicadores de Tendencia Central
# Media aritmética
media2 <- round(mean(Temp_min), 0)
media2## [1] 8# Moda
# Moda
max_frecuencia2 <- max(TDF_Temp_Mínima_final$ni)
moda2 <- TDF_Temp_Mínima_final$Mc[TDF_Temp_Mínima_final$ni == max_frecuencia2]
moda2## NULL# Mediana
mediana2 <- median(Temp_min)
mediana2## [1] 8.005# INDICADORES DE DISPERSIÓN #
# Desviación Estándar
# Varianza
varianza2 <- var(Temp_min)
varianza2## [1] 1.888054sd2 <- sd(Temp_min)
sd2## [1] 1.374065# Coeficiente de Variación
cv2 <- round((sd2 / media2) * 100, 2)
cv2## [1] 17.18# INDICADORES DE FORMA #
# Coeficiente deAsimetría
library("e1071")
asimetria2 <- skewness(Temp_min, type = 2)
asimetria2## [1] -0.4376627#Curtosis
curtosis2 <- kurtosis(Temp_min)
curtosis2## [1] 0.5662281# TABLA RESUMEN FINAL
tabla_indicadores2 <- data.frame(
"Variable" = c("Temperatura Mínima"),
"Rango" = c(paste0("[", min(Temp_min), " ; ", max(Temp_min), "]")),
"X" = c(round(media2, 0)),
"Me" = c(round(mediana2, 0)),
"Mo" = c(paste(moda2, collapse = ", ")),
"V" = c(round(varianza2,2)),
"Sd" = c(round(sd2, 0)),
"Cv" = c(cv2),
"As" = c(round(asimetria2, 2)),
"K" = c(round(curtosis2, 2)),
"Valores Atípicos" = "7"
)
library(gt)
tabla_indicadores_gt2 <- tabla_indicadores2 %>%
gt() %>%
tab_header(
title = md("Tabla N°3.1"),
subtitle = md("*Indicadores estadísticos de la variable Temperatura Mínima*")
) %>%
tab_source_note(
source_note = md("Autor: Grupo 3")
) %>%
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",
table_body.hlines.color = "gray",
table_body.border.bottom.color = "black",
row.striping.include_table_body = TRUE,
heading.border.bottom.color = "black"
) %>%
tab_style(
style = cell_text(weight = "bold"),
locations = cells_body(
rows = Variable == "Temperatura Mínima"
)
)
tabla_indicadores_gt2| Tabla N°3.1 | ||||||||||
| Indicadores estadísticos de la variable Temperatura Mínima | ||||||||||
| Variable | Rango | X | Me | Mo | V | Sd | Cv | As | K | Valores.Atípicos |
|---|---|---|---|---|---|---|---|---|---|---|
| Temperatura Mínima | [2.65 ; 10.85] | 8 | 8 | 1.89 | 1 | 17.18 | -0.44 | 0.57 | 7 | |
| Autor: Grupo 3 | ||||||||||
#CONCLUSIÓN
#La variable temperatura min, fluctúa entre 2.65 y 10.85, y sus valores giran entorno a 8 con una desviación estandar de 1,
#siendo un conjunto de datos homogéneo, los valores se acumulan de manera parcialmente fuerte en la parte medianamente alta de la variable,
#con presencia de 7 valores atípicos.
#Precipitación
#Extracción Variable Cuantitativa Continua
Precipitacion<- datos$Precipitation
minp <-min(Precipitacion)
maxp <-max(Precipitacion)
Rp <-maxp-minp
Kp <- floor(1+3.33*log10(length(Precipitacion)))
Ap<-Rp/Kp
Lip <-round(seq(from=minp,to=maxp-Ap,by=Ap),2)
Lsp <-round(seq(from=minp+Ap,to=maxp,by=Ap),2)
Mcp <-(Lip+Lsp)/2
nip<-c()
for (i in 1:Kp) {
if (i < Kp) {
nip[i] <- length(subset(Precipitacion, Precipitacion >= Lip[i] & Precipitacion < Lsp[i]))
} else {
nip[i] <- length(subset(Precipitacion, Precipitacion >= Lip[i] & Precipitacion <= Lsp[i]))
}
}
sum(nip)## [1] 366hip <-nip/sum(nip)*100
Ni_ascp<-cumsum(nip)
Hi_ascp<-cumsum(hip)
Ni_descp<-rev(cumsum(rev(nip)))
Hi_descp<-rev(cumsum(rev(hip)))
TDF_Precipitacion <- data.frame(
Lip, Lsp, Mcp, nip, round(hip, 2), Ni_ascp, Ni_descp, round(Hi_ascp, 2), round(Hi_descp, 2)
)
colnames(TDF_Precipitacion) <- c("Li","Ls","Mc","ni","hi","Ni_asc","Ni_desc","Hi_asc(%)","Hi_desc(%)")
#Crear fila de totales
totales<-c(
Li="TOTAL",
Ls="-",
Mc="-",
ni=sum(nip),
hi=sum(hip),
Ni_asc="-",
Ni_desc="-",
Hi_asc="-",
Hi_desc="-")
TDF_Precipitacion_final <-rbind(TDF_Precipitacion,totales)
library(dplyr)
library(gt)
TDF_Precipitacion_final %>%
gt() %>%
tab_header(
title = md("Tabla Nro. 5"),
subtitle = md("*Tabla de distribución de la Precipitación en el Volcan Antisana (mm)*")
) %>%
tab_source_note(
source_note = md("Autor: Grupo 3")
) %>%
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. 5 | ||||||||
| Tabla de distribución de la Precipitación en el Volcan Antisana (mm) | ||||||||
| Li | Ls | Mc | ni | hi | Ni_asc | Ni_desc | Hi_asc(%) | Hi_desc(%) |
|---|---|---|---|---|---|---|---|---|
| 0.01 | 10.53 | 5.27 | 158 | 43.17 | 158 | 366 | 43.17 | 100 |
| 10.53 | 21.06 | 15.795 | 89 | 24.32 | 247 | 208 | 67.49 | 56.83 |
| 21.06 | 31.58 | 26.32 | 56 | 15.3 | 303 | 119 | 82.79 | 32.51 |
| 31.58 | 42.1 | 36.84 | 33 | 9.02 | 336 | 63 | 91.8 | 17.21 |
| 42.1 | 52.63 | 47.365 | 16 | 4.37 | 352 | 30 | 96.17 | 8.2 |
| 52.63 | 63.15 | 57.89 | 9 | 2.46 | 361 | 14 | 98.63 | 3.83 |
| 63.15 | 73.67 | 68.41 | 3 | 0.82 | 364 | 5 | 99.45 | 1.37 |
| 73.67 | 84.2 | 78.935 | 0 | 0 | 364 | 2 | 99.45 | 0.55 |
| 84.2 | 94.72 | 89.46 | 2 | 0.55 | 366 | 2 | 100 | 0.55 |
| TOTAL | - | - | 366 | 100 | - | - | - | - |
| Autor: Grupo 3 | ||||||||
# Histograma
histoP <- hist(
Precipitacion,
main = "Gráfica Nº1: Distribución de la Precipitación en el Volcan Antisana",
xlab = "Precitación(°C)",
ylab = "Cantidad",
col = "blue"
)
#Simplificación con el histograma
Hist_Precipitacion<-hist(Precipitacion,breaks = 8,plot = F)
kp<-length(Hist_Precipitacion$breaks)
Lip<-Hist_Precipitacion$breaks[1:(length(Hist_Precipitacion$breaks)-1)]
Lsp<-Hist_Precipitacion$breaks[2:length(Hist_Precipitacion$breaks)]
nip<-Hist_Precipitacion$counts
sum(nip)## [1] 366Mcp<-Hist_Precipitacion$mids
hip<-(nip/sum(nip))
sum(hip)## [1] 1Ni_ascp<-cumsum(nip)
Hi_ascp<-cumsum(hip)
Ni_descp<-rev(cumsum(rev(nip)))
Hi_descp<-rev(cumsum(rev(hip)))
TDF_Precipitacion_F<-data.frame(Li=round(Lip,2),
Ls=round(Lsp,2),
Mc=round(Mcp,2),
ni=nip,
hi=round(hip*100,2),
Ni_asc=Ni_ascp,
Ni_desc=Ni_descp,
Hi_asc=round(Hi_ascp*100,2),
Hi_desc=round(Hi_descp*100,2))
colnames(TDF_Precipitacion_F)<-c("Lim inf","Lim sup","MC","ni","hi(%)","Ni asc","Ni desc","Hi asc(%)","Hi desc(%)")
#Crear fila de totales
totales<-c(Li="TOTAL",
Ls="-",
Mc="-",
ni = sum(as.numeric(TDF_Precipitacion_F$ni)),
hi = sum(as.numeric(TDF_Precipitacion_F$hi)),
Ni_asc="-",
Ni_desc="-",
Hi_asc="-",
Hi_desc="-")
TDF_Precipitacion_F<-rbind(TDF_Precipitacion_F,totales)
library(dplyr)
library(gt)
TDF_Precipitacion_F %>%
gt() %>%
tab_header(
title = md("Tabla Nro. 6"),
subtitle = md("*Tabla Simplificada de distribución de la Precipitación en el volcan Antisana*")
) %>%
tab_source_note(
source_note = md("Autor: Grupo 3")
) %>%
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. 6 | ||||||||
| Tabla Simplificada de distribución de la Precipitación en el volcan Antisana | ||||||||
| Lim inf | Lim sup | MC | ni | hi(%) | Ni asc | Ni desc | Hi asc(%) | Hi desc(%) |
|---|---|---|---|---|---|---|---|---|
| 0 | 10 | 5 | 150 | 40.98 | 150 | 366 | 40.98 | 100 |
| 10 | 20 | 15 | 92 | 25.14 | 242 | 216 | 66.12 | 59.02 |
| 20 | 30 | 25 | 58 | 15.85 | 300 | 124 | 81.97 | 33.88 |
| 30 | 40 | 35 | 27 | 7.38 | 327 | 66 | 89.34 | 18.03 |
| 40 | 50 | 45 | 23 | 6.28 | 350 | 39 | 95.63 | 10.66 |
| 50 | 60 | 55 | 10 | 2.73 | 360 | 16 | 98.36 | 4.37 |
| 60 | 70 | 65 | 4 | 1.09 | 364 | 6 | 99.45 | 1.64 |
| 70 | 80 | 75 | 0 | 0 | 364 | 2 | 99.45 | 0.55 |
| 80 | 90 | 85 | 1 | 0.27 | 365 | 2 | 99.73 | 0.55 |
| 90 | 100 | 95 | 1 | 0.27 | 366 | 1 | 100 | 0.27 |
| TOTAL | - | - | 366 | 99.99 | - | - | - | - |
| Autor: Grupo 3 | ||||||||
#Gráficas
hist(Precipitacion, breaks = 10,
main = "Gráfica N°3 Distribución para la Precipitación en el Volcan Antisana ",
xlab = "Precipitación (mm)",
ylab = "Cantidad",
ylim = c(0,max(nip)),
col = "yellow",
cex.main = 0.9,
cex.lab = 1,
cex.axis = 0.9,
xaxt = "n")
axis(1, at = Hist_Precipitacion$breaks,
labels = Hist_Precipitacion$breaks, las = 1,
cex.axis = 0.9)
hist(Precipitacion, breaks = 10,
main = "Gráfica N°4: Distribución de la Precipitacion en el volcan Antisana ",
xlab = "Precipitación (mm)",
ylab = "Cantidad",
ylim = c(0, length(Precipitacion)),
col = "green",
cex.main = 0.9,
cex.lab = 1,
cex.axis = 0.9,
xaxt = "n")
axis(1, at = Hist_Precipitacion$breaks,
labels = Hist_Precipitacion$breaks, las = 1,
cex.axis = 0.9)
TDF_Precipitacion_F$hi <- as.numeric(TDF_Precipitacion_F$hi)
datos_grafico <- TDF_Precipitacion_F[1:(nrow(TDF_Precipitacion_F) - 1), ]
barplot(
datos_grafico$hi,
space = 0,
col = "blue",
main = "Gráfica N°5: Distribución porcentual de la Precipitación en el Volcán Antisana",
xlab = "Precipitación (mm)",
ylab = "Porcentaje (%)",
names.arg = datos_grafico$Mcp,
ylim = c(0, max(datos_grafico$hi) + 5)
)
datos_grafico$hi <- as.numeric(datos_grafico$hi)
barplot(
datos_grafico$hi,
space = 0,
col = "skyblue",
main = "Gráfica N°6: Distribución porcentual de la Precipitación en el Volcán Antisana",
xlab = "Precipitación (mm)",
ylab = "Porcentaje (%)",
names.arg = datos_grafico$Mcp,
ylim = c(0, 100)
)
# Boxplot
boxplot(
Precipitacion,
horizontal = TRUE,
col = "pink",
main = "Gráfica Nº7: Distribución de la Precipitación",
xlab = "Precipitación (mm)",
outline = TRUE,
pch = 19
)
# Ojivas
plot(
Lip, Ni_descp,
main = "Gráfica Nº8: Distribución Ascendente y Descendente de la Precipitación",
xlab = "Precipitación(mm)",
ylab = "Cantidad",
xlim = c(0, 100),
col = "red",
type = "o",
lwd = 3
)
lines(
Lsp, Ni_ascp,
col = "green",
type = "o",
lwd = 3
)
# Ojiva Porcentual
plot(
Lip, Hi_descp,
main = "Gráfica Nº9: Distribución Ascendente y Descendente de la Precipitación",
xlab = "Precipitación(mm)",
ylab = "Porcentaje (%)",
xlim = c(0, 100),
col = "red",
type = "o",
lwd = 2
)
lines(
Lsp, Hi_ascp,
col = "blue",
type = "o",
lwd = 3
)
# INDICADORES ESTADISTICOS
# Indicadores de Tendencia Central
# Media aritmética
mediap <- round(mean(Precipitacion), 0)
mediap## [1] 17# Moda
max_frecuenciap <- max(TDF_Precipitacion_F$ni)
modap <- TDF_Precipitacion_F$MC[TDF_Precipitacion_F$ni == max_frecuenciap]
modap## [1] "15"# Mediana
medianap <- median(Precipitacion)
medianap## [1] 12.94# INDICADORES DE DISPERSIÓN #
# Desviación Estándar
# Varianza
varianzap <- var(Precipitacion)
varianzap## [1] 259.6987sdp <- sd(Precipitacion)
sdp## [1] 16.11517# Coeficiente de Variación
cvp <- round((sdp / mediap) * 100, 2)
cvp## [1] 94.8# INDICADORES DE FORMA #
# Coeficiente deAsimetría
library("e1071")
asimetriap <- skewness(Precipitacion, type = 2)
asimetriap## [1] 1.305768#Curtosis
curtosisp <- kurtosis(Precipitacion)
curtosisp## [1] 1.951113# TABLA RESUMEN FINAL
tabla_indicadoresp <- data.frame(
"Variable" = c("Precipitación"),
"Rango" = c(paste0("[", min(Precipitacion), " ; ", max(Precipitacion), "]")),
"X" = c(round(mediap, 0)),
"Me" = c(round(medianap, 0)),
"Mo" = c(paste(modap, collapse = ", ")),
"V" = c(round(varianzap,2)),
"Sd" = c(round(sdp, 0)),
"Cv" = c(cvp),
"As" = c(round(asimetriap, 2)),
"K" = c(round(curtosisp, 2)),
"Valores Atípicos" = "8"
)
library(gt)
tabla_indicadores_gtp <- tabla_indicadoresp %>%
gt() %>%
tab_header(
title = md("Tabla N°4.1"),
subtitle = md("*Indicadores estadísticos de la variable Precipitación*")
) %>%
tab_source_note(
source_note = md("Autor: Grupo 3")
) %>%
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",
table_body.hlines.color = "gray",
table_body.border.bottom.color = "black",
row.striping.include_table_body = TRUE,
heading.border.bottom.color = "black"
) %>%
tab_style(
style = cell_text(weight = "bold"),
locations = cells_body(
rows = Variable == "Precipitación"
)
)
tabla_indicadores_gtp| Tabla N°4.1 | ||||||||||
| Indicadores estadísticos de la variable Precipitación | ||||||||||
| Variable | Rango | X | Me | Mo | V | Sd | Cv | As | K | Valores.Atípicos |
|---|---|---|---|---|---|---|---|---|---|---|
| Precipitación | [0.01 ; 94.72] | 17 | 13 | 15 | 259.7 | 16 | 94.8 | 1.31 | 1.95 | 8 |
| Autor: Grupo 3 | ||||||||||
#CONCLUSIÓN:
#La variable Precipitación, fluctúa entre 0,01 y 94,72, y sus valores giran entorno a 17 con una desviación estandar de 16,
#siendo un conjunto de datos muy heterogéneo, los valores se acumulan de manera fuerte en la parte baja de la variable,
#con presencia de 8 valores atípicos.
#Viento
Viento<- datos$Wind
minV <-min(Viento)
maxV <-max(Viento)
RV <-maxV-minV
KV <- floor(1+3.33*log10(length(Viento)))
AV<-RV/KV
LiV <-round(seq(from=minV,to=maxV-AV,by=AV),2)
LsV <-round(seq(from=minV+AV,to=maxV,by=AV),2)
McV <-(LiV+LsV)/2
niV<-c()
for (i in 1:KV) {
if (i < KV) {
niV[i] <- length(subset(Viento, Viento >= LiV[i] & Viento < LsV[i]))
} else {
niV[i] <- length(subset(Viento, Viento >= LiV[i] & Viento <= LsV[i]))
}
}
sum(niV)## [1] 366hiV <-niV/sum(niV)*100
Ni_ascV<-cumsum(niV)
Hi_ascV<-cumsum(hiV)
Ni_descV<-rev(cumsum(rev(niV)))
Hi_descV<-rev(cumsum(rev(hiV)))
TDF_Viento <- data.frame(
LiV, LsV, McV, niV, round(hiV, 2), Ni_ascV, Ni_descV, round(Hi_ascV, 2), round(Hi_descV, 2)
)
colnames(TDF_Viento) <- c("Li","Ls","Mc","ni","hi","Ni_asc","Ni_desc","Hi_asc(%)","Hi_desc(%)")
#Crear fila de totales
totales<-c(
Li="TOTAL",
Ls="-",
Mc="-",
ni=sum(niV),
hi=sum(hiV),
Ni_asc="-",
Ni_desc="-",
Hi_asc="-",
Hi_desc="-")
TDF_Viento_final <-rbind(TDF_Viento,totales)
library(dplyr)
library(gt)
TDF_Viento_final %>%
gt() %>%
tab_header(
title = md("Tabla Nro. 7"),
subtitle = md("*Tabla de distribución del Viento en el Volcan Antisana *")
) %>%
tab_source_note(
source_note = md("Autor: Grupo 3")
) %>%
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. 7 | ||||||||
| *Tabla de distribución del Viento en el Volcan Antisana * | ||||||||
| Li | Ls | Mc | ni | hi | Ni_asc | Ni_desc | Hi_asc(%) | Hi_desc(%) |
|---|---|---|---|---|---|---|---|---|
| 0.59 | 0.86 | 0.725 | 2 | 0.55 | 2 | 366 | 0.55 | 100 |
| 0.86 | 1.12 | 0.99 | 23 | 6.28 | 25 | 364 | 6.83 | 99.45 |
| 1.12 | 1.39 | 1.255 | 56 | 15.3 | 81 | 341 | 22.13 | 93.17 |
| 1.39 | 1.66 | 1.525 | 78 | 21.31 | 159 | 285 | 43.44 | 77.87 |
| 1.66 | 1.92 | 1.79 | 71 | 19.4 | 230 | 207 | 62.84 | 56.56 |
| 1.92 | 2.19 | 2.055 | 62 | 16.94 | 292 | 136 | 79.78 | 37.16 |
| 2.19 | 2.46 | 2.325 | 48 | 13.11 | 340 | 74 | 92.9 | 20.22 |
| 2.46 | 2.72 | 2.59 | 23 | 6.28 | 363 | 26 | 99.18 | 7.1 |
| 2.72 | 2.99 | 2.855 | 3 | 0.82 | 366 | 3 | 100 | 0.82 |
| TOTAL | - | - | 366 | 100 | - | - | - | - |
| Autor: Grupo 3 | ||||||||
# Histograma
histoV <- hist(
Viento,
main = "Gráfica Nº1: Distribución del Viento en el Volcan Antisana",
xlab = "Viento(m/s)",
ylab = "Cantidad",
col = "blue"
)
#Simplificación con el histograma
Hist_Viento<-hist(Viento,breaks = 8,plot = F)
kV<-length(Hist_Viento$breaks)
LiV<-Hist_Viento$breaks[1:(length(Hist_Viento$breaks)-1)]
LsV<-Hist_Viento$breaks[2:length(Hist_Viento$breaks)]
niV<-Hist_Viento$counts
sum(niV)## [1] 366McV<-Hist_Viento$mids
hiV<-(niV/sum(niV))
sum(hiV)## [1] 1Ni_ascV<-cumsum(niV)
Hi_ascV<-cumsum(hiV)
Ni_descV<-rev(cumsum(rev(niV)))
Hi_descV<-rev(cumsum(rev(hiV)))
TDF_Viento_F<-data.frame(Li=round(LiV,2),
Ls=round(LsV,2),
Mc=round(McV,2),
ni=niV,
hi=round(hiV*100,2),
Ni_asc=Ni_ascV,
Ni_desc=Ni_descV,
Hi_asc=round(Hi_ascV*100,2),
Hi_desc=round(Hi_descV*100,2))
colnames(TDF_Viento_F)<-c("Lim inf","Lim sup","MC","ni","hi(%)","Ni asc","Ni desc","Hi asc(%)","Hi desc(%)")
#Crear fila de totales
totales<-c(Li="TOTAL",
Ls="-",
Mc="-",
ni = sum(as.numeric(TDF_Viento_F$ni)),
hi = sum(as.numeric(TDF_Viento_F$hi)),
Ni_asc="-",
Ni_desc="-",
Hi_asc="-",
Hi_desc="-")
TDF_Viento_F<-rbind(TDF_Viento_F,totales)
library(dplyr)
library(gt)
TDF_Viento_F %>%
gt() %>%
tab_header(
title = md("Tabla Nro. 8"),
subtitle = md("*Tabla Simplificada de distribución del Viento en el volcan Antisana*")
) %>%
tab_source_note(
source_note = md("Autor: Grupo 3")
) %>%
tab_options(
table.border.top.color = "black",
table.border.bottom.color = "black",
table.border.top.style = "solid",
table.border.bottom.style = "solid",
column_labels.border.top.color = "black",
column_labels.border.bottom.color = "black",
column_labels.border.bottom.width = px(2),
row.striping.include_table_body = TRUE,
heading.border.bottom.color = "black",
heading.border.bottom.width = px(2),
table_body.hlines.color = "gray",
table_body.border.bottom.color = "black"
)| Tabla Nro. 8 | ||||||||
| Tabla Simplificada de distribución del Viento en el volcan Antisana | ||||||||
| Lim inf | Lim sup | MC | ni | hi(%) | Ni asc | Ni desc | Hi asc(%) | Hi desc(%) |
|---|---|---|---|---|---|---|---|---|
| 0.5 | 1 | 0.75 | 12 | 3.28 | 12 | 366 | 3.28 | 100 |
| 1 | 1.5 | 1.25 | 107 | 29.23 | 119 | 354 | 32.51 | 96.72 |
| 1.5 | 2 | 1.75 | 130 | 35.52 | 249 | 247 | 68.03 | 67.49 |
| 2 | 2.5 | 2.25 | 96 | 26.23 | 345 | 117 | 94.26 | 31.97 |
| 2.5 | 3 | 2.75 | 21 | 5.74 | 366 | 21 | 100 | 5.74 |
| TOTAL | - | - | 366 | 100 | - | - | - | - |
| Autor: Grupo 3 | ||||||||
#Gráficas
hist(Viento, breaks = 10,
main = "Gráfica N°3 Distribución para el Viento en el Volcan Antisana ",
xlab = "Viento (m/S)",
ylab = "Cantidad",
ylim = c(0,max(niV)),
col = "yellow",
cex.main = 0.9,
cex.lab = 1,
cex.axis = 0.9,
xaxt = "n")
axis(1, at = Hist_Viento$breaks,
labels = Hist_Viento$breaks, las = 1,
cex.axis = 0.9)
hist(Viento, breaks = 10,
main = "Gráfica N°4: Distribución del Viento en el volcan Antisana ",
xlab = "Viento (m/s)",
ylab = "Cantidad",
ylim = c(0, length(Viento)),
col = "green",
cex.main = 0.9,
cex.lab = 1,
cex.axis = 0.9,
xaxt = "n")
axis(1, at = Hist_Viento$breaks,
labels = Hist_Viento$breaks, las = 1,
cex.axis = 0.9)
TDF_Viento_F$`hi(%)` <- as.numeric(TDF_Viento_F$`hi(%)`)
datos_grafico_Viento <- TDF_Viento_F[1:(nrow(TDF_Viento_F)-1), ]
post <- barplot(datos_grafico_Viento$`hi(%)`,
space = 0,
col = "blue",
main = "Gráfica N°5: Distribución porcentual del viento en el volcán Antisana",
xlab = "Viento (m/s)",
ylab = "Porcentaje (%)",
ylim = c(0, max(datos_grafico_Viento$`hi(%)`) + 5))
axis(1, at = post, labels = datos_grafico_Viento$MC, las = 1, cex.axis = 0.8)
datos_grafico_Viento$hi <- as.numeric(datos_grafico_Viento$hi)
barplot(
datos_grafico_Viento$hi,
space = 0,
col = "skyblue",
main = "Gráfica N°6: Distribución porcentual de la Precipitación en el Volcán Antisana",
xlab = "Viento (m/S)",
ylab = "Porcentaje (%)",
names.arg = datos_grafico_Viento$McV,
ylim = c(0, 100)
)
# Boxplot
boxplot(
Viento,
horizontal = TRUE,
col = "pink",
main = "Gráfica Nº7: Distribución del Viento",
xlab = "Viento (m/S)",
outline = TRUE,
pch = 19
)
# Ojivas
plot(
LiV, Ni_descV,
main = "Gráfica Nº8: Distribución Ascendente y Descendente del Viento",
xlab = " Viento (m/S)",
ylab = "Cantidad",
xlim = c(0, 100),
col = "red",
type = "o",
lwd = 3
)
lines(
LsV, Ni_ascV,
col = "green",
type = "o",
lwd = 3
)
# Ojiva Porcentual
plot(
LiV, Hi_descV,
main = "Gráfica Nº9: Distribución Ascendente y Descendente del Viento",
xlab = " Viento",
ylab = "Porcentaje (%)",
xlim = c(0, 100),
col = "red",
type = "o",
lwd = 2
)
lines(
LsV, Hi_ascV,
col = "blue",
type = "o",
lwd = 3
)
# INDICADORES ESTADISTICOS
# Indicadores de Tendencia Central
# Media aritmética
mediav <- round(mean(Viento), 0)
mediav## [1] 2# Moda
max_frecuenciav <- max(TDF_Viento_F$ni)
modaV <- TDF_Viento_F$MC[TDF_Viento_F$ni == max_frecuenciav]
modaV## [1] "2.25"# Mediana
medianaV <- median(Viento)
medianaV## [1] 1.75# INDICADORES DE DISPERSIÓN #
# Desviación Estándar
# Varianza
varianzaV <- var(Viento)
varianzaV## [1] 0.2077148sdV <- sd(Viento)
sdV## [1] 0.4557574# Coeficiente de Variación
cvV <- round((sdV / mediav) * 100, 2)
cvV## [1] 22.79# INDICADORES DE FORMA #
# Coeficiente deAsimetría
library("e1071")
asimetriaV <- skewness(Viento, type = 2)
asimetriaV## [1] 0.1112888#Curtosis
curtosisV <- kurtosis(Viento)
curtosisV## [1] -0.719341# TABLA RESUMEN FINAL
tabla_indicadoresV <- data.frame(
"Variable" = c("Viento"),
"Rango" = c(paste0("[", min(Viento), " ; ", max(Viento), "]")),
"X" = c(round(mediav, 0)),
"Me" = c(round(medianaV, 0)),
"Mo" = c(paste(modaV, collapse = ", ")),
"V" = c(round(varianzaV,2)),
"Sd" = c(round(sdV, 0)),
"Cv" = c(cvV),
"As" = c(round(asimetriaV, 2)),
"K" = c(round(curtosisV, 2)),
"Valores Atípicos" = "-"
)
library(gt)
tabla_indicadores_gtV <- tabla_indicadoresV %>%
gt() %>%
tab_header(
title = md("Tabla N°8.1"),
subtitle = md("*Indicadores estadísticos de la variable Viento*")
) %>%
tab_source_note(
source_note = md("Autor: Grupo 3")
) %>%
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",
table_body.hlines.color = "gray",
table_body.border.bottom.color = "black",
row.striping.include_table_body = TRUE,
heading.border.bottom.color = "black"
) %>%
tab_style(
style = cell_text(weight = "bold"),
locations = cells_body(
rows = Variable == "Precipitación"
)
)
tabla_indicadores_gtV| Tabla N°8.1 | ||||||||||
| Indicadores estadísticos de la variable Viento | ||||||||||
| Variable | Rango | X | Me | Mo | V | Sd | Cv | As | K | Valores.Atípicos |
|---|---|---|---|---|---|---|---|---|---|---|
| Viento | [0.59 ; 2.99] | 2 | 2 | 2.25 | 0.21 | 0 | 22.79 | 0.11 | -0.72 | - |
| Autor: Grupo 3 | ||||||||||
#CONLUSIÓN:
#La variable viento, fluctúa entre 0.59 y 2.99, y sus valores giran entorno a 2 con una desviación estandar de 0.45,
#siendo un conjunto de datos homogéneo, los valores se acumulan de manera parcialmente debil en la parte media de la variable,
#sin presencia de valores atípicos.
# Humead Relativa
Humedad<- datos$Relative.Humidity
minH <-min(Humedad)
maxH <-max(Humedad)
RH <-maxH-minH
KH <- floor(1+3.33*log10(length(Humedad)))
AH<-RH/KH
LiH <-round(seq(from=minH,to=maxH-AH,by=AH),2)
LsH <-round(seq(from=minH+AH,to=maxH,by=AH),2)
McH <-(LiH+LsH)/2
niH<-c()
for (i in 1:KH) {
if (i < KH) {
niH[i] <- length(subset(Humedad, Humedad >= LiH[i] & Humedad< LsH[i]))
} else {
niH[i] <- length(subset(Humedad, Humedad >= LiH[i] & Humedad <= LsH[i]))
}
}
sum(niH)## [1] 366hiH <-niH/sum(niH)*100
Ni_ascH<-cumsum(niH)
Hi_ascH<-cumsum(hiH)
Ni_descH<-rev(cumsum(rev(niH)))
Hi_descH<-rev(cumsum(rev(hiH)))
TDF_Humedad <- data.frame(
LiH, LsH, McH, niH, round(hiH, 2), Ni_ascH, Ni_descH, round(Hi_ascH, 2), round(Hi_descH, 2)
)
colnames(TDF_Humedad) <- c("Li","Ls","Mc","ni","hi","Ni_asc","Ni_desc","Hi_asc(%)","Hi_desc(%)")
#Crear fila de totales
totales<-c(
Li="TOTAL",
Ls="-",
Mc="-",
ni=sum(niH),
hi=sum(hiH),
Ni_asc="-",
Ni_desc="-",
Hi_asc="-",
Hi_desc="-")
TDF_Humedad_final <-rbind(TDF_Humedad,totales)
library(dplyr)
library(gt)
TDF_Humedad_final %>%
gt() %>%
tab_header(
title = md("Tabla Nro. 9"),
subtitle = md("*Tabla de distribución de la Humedad Relativa en el Volcan Antisana *")
) %>%
tab_source_note(
source_note = md("Autor: Grupo 3")
) %>%
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. 9 | ||||||||
| *Tabla de distribución de la Humedad Relativa en el Volcan Antisana * | ||||||||
| Li | Ls | Mc | ni | hi | Ni_asc | Ni_desc | Hi_asc(%) | Hi_desc(%) |
|---|---|---|---|---|---|---|---|---|
| 0.56 | 0.61 | 0.585 | 2 | 0.55 | 2 | 366 | 0.55 | 100 |
| 0.61 | 0.66 | 0.635 | 15 | 4.1 | 17 | 364 | 4.64 | 99.45 |
| 0.66 | 0.7 | 0.68 | 16 | 4.37 | 33 | 349 | 9.02 | 95.36 |
| 0.7 | 0.75 | 0.725 | 20 | 5.46 | 53 | 333 | 14.48 | 90.98 |
| 0.75 | 0.8 | 0.775 | 19 | 5.19 | 72 | 313 | 19.67 | 85.52 |
| 0.8 | 0.85 | 0.825 | 20 | 5.46 | 92 | 294 | 25.14 | 80.33 |
| 0.85 | 0.89 | 0.87 | 28 | 7.65 | 120 | 274 | 32.79 | 74.86 |
| 0.89 | 0.94 | 0.915 | 53 | 14.48 | 173 | 246 | 47.27 | 67.21 |
| 0.94 | 0.99 | 0.965 | 193 | 52.73 | 366 | 193 | 100 | 52.73 |
| TOTAL | - | - | 366 | 100 | - | - | - | - |
| Autor: Grupo 3 | ||||||||
# Histograma
histoH <- hist(
Humedad,
main = "Gráfica Nº1: Distribución de la Humedad Relativa en el Volcan Antisana",
xlab = "Humedad(%)",
ylab = "Cantidad",
col = "blue"
)
#Simplificación con el histograma
Hist_Humedad<-hist(Humedad,breaks = 8,plot = F)
kH<-length(Hist_Viento$breaks)
LiH<-Hist_Humedad$breaks[1:(length(Hist_Humedad$breaks)-1)]
LsH<-Hist_Humedad$breaks[2:length(Hist_Humedad$breaks)]
niH<-Hist_Humedad$counts
sum(niH)## [1] 366McH<-Hist_Humedad$mids
hiH<-(niH/sum(niH))
sum(hiH)## [1] 1Ni_ascH<-cumsum(niH)
Hi_ascH<-cumsum(hiH)
Ni_descH<-rev(cumsum(rev(niH)))
Hi_descH<-rev(cumsum(rev(hiH)))
TDF_Humedad_F<-data.frame(Li=round(LiH,2),
Ls=round(LsH,2),
Mc=round(McH,2),
ni=niH,
hi=round(hiH*100,2),
Ni_asc=Ni_ascH,
Ni_desc=Ni_descH,
Hi_asc=round(Hi_ascH*100,2),
Hi_desc=round(Hi_descH*100,2))
colnames(TDF_Humedad_F)<-c("Lim inf","Lim sup","MC","ni","hi(%)","Ni asc","Ni desc","Hi asc(%)","Hi desc(%)")
#Crear fila de totales
totales<-c(Li="TOTAL",
Ls="-",
Mc="-",
ni = sum(as.numeric(TDF_Humedad_F$ni)),
hi = sum(as.numeric(TDF_Humedad_F$hi)),
Ni_asc="-",
Ni_desc="-",
Hi_asc="-",
Hi_desc="-")
TDF_Humedad_F<-rbind(TDF_Humedad_F,totales)
library(dplyr)
library(gt)
TDF_Humedad_F %>%
gt() %>%
tab_header(
title = md("Tabla Nro. 10"),
subtitle = md("*Tabla Simplificada de distribución de la Humedad Relativa en el volcan Antisana*")
) %>%
tab_source_note(
source_note = md("Autor: Grupo 3")
) %>%
tab_options(
table.border.top.color = "black",
table.border.bottom.color = "black",
table.border.top.style = "solid",
table.border.bottom.style = "solid",
column_labels.border.top.color = "black",
column_labels.border.bottom.color = "black",
column_labels.border.bottom.width = px(2),
row.striping.include_table_body = TRUE,
heading.border.bottom.color = "black",
heading.border.bottom.width = px(2),
table_body.hlines.color = "gray",
table_body.border.bottom.color = "black"
)| Tabla Nro. 10 | ||||||||
| Tabla Simplificada de distribución de la Humedad Relativa en el volcan Antisana | ||||||||
| Lim inf | Lim sup | MC | ni | hi(%) | Ni asc | Ni desc | Hi asc(%) | Hi desc(%) |
|---|---|---|---|---|---|---|---|---|
| 0.55 | 0.6 | 0.58 | 2 | 0.55 | 2 | 366 | 0.55 | 100 |
| 0.6 | 0.65 | 0.62 | 15 | 4.1 | 17 | 364 | 4.64 | 99.45 |
| 0.65 | 0.7 | 0.68 | 18 | 4.92 | 35 | 349 | 9.56 | 95.36 |
| 0.7 | 0.75 | 0.73 | 21 | 5.74 | 56 | 331 | 15.3 | 90.44 |
| 0.75 | 0.8 | 0.78 | 18 | 4.92 | 74 | 310 | 20.22 | 84.7 |
| 0.8 | 0.85 | 0.83 | 25 | 6.83 | 99 | 292 | 27.05 | 79.78 |
| 0.85 | 0.9 | 0.88 | 41 | 11.2 | 140 | 267 | 38.25 | 72.95 |
| 0.9 | 0.95 | 0.92 | 59 | 16.12 | 199 | 226 | 54.37 | 61.75 |
| 0.95 | 1 | 0.98 | 167 | 45.63 | 366 | 167 | 100 | 45.63 |
| TOTAL | - | - | 366 | 100.01 | - | - | - | - |
| Autor: Grupo 3 | ||||||||
#Gráficas
hist(Humedad, breaks = 10,
main = "Gráfica N°3 Distribución para la Humedad Relativa en el Volcan Antisana ",
xlab = "Humedad Relativa (%)",
ylab = "Cantidad",
ylim = c(0,max(niH)),
col = "yellow",
cex.main = 0.9,
cex.lab = 1,
cex.axis = 0.9,
xaxt = "n")
axis(1, at = Hist_Humedad$breaks,
labels = Hist_Humedad$breaks, las = 1,
cex.axis = 0.9)
hist(Humedad, breaks = 10,
main = "Gráfica N°4: Distribución de la Humedad Relativa en el volcan Antisana ",
xlab = "Humedad Relativa (%)",
ylab = "Cantidad",
ylim = c(0, length(Humedad)),
col = "green",
cex.main = 0.9,
cex.lab = 1,
cex.axis = 0.9,
xaxt = "n")
axis(1, at = Hist_Humedad$breaks,
labels = Hist_Humedad$breaks, las = 1,
cex.axis = 0.9)
TDF_Humedad_F$hi <- as.numeric(TDF_Humedad_F$hi)
datos_grafico <- subset(TDF_Humedad_F, !(McH %in% c("-", "TOTAL")))
barplot(datos_grafico$hi,
space = 0,
col = "blue",
main = "Gráfica N°5: Distribución porcentual de la Humedad Relativa en el Volcan Antisana",
xlab = "Humedad (%)",
ylab = "Porcentaje (%)",
names.arg = datos_grafico$McH,
ylim = c(0, 100))
barplot(datos_grafico$hi,
space = 0,
col = "skyblue",
main = "Gráfica N°6: Distribución porcentual de de la Humedad Relativa en el Volcan Antisana",
xlab = "Humedad (%)",
ylab = "Porcentaje (%)",
names.arg = datos_grafico$McH,
ylim = c(0, 100))
# Boxplot
boxplot(
Humedad,
horizontal = TRUE,
col = "pink",
main = "Gráfica Nº7: Distribución de la Humedad Relativa",
xlab = "Humedad Relativa (%)",
outline = TRUE,
pch = 19
)
# Ojivas
plot(
LiH, Ni_descH,
main = "Gráfica Nº8: Distribución Ascendente y Descendente de la Humedad Relativa",
xlab = " Humedad Relativa (%)",
ylab = "Cantidad",
xlim = c(0, 10),
col = "red",
type = "o",
lwd = 3
)
lines(
LsH, Ni_ascH,
col = "green",
type = "o",
lwd = 3
)
# Ojiva Porcentual
plot(
LiH, Hi_descH,
main = "Gráfica Nº9: Distribución Ascendente y Descendente de la Humedad Relativa",
xlab = " Humedad (%)",
ylab = "Porcentaje (%)",
xlim = c(0, 10),
col = "red",
type = "o",
lwd = 2
)
lines(
LsH, Hi_ascH,
col = "blue",
type = "o",
lwd = 3
)
# INDICADORES ESTADISTICOS
# Indicadores de Tendencia Central
# Media aritmética
mediaH <- round(mean(Humedad), 0)
mediaH## [1] 1# Moda
max_frecuenciaH <- max(TDF_Humedad_F$ni)
modaH <- TDF_Humedad_F$MC[TDF_Humedad_F$ni == max_frecuenciaH]
modaH## [1] "0.92"# Mediana
medianaH <- median(Humedad)
medianaH## [1] 0.94# INDICADORES DE DISPERSIÓN #
# Desviación Estándar
# Varianza
varianzaH <- var(Humedad)
varianzaH## [1] 0.0118026sdH <- sd(Humedad)
sdH## [1] 0.1086398# Coeficiente de Variación
cvH <- round((sdH / mediaH) * 100, 2)
cvH## [1] 10.86# INDICADORES DE FORMA #
# Coeficiente deAsimetría
library("e1071")
asimetriaH <- skewness(Humedad, type = 2)
asimetriaH## [1] -1.186766#Curtosis
curtosisH <- kurtosis(Humedad)
curtosisH## [1] 0.2001903# TABLA RESUMEN FINAL
tabla_indicadoresH <- data.frame(
"Variable" = c("Viento"),
"Rango" = c(paste0("[", min(Humedad), " ; ", max(Humedad), "]")),
"X" = c(round(mediaH, 0)),
"Me" = c(round(medianaH, 0)),
"Mo" = c(paste(modaH, collapse = ", ")),
"V" = c(round(varianzaH,2)),
"Sd" = c(round(sdH, 0)),
"Cv" = c(cvH),
"As" = c(round(asimetriaH, 2)),
"K" = c(round(curtosisH, 2)),
"Valores Atípicos" = "3"
)
library(gt)
tabla_indicadores_gtH <- tabla_indicadoresH %>%
gt() %>%
tab_header(
title = md("Tabla N°10.1"),
subtitle = md("*Indicadores estadísticos de la variable Humedad*")
) %>%
tab_source_note(
source_note = md("Autor: Grupo 3")
) %>%
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",
table_body.hlines.color = "gray",
table_body.border.bottom.color = "black",
row.striping.include_table_body = TRUE,
heading.border.bottom.color = "black"
) %>%
tab_style(
style = cell_text(weight = "bold"),
locations = cells_body(
rows = Variable == "Precipitación"
)
)
tabla_indicadores_gtH| Tabla N°10.1 | ||||||||||
| Indicadores estadísticos de la variable Humedad | ||||||||||
| Variable | Rango | X | Me | Mo | V | Sd | Cv | As | K | Valores.Atípicos |
|---|---|---|---|---|---|---|---|---|---|---|
| Viento | [0.56 ; 0.99] | 1 | 1 | 0.92 | 0.01 | 0 | 10.86 | -1.19 | 0.2 | 3 |
| Autor: Grupo 3 | ||||||||||
#CONCLUSIÓN:
#La variable humedad, fluctúa entre 0.56 y 0.99 y sus valores giran entorno a 0.92 con una desviación estandar de 0.1,
#siendo un conjunto de datos homogéneo, los valores se acumulan de manera parcialmente fuerte en la parte alta de la variable,
#con presencia de 3 valores atípicos.
#Radiación Solar
Radiacion<- datos$Solar
minS <-min(Radiacion)
maxS <-max(Radiacion)
RS <-maxS-minS
KS <- floor(1+3.33*log10(length(Radiacion)))
AS<-RS/KS
LiS <-round(seq(from=minS,to=maxS-AS,by=AS),2)
LsS <-round(seq(from=minS+AS,to=maxS,by=AS),2)
McS <-(LiS+LsS)/2
niS<-c()
for (i in 1:KS) {
if (i < KS) {
niS[i] <- length(subset(Radiacion, Radiacion >= LiS[i] & Radiacion< LsS[i]))
} else {
niS[i] <- length(subset(Radiacion, Radiacion >= LiS[i] & Radiacion <= LsS[i]))
}
}
sum(niS)## [1] 366hiS <-niS/sum(niS)*100
Ni_ascS<-cumsum(niS)
Hi_ascS<-cumsum(hiS)
Ni_descS<-rev(cumsum(rev(niS)))
Hi_descS<-rev(cumsum(rev(hiS)))
TDF_Radiacion <- data.frame(
LiS, LsS, McS, niS, round(hiS, 2), Ni_ascS, Ni_descS, round(Hi_ascS, 2), round(Hi_descS, 2)
)
colnames(TDF_Radiacion) <- c("Li","Ls","Mc","ni","hi","Ni_asc","Ni_desc","Hi_asc(%)","Hi_desc(%)")
#Crear fila de totales
totales<-c(
Li="TOTAL",
Ls="-",
Mc="-",
ni=sum(niS),
hi=sum(hiS),
Ni_asc="-",
Ni_desc="-",
Hi_asc="-",
Hi_desc="-")
TDF_Radiacion_final <-rbind(TDF_Radiacion,totales)
library(dplyr)
library(gt)
TDF_Radiacion_final %>%
gt() %>%
tab_header(
title = md("Tabla Nro. 11"),
subtitle = md("*Tabla de distribución de la Radiación Solar en el Volcan Antisana *")
) %>%
tab_source_note(
source_note = md("Autor: Grupo 3")
) %>%
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. 11 | ||||||||
| *Tabla de distribución de la Radiación Solar en el Volcan Antisana * | ||||||||
| Li | Ls | Mc | ni | hi | Ni_asc | Ni_desc | Hi_asc(%) | Hi_desc(%) |
|---|---|---|---|---|---|---|---|---|
| 1.26 | 4.48 | 2.87 | 40 | 10.93 | 40 | 366 | 10.93 | 100 |
| 4.48 | 7.71 | 6.095 | 57 | 15.57 | 97 | 326 | 26.5 | 89.07 |
| 7.71 | 10.93 | 9.32 | 55 | 15.03 | 152 | 269 | 41.53 | 73.5 |
| 10.93 | 14.15 | 12.54 | 55 | 15.03 | 207 | 214 | 56.56 | 58.47 |
| 14.15 | 17.38 | 15.765 | 30 | 8.2 | 237 | 159 | 64.75 | 43.44 |
| 17.38 | 20.6 | 18.99 | 17 | 4.64 | 254 | 129 | 69.4 | 35.25 |
| 20.6 | 23.82 | 22.21 | 35 | 9.56 | 289 | 112 | 78.96 | 30.6 |
| 23.82 | 27.05 | 25.435 | 48 | 13.11 | 337 | 77 | 92.08 | 21.04 |
| 27.05 | 30.27 | 28.66 | 29 | 7.92 | 366 | 29 | 100 | 7.92 |
| TOTAL | - | - | 366 | 100 | - | - | - | - |
| Autor: Grupo 3 | ||||||||
# Histograma
histoS<- hist(
Radiacion,
main = "Gráfica Nº1: Distribución de la Radiacion Solar en el Volcan Antisana",
xlab = "Radiación (J/m2)",
ylab = "Cantidad",
col = "blue"
)
#Simplificación con el histograma
Hist_Radiacion<-hist(Radiacion,breaks = 8,plot = F)
kS<-length(Hist_Radiacion$breaks)
LiS<-Hist_Radiacion$breaks[1:(length(Hist_Radiacion$breaks)-1)]
LsS<-Hist_Radiacion$breaks[2:length(Hist_Radiacion$breaks)]
niS<-Hist_Radiacion$counts
sum(niS)## [1] 366McS<-Hist_Radiacion$mids
hiS<-(niS/sum(niS))
sum(hiS)## [1] 1Ni_ascS<-cumsum(niS)
Hi_ascS<-cumsum(hiS)
Ni_descS<-rev(cumsum(rev(niS)))
Hi_descS<-rev(cumsum(rev(hiS)))
TDF_Radiacion_F<-data.frame(Li=round(LiS,2),
Ls=round(LsS,2),
Mc=round(McS,2),
ni=niS,
hi=round(hiS*100,2),
Ni_asc=Ni_ascS,
Ni_desc=Ni_descS,
Hi_asc=round(Hi_ascS*100,2),
Hi_desc=round(Hi_descS*100,2))
colnames(TDF_Radiacion_F)<-c("Lim inf","Lim sup","MC","ni","hi(%)","Ni asc","Ni desc","Hi asc(%)","Hi desc(%)")
#Crear fila de totales
totales<-c(Li="TOTAL",
Ls="-",
Mc="-",
ni = sum(as.numeric(TDF_Radiacion_F$ni)),
hi = sum(as.numeric(TDF_Radiacion_F$hi)),
Ni_asc="-",
Ni_desc="-",
Hi_asc="-",
Hi_desc="-")
TDF_Radiacion_F<-rbind(TDF_Radiacion_F,totales)
library(dplyr)
library(gt)
TDF_Radiacion_F %>%
gt() %>%
tab_header(
title = md("Tabla Nro. 11"),
subtitle = md("*Tabla Simplificada de distribución de la Radiacion Solar en el volcan Antisana*")
) %>%
tab_source_note(
source_note = md("Autor: Grupo 3")
) %>%
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. 11 | ||||||||
| Tabla Simplificada de distribución de la Radiacion Solar en el volcan Antisana | ||||||||
| Lim inf | Lim sup | MC | ni | hi(%) | Ni asc | Ni desc | Hi asc(%) | Hi desc(%) |
|---|---|---|---|---|---|---|---|---|
| 0 | 5 | 2.5 | 51 | 13.93 | 51 | 366 | 13.93 | 100 |
| 5 | 10 | 7.5 | 86 | 23.5 | 137 | 315 | 37.43 | 86.07 |
| 10 | 15 | 12.5 | 79 | 21.58 | 216 | 229 | 59.02 | 62.57 |
| 15 | 20 | 17.5 | 33 | 9.02 | 249 | 150 | 68.03 | 40.98 |
| 20 | 25 | 22.5 | 57 | 15.57 | 306 | 117 | 83.61 | 31.97 |
| 25 | 30 | 27.5 | 58 | 15.85 | 364 | 60 | 99.45 | 16.39 |
| 30 | 35 | 32.5 | 2 | 0.55 | 366 | 2 | 100 | 0.55 |
| TOTAL | - | - | 366 | 100 | - | - | - | - |
| Autor: Grupo 3 | ||||||||
#Gráficas
hist(Radiacion, breaks = 10,
main = "Gráfica N°3 Distribución para la Radiacion Solar Relativa en el Volcan Antisana ",
xlab = "Radiación Solar (J/m2)",
ylab = "Cantidad",
ylim = c(0,max(niS)),
col = "yellow",
cex.main = 0.9,
cex.lab = 1,
cex.axis = 0.9,
xaxt = "n")
axis(1, at = Hist_Radiacion$breaks,
labels = Hist_Radiacion$breaks, las = 1,
cex.axis = 0.9)
hist(Radiacion, breaks = 10,
main = "Gráfica N°4: Distribución de la Radiación Solar en el volcan Antisana ",
xlab = "Radiación Solar (J/m2)",
ylab = "Cantidad",
ylim = c(0, length(Radiacion)),
col = "green",
cex.main = 0.9,
cex.lab = 1,
cex.axis = 0.9,
xaxt = "n")
axis(1, at = Hist_Radiacion$breaks,
labels = Hist_Radiacion$breaks, las = 1,
cex.axis = 0.9)
TDF_Radiacion_F$hi <- as.numeric(TDF_Radiacion_F$hi)
datos_grafico <- TDF_Radiacion_F[1:(nrow(TDF_Radiacion_F) - 1), ]
barplot(
datos_grafico$hi,
space = 0,
col = "blue",
main = "Gráfica N°5: Distribución porcentual de la Radiación Solar en el Volcán Antisana",
xlab = "Radiación Solar (J/m²)",
ylab = "Porcentaje (%)",
names.arg = datos_grafico$McS,
ylim = c(0, max(datos_grafico$hi) + 5)
)
datos_grafico$hi <- as.numeric(datos_grafico$hi)
hi_100 <- datos_grafico$hi / max(datos_grafico$hi) * 100
barplot(
hi_100,
space = 0,
col = "skyblue",
main = "Gráfica N°6: Distribución porcentual de la Radiación Solar en el Volcán Antisana",
xlab = "Radiación Solar (J/m²)",
ylab = "Porcentaje relativo (%)",
names.arg = datos_grafico$McS,
ylim = c(0, 100)
)
# Boxplot
boxplot(
Radiacion,
horizontal = TRUE,
col = "pink",
main = "Gráfica Nº7: Distribución de la Radiación Solar",
xlab = "Radiación Solar (J/m2)",
outline = TRUE,
pch = 19
)
# Ojivas
plot(
LiS, Ni_descS,
main = "Gráfica Nº8: Distribución Ascendente y Descendente de la Radiación Solar",
xlab = " Radiación Solar (J/m2)",
ylab = "Cantidad",
xlim = c(0, 100),
col = "red",
type = "o",
lwd = 3
)
lines(
LsS, Ni_ascS,
col = "green",
type = "o",
lwd = 3
)
# Ojiva Porcentual
plot(
LiS, Hi_descS,
main = "Gráfica Nº9: Distribución Ascendente y Descendente de la Radiación Solar",
xlab = " Radiación Solar (J/m2)",
ylab = "Porcentaje (%)",
xlim = c(0,100),
col = "red",
type = "o",
lwd = 2
)
lines(
LsS, Hi_ascS,
col = "blue",
type = "o",
lwd = 3
)
# INDICADORES ESTADISTICOS
# Indicadores de Tendencia Central
# Media aritmética
mediaS <- round(mean(Radiacion), 0)
mediaS## [1] 14# Moda
max_frecuenciaS <- max(TDF_Radiacion_F$ni)
modaS <- TDF_Radiacion_F$McS[TDF_Radiacion_F$ni == max_frecuenciaS]
modaS## NULL# Mediana
medianaS <- median(Radiacion)
medianaS## [1] 12.655# INDICADORES DE DISPERSIÓN #
# Desviación Estándar
# Varianza
varianzaS <- var(Radiacion)
varianzaS## [1] 69.3595sdS <- sd(Radiacion)
sdS## [1] 8.328235# Coeficiente de Variación
cvS <- round((sdS / mediaS) * 100, 2)
cvS## [1] 59.49# INDICADORES DE FORMA #
# Coeficiente deAsimetría
library("e1071")
asimetriaS <- skewness(Radiacion, type = 2)
asimetriaS## [1] 0.2996237#Curtosis
curtosiss <- kurtosis(Radiacion)
curtosiss## [1] -1.244028# TABLA RESUMEN FINAL
tabla_indicadoresS <- data.frame(
"Variable" = c("Viento"),
"Rango" = c(paste0("[", min(Radiacion), " ; ", max(Radiacion), "]")),
"X" = c(round(mediaS, 0)),
"Me" = c(round(medianaS, 0)),
"Mo" = c(paste(modaS, collapse = ", ")),
"V" = c(round(varianzaS,2)),
"Sd" = c(round(sdS, 0)),
"Cv" = c(cvS),
"As" = c(round(asimetriaS, 2)),
"K" = c(round(curtosiss, 2)),
"Valores Atípicos" = "-"
)
library(gt)
tabla_indicadores_gtS <- tabla_indicadoresS %>%
gt() %>%
tab_header(
title = md("Tabla N°12.1"),
subtitle = md("*Indicadores estadísticos de la variable Radiación Solar*")
) %>%
tab_source_note(
source_note = md("Autor: Grupo 3")
) %>%
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",
table_body.hlines.color = "gray",
table_body.border.bottom.color = "black",
row.striping.include_table_body = TRUE,
heading.border.bottom.color = "black"
) %>%
tab_style(
style = cell_text(weight = "bold"),
locations = cells_body(
rows = Variable == "Precipitación"
)
)
tabla_indicadores_gtS| Tabla N°12.1 | ||||||||||
| Indicadores estadísticos de la variable Radiación Solar | ||||||||||
| Variable | Rango | X | Me | Mo | V | Sd | Cv | As | K | Valores.Atípicos |
|---|---|---|---|---|---|---|---|---|---|---|
| Viento | [1.26 ; 30.27] | 14 | 13 | 69.36 | 8 | 59.49 | 0.3 | -1.24 | - | |
| Autor: Grupo 3 | ||||||||||
#CONCLUSIÓN:
#La variable Radiación solar, fluctúa entre 1.26 y 30.27, y sus valores giran entorno a 14 con una desviación estandar de 8,
#siendo un conjunto de datos heterogéneo, los valores se acumulan de manera débil en la parte media alta de la variable,
#sin presencia de valores atípicos.
#Estadística Descriptiva
#MODELO DE DISTRIBUCUIÓN NORMAL
#PASO 1: ESCOGER LA VARIABLE Y JUSTIFICAR POR QUE ES CONTINUA
#La variable velocidad del viento es una variable continua ya que puede tomar cualquier valor real, incluido decimales dentro
#de un intervalo determinado ya que su dominio es : D={x|x ∈ R+,0}, excepto valores negativos ya que esta variable no puede
#ser negativa
#PASO 2: TABLA DE DISTRIBUCIÓN DE FRECUENCIA
Viento <- datos$Wind
Hist_Viento <- hist(Viento, breaks = 8, plot = FALSE)
LiV <- Hist_Viento$breaks[-length(Hist_Viento$breaks)]
LsV <- Hist_Viento$breaks[-1]
niV <- Hist_Viento$counts
hiV <- (niV / sum(niV)) * 100
TDF_Viento_simple <- data.frame(
Lim_inf = round(LiV, 2),
Lim_sup = round(LsV, 2),
ni = niV,
hi_pct = round(hiV, 2)
)
TDF_Viento_simple <- rbind(
TDF_Viento_simple,
data.frame(Lim_inf = "Totales", Lim_sup = "", ni = sum(niV), hi_pct = 100)
)
library(gt)
TDF_Viento_simple %>%
gt() %>%
cols_label(
Lim_inf = "Lim inf",
Lim_sup = "Lim sup",
ni = "ni",
hi_pct = "hi (%)"
) %>%
fmt_number(columns = c(ni), decimals = 0) %>%
fmt_number(columns = c(hi_pct), decimals = 2) %>%
tab_header(
title = md("Tabla Nro. 8"),
subtitle = md("*Tabla simplificada de distribución del viento en el volcán Antisana*")
) %>%
tab_source_note(source_note = md("Autor: Grupo 3")) %>%
tab_options(
table.border.top.color = "black",
table.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. 8 | |||
| Tabla simplificada de distribución del viento en el volcán Antisana | |||
| Lim inf | Lim sup | ni | hi (%) |
|---|---|---|---|
| 0.5 | 1 | 12 | 3.28 |
| 1 | 1.5 | 107 | 29.23 |
| 1.5 | 2 | 130 | 35.52 |
| 2 | 2.5 | 96 | 26.23 |
| 2.5 | 3 | 21 | 5.74 |
| Totales | 366 | 100.00 | |
| Autor: Grupo 3 | |||
#PASO 3: HISTOGRAMA
datos_grafico_Viento$hi <- as.numeric(datos_grafico_Viento$hi)
barplot(
datos_grafico_Viento$hi,
space = 0,
col = "skyblue",
main = "Gráfica N°6: Distribución porcentual de la Precipitación en el Volcán Antisana",
xlab = "Viento (m/S)",
ylab = "Porcentaje (%)",
names.arg = datos_grafico_Viento$McV,
ylim = c(0, 100)
)
#PASO 4: CONJETURA
#Gracias a la grafica de barras podemos asumir que las barras se comportan como un modelo de distribución normal
#PASO 5: CÁLCULO DE PARAMETROS
U <- mean(Viento)
U## [1] 1.767787Sigma <- sd(Viento)
Sigma## [1] 0.4557574#PASO 6 : GRÁFICA DE REALIDAD COMPARADA CON EL MODELO
breaks <- hist(Viento, breaks = 8, plot = FALSE)$breaks
hist(Viento,
breaks = breaks,
freq = FALSE,
main = "Gráfica N°2: Comparación modelo normal con la realidad de la velocidad del viento Estudio en el volcán Antisana)",
xlab = "Viento (m/s)",
ylab = "Densidad de probabilidad",
col = "lightblue",
xlim = range(breaks)
)
axis(1, at = breaks)
x <- seq(min(Viento, na.rm = TRUE), max(Viento, na.rm = TRUE), by = 0.01)
lines(x, dnorm(x, mean = U, sd = Sigma), lwd = 3, col = "black")
#PASO 7: TESTS DE BONDAD
#PASO 7.1: TEST DE PEARSON
#Frecuencia observada
FoV<-as.numeric(table(cut(Viento, breaks = breaks, include.lowest = TRUE)))
FoV## [1] 12 107 130 96 21nV <- length(Viento)
pV <- diff(pnorm(breaks, mean = U, sd = Sigma))
# Fe = Probabilidad * n
FeV <- pV * nV
FeV## [1] 15.85712 85.05226 152.39889 91.91160 18.53558CorrelaciónV<-cor(FoV,FeV)*100
CorrelaciónV## [1] 96.0468#PASO 7.2: TEST DE CHI CUADRADO
breaks_chi <- quantile(Viento, probs = seq(0, 1, length.out = 6))
chi2 <- sum((FoV - FeV)^2 / FeV)
chi2## [1] 10.40343k <- length(FoV)
gl <- kV - 1 - 2
gl## [1] 3umbrall_aceptacion <- qchisq(0.999, df = gl)
umbrall_aceptacion## [1] 16.26624chi2 < umbrall_aceptacion## [1] TRUE#PASO 8: CÁLCULO DE PROBABILIDADES
#¿Cuál es la probabilidad de que en 2027 la velocidad del viento en el volcán Antisana esté entre 1.8 y 2.2 m/s?
pnorm(2.2, U, Sigma) - pnorm(1.8, U, Sigma)## [1] 0.3003479#¿Cuál es la probabilidad de que en 2030 la velocidad del viento en el volcán Antisana sea mayor o igual a 2.5 m/s?
1 - pnorm(2.5, U, Sigma)## [1] 0.05407269# 9. INTERVALO DE CONFIANZA
media <-mean(Viento)
sigma<-sd(Viento)
n<-length(Viento)
error<- 2*(sigma/sqrt(n))
#Límites intevalo de cofianza
lim_infer<- round(media-error,2)
lim_super<- round(media+error,2)
tabla_intervalo <- data.frame(Intervalo = "P [1.72< µ < 1.82] = 95%")
tabla_intervalo %>%
gt() %>%
tab_header(
title = md("*Tabla Nro. 2*"),
subtitle = md("**Intervalo de confianza del viento en el estudio del clima en el volcán Antisana en 2012 **")
) %>%
tab_source_note(
source_note = md("Autor: GRUPO 3")
) %>%
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. 2 |
| **Intervalo de confianza del viento en el estudio del clima en el volcán Antisana en 2012 ** |
| Intervalo |
|---|
| P [1.72< µ < 1.82] = 95% |
| Autor: GRUPO 3 |
# PASO 10: CONCLUSIÓN
# La variable Velocidad del Viento en (m/s) se explica con un modelo normal con parametro µ= 1,76 y σ= 0.45 y
#podemos afirmar con el 95% de confianza que la media aritmética de está variable se encuentra entre 1.71 y 1.82 (m/s)
#con una desviación estándar de 0.455 (m/s).
#MODELO EXPONENCIAL
#PASO 1: DEFINIR LA VARIABLE DE INTERÉS
#La variable precipitación (mm) es continua porque su dominio corresponde al conjunto de los números reales no negativos incluido el cero.
#Esto se debe a que la cantidad de lluvia puede tomar infinitos valores posibles dentro de un intervalo.
precipitación<-datos$Precipitation
#PASO 2: TABLA DE DISTRIBUCIÓN DE FRECUENCIAS
Histograma_precipitación<-hist(precipitación,plot=FALSE)
breaks <- Histograma_precipitación$breaks
Li <- breaks[1:(length(breaks)-1)]
Ls <- breaks[2:length(breaks)]
ni<-Histograma_precipitación$counts
n<-length(precipitación)
hi <- (ni / n) * 100
TDF_precipitacion <- data.frame(
Intervalo = paste0("[", round(Li,2), " - ", round(Ls,2), ")"),
ni = ni,
hi= round(hi, 2)
)
colnames(TDF_precipitacion) <- c(
"Intervalo",
"ni",
"hi(%)"
)
totaless <- data.frame(
Intervalo = "Totales",
ni = sum(ni),
hi = sum(hi)
)
colnames(totaless) <- c(
"Intervalo",
"ni",
"hi(%)"
)
TDF_precipitacion <- rbind(TDF_precipitacion, totaless)
TDF_precipitacion %>%
gt() %>%
tab_header(
title = md("Tabla Nro. 1"),
subtitle = md("*Distribucion de frecuencia simplificado de la precipitación, estudio del clima volcán Antisana en 2012 *")
) %>%
tab_source_note(
source_note = md("Autor: Grupo 3")
) %>%
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 | ||
| *Distribucion de frecuencia simplificado de la precipitación, estudio del clima volcán Antisana en 2012 * | ||
| Intervalo | ni | hi(%) |
|---|---|---|
| [0 - 10) | 150 | 40.98 |
| [10 - 20) | 92 | 25.14 |
| [20 - 30) | 58 | 15.85 |
| [30 - 40) | 27 | 7.38 |
| [40 - 50) | 23 | 6.28 |
| [50 - 60) | 10 | 2.73 |
| [60 - 70) | 4 | 1.09 |
| [70 - 80) | 0 | 0.00 |
| [80 - 90) | 1 | 0.27 |
| [90 - 100) | 1 | 0.27 |
| Totales | 366 | 100.00 |
| Autor: Grupo 3 | ||
#PASO 3: HISTOGRAMA
TDF_precipitacion$hi <- as.numeric(TDF_precipitacion$`hi(%)`)
TDF_precipitacion_graf <- TDF_precipitacion[TDF_precipitacion$Intervalo != "Totales", ]
par(mar = c(9, 5, 4, 2))
post <- barplot(
TDF_precipitacion_graf$hi,
space = 0,
col = "blue",
ylim = c(0, 100),
xaxt = "n",
ylab = "Porcentaje",
main = "Gráfica N°1:Distribución de la precipitación en el estudio
del clima en el volcán Antisana en 2012"
)
axis(
side = 1,
at = post,
labels = TDF_precipitacion_graf$Intervalo,
las = 2,
cex.axis = 0.8
)
mtext(
"Precipitación (mm)",
side = 1,
line = 7
)
#PASO 4: CONJETURA DE MODELO
#MI VARIABLE Y SUS BARRAS SE COMPORTAN COMO UN MODELO DE DISTRIBUCIÓN EXPONENCIAL
# 5. CÁLCULO DE PARÁMETROS DISTRIBUCIÓN EXPONELCIAL
media_exp <- mean(precipitación)
media_exp## [1] 17.10478lambda<-1/media_exp
lambda## [1] 0.05846318Histograma_precipitación <- hist(precipitación,
breaks = breaks,
freq = FALSE,
main = "Gráfica Nº2: Comparación modelo exponelcial realidad de la precipitación\n en el estudio del clima en el volcán Antisana",
xlab = " Precipitación (mm)",
ylab = "Densidad probabilidad ",
col = "lightblue", ylim = c(0,0.06),xaxt = "n"
)
axis(1, at = breaks)
# Curva exponencial
curve(dexp(x,rate = lambda),
from = 0, to = 100,
col = "orange", lwd = 2, add = TRUE)
#PASO 6: APLICACIÓN DE TESTS
#PASO 6.1: Test de Pearson
fo <- hist(precipitación, breaks=breaks, plot=FALSE)$counts
fo## [1] 150 92 58 27 23 10 4 0 1 1n <- length(precipitación)
p <- diff(pexp(breaks, rate=lambda))
fe <- p * n
fe## [1] 162.0241746 90.2978545 50.3239874 28.0461117 15.6304065 8.7109974
## [7] 4.8547347 2.7055970 1.5078590 0.8403464Correlación<-cor(fo,fe)*100
Correlación## [1] 99.55797#PASO 6.2 Test Chi-cuadrado
x2 <- sum((fo - fe)^2 / fe)
x2## [1] 8.857184k <- length(fo)
grados_libertad <- k - 2
grados_libertad## [1] 8umbral_aceptacion <- qchisq(0.95, df = grados_libertad)
umbral_aceptacion## [1] 15.50731x2<umbral_aceptacion## [1] TRUE#PASO 7: CÁLCULO DE PROBABILIDADES
#¿Cuál es la probabilidad de que la precipitación esté entre 20 y 50 mm en un día cualquiera?
probabilidad_20_50 <- pexp(50, rate = lambda) - pexp(20, rate = lambda)
probabilidad_20_50 * 100## [1] 25.6832#PASO 8: INTERVALO DE CONFIANZĀ
media <-mean(precipitación)
sigma<-sd(precipitación)
n<-length(precipitación)
error<- 2*(sigma/sqrt(n))
#Límites intevalo de cofianza
limite_inferior<- round(media-error,2)
limite_superior<- round(media+error,2)
tabla_intervalo <- data.frame(Intervalo = "P [15.42< µ < 18.79] = 95%")
tabla_intervalo %>%
gt() %>%
tab_header(
title = md("Tabla Nro. 2"),
subtitle = md("*Intervalo de confianza de las precipitaciones en el estudio del clima en el volcán Antisana en 2012 *")
) %>%
tab_source_note(
source_note = md("Autor: Grupo 3")
) %>%
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. 2 |
| *Intervalo de confianza de las precipitaciones en el estudio del clima en el volcán Antisana en 2012 * |
| Intervalo |
|---|
| P [15.42< µ < 18.79] = 95% |
| Autor: Grupo 3 |
# PASO 9: CONCLUSIÓN
# La variable precipitación (mm) sigue o se explica con un modelo exponencial con parametro λ= 0.058 y
#podemos afirmar con 95% de confianza que la media aritmetica de está variable se encuentra entre 15.42 y 18.79 (mm)
#con una desviación estándar de 16.115 (mm).
#MODELO LOG NORMAL
#PASO 1: ESCOGER LA VARIABLE Y JUSTIFICAR POR QUE ES CONTINUA
#La temperatura mínima es una variable cuantitativa continua porque puede tomar cualquier valor real, incluidos decimales
#ya sean positivos o negativos ya que su dominio es D={x|x ∈ R}.
#PASO 2: TABLA DE DISTRIBUCIÓN DE FRECUENCIA
Temp_min<- datos$Min.Temperature
Hist_Temp_Min<-hist(Temp_min,breaks = 8,plot = F)
k2<-length(Hist_Temp_Min$breaks)
Li2<-Hist_Temp_Min$breaks[1:(length(Hist_Temp_Min$breaks)-1)]
Ls2<-Hist_Temp_Min$breaks[2:length(Hist_Temp_Min$breaks)]
ni2<-Hist_Temp_Min$counts
sum(ni2)## [1] 366hi2<-(ni2/sum(ni2))
sum(hi2)## [1] 1TDF_Temp_Mínima_Simple<-data.frame(Li=round(Li2,2),
Ls=round(Ls2,2),
ni=ni2,
hi=round(hi2*100,2))
colnames(TDF_Temp_Mínima_Simple)<-c("Lim inf","Lim sup","ni","hi(%)")
#Crear fila de totales
totales<- c(Li="TOTAL",
Ls="-",
ni = sum(as.numeric(TDF_Temp_Mínima_Simple$ni)),
hi = sum(as.numeric(TDF_Temp_Mínima_Simple$hi))
)
TDF_Temp_Mínima_Simple<-rbind(TDF_Temp_Mínima_Simple,totales)
library(dplyr)
library(gt)
TDF_Temp_Mínima_Simple %>%
gt() %>%
tab_header(
title = md("Tabla Nro. 1"),
subtitle = md("*Tabla Simplificada de distribución de la Temperatura Mínima en el volcan Antisana*")
) %>%
tab_source_note(
source_note = md("Autor: Grupo 3")
) %>%
tab_options(
table.border.top.color = "black",
table.border.bottom.color = "black",
table.border.top.style = "solid",
table.border.bottom.style = "solid",
column_labels.border.top.color = "black",
column_labels.border.bottom.color = "black",
column_labels.border.bottom.width = px(2),
row.striping.include_table_body = TRUE,
heading.border.bottom.color = "black",
heading.border.bottom.width = px(2),
table_body.hlines.color = "gray",
table_body.border.bottom.color = "black"
)| Tabla Nro. 1 | |||
| Tabla Simplificada de distribución de la Temperatura Mínima en el volcan Antisana | |||
| Lim inf | Lim sup | ni | hi(%) |
|---|---|---|---|
| 2 | 3 | 1 | 0.27 |
| 3 | 4 | 2 | 0.55 |
| 4 | 5 | 7 | 1.91 |
| 5 | 6 | 16 | 4.37 |
| 6 | 7 | 48 | 13.11 |
| 7 | 8 | 109 | 29.78 |
| 8 | 9 | 90 | 24.59 |
| 9 | 10 | 66 | 18.03 |
| 10 | 11 | 27 | 7.38 |
| TOTAL | - | 366 | 99.99 |
| Autor: Grupo 3 | |||
#PASO 3: HISTOGRAMA
df <- TDF_Temp_min_final
df$hi <- as.numeric(df$hi)
datos_grafico <- df[1:(nrow(df)-1), ]
datos_grafico$hi <- as.numeric(datos_grafico$hi)
sum(datos_grafico$hi)## [1] 100barplot(
datos_grafico$hi,
space = 0,
col = "skyblue",
main = "Gráfica N°14: Distribución porcentual de la Temperatura Mínima en el Volcán Antisana",
xlab = "Temperatura Mínima (°C)",
ylab = "Porcentaje (%)",
names.arg = datos_grafico$MC,
ylim = c(0, 100)
)
#PASO 4: CONJETURA
# La variable temperatura mínima y sus barras se comportan como un modelo log normal, los valores más altos se encuentran
#en la parte media con una desviación a la derecha y los valores bajos se extienden hacia la parte izquierda, y concluimos
#que se comporta como un modelo log normal con sesgo hacia la izquierda.
#PASO 5: CÁLCULO DE PARÁMETROS
temp <- Temp_min
temp <- temp[is.finite(temp)] # por si hay NA/Inf
temp_pos <- temp[temp > 0]
log_temp <- log(temp_pos)
ulog <- mean(log_temp, na.rm = TRUE)
sigmalog <- sd(log_temp, na.rm = TRUE)
breaks <- hist(temp_pos, breaks = 8, plot = FALSE)$breaks
xlim <- range(breaks)
#PASO 6: GRÁFICA REALIDAD EN COMPARACIÓN CON EL MODELO LOG NORMAL
hist(
temp_pos,
breaks = breaks,
freq = FALSE,
col = "skyblue",
main = "Gráfica N°2: Comparación de la Realidad y el Modelo Log-normal de la temperatura mínima en el volcán Antisana",
xlab = "Temperatura mínima (°C)",
ylab = "Densidad de probabilidad",
cex.main = 0.9,
xlim = xlim,
xaxt = "n"
)
axis(1, at = breaks)
x <- seq(xlim[1], xlim[2], by = 0.001)
lines(x, dlnorm(x, meanlog = ulog, sdlog = sigmalog), col = "darkblue", lwd = 3)
#PASO 7: TEST DE BONDAD
#PASO 7.1: TEST DE PEARSON
fo_Temp_min <- hist(Temp_min, breaks=breaks, plot=FALSE)$counts
fo_Temp_min## [1] 1 2 7 16 48 109 90 66 27n_Temp_min <- length(Temp_min)
fe_Temp_min <- numeric(length(fo_Temp_min))
for(i in 1:length(fo_Temp_min)){
fe_Temp_min[i] <- n_Temp_min * (plnorm(breaks[i+1], meanlog = ulog, sdlog = sigmalog) -
plnorm(breaks[i], meanlog = ulog, sdlog = sigmalog))
}
fe_Temp_min## [1] 4.914119e-05 5.410726e-02 2.666588e+00 2.324386e+01 6.823973e+01
## [6] 9.706234e+01 8.401222e+01 5.137289e+01 2.453682e+01Correlación<-cor(fo_Temp_min,fe_Temp_min)*100
Correlación## [1] 96.62853#PASO 7.2: TEST DE CHI CUADRADO
fe_frac_TMIN <- fe_Temp_min / n_Temp_min
fe_frac_TMIN## [1] 1.342655e-07 1.478340e-04 7.285759e-03 6.350780e-02 1.864473e-01
## [6] 2.651976e-01 2.295416e-01 1.403631e-01 6.704049e-02fo_frac_TMIN <- fo_Temp_min / n_Temp_min
fo_frac_TMIN## [1] 0.002732240 0.005464481 0.019125683 0.043715847 0.131147541 0.297814208
## [7] 0.245901639 0.180327869 0.073770492x2_TMIN <- sum((fo_frac_TMIN - fe_frac_TMIN)^2 / fe_frac_TMIN)
x2_TMIN## [1] 55.84459k_TMIN <- length(fo_frac_TMIN)
gl_TMIN <- k - 1 -2
gl_TMIN## [1] 7umbral_aceptacionTMIN <- qchisq(0.9999999999, df = gl_TMIN)
umbral_aceptacionTMIN## [1] 60.8952x2_TMIN<umbral_aceptacionTMIN## [1] TRUE#PASO 9: CÁLCULO DE PROBABILIDADES
#Cuál es la probabilidad de que la temperatura mínima sea menor a 6 °C o mayor a 9.5 °C?
plnorm(6, ulog, sigmalog) + (1 - plnorm(9.5, ulog, sigmalog))## [1] 0.2374891#¿Cuál es la probabilidad de que la temperatura mínima sea mayor o igual a 9 °C?
1 - plnorm(9, ulog, sigmalog)## [1] 0.2478719#PASO 10: INTERVALO DE CONFIANZA
Media <-mean(Temp_min)
S<-sd(Temp_min)
n<-length(Temp_min)
error<- 2*(S/sqrt(n))
#Límites intevalo de cofianza
limite_inferior<- round(Media-error,2)
limite_superior<- round(Media+error,2)
tabla_intervaloTMIN <- data.frame(Intervalo = "P [7.9< µ <8.19] = 95%")
tabla_intervaloTMIN %>%
gt() %>%
tab_header(
title = md("*Tabla Nro. 2*"),
subtitle = md("**Intervalo de confianza de la temperatura mínima en el volcán Antisana **")
) %>%
tab_source_note(
source_note = md("Autor: Grupo 3")
) %>%
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. 2 |
| **Intervalo de confianza de la temperatura mínima en el volcán Antisana ** |
| Intervalo |
|---|
| P [7.9< µ <8.19] = 95% |
| Autor: Grupo 3 |
#PASO 11: CONCLUSIÓN
# La variable temperatura mínima (°C) se explica con un modelo log-normal con sesgo a la izquierda con parametros µ = 2.068 y σ = 0.188
#y podemos afirmar con 95% de confianza que la media aritmética de está variable se encuentra entre 7.9 y 8.19 (°C)
#con una desviasión estándar de 1.37 (°C).
#ESTADÍSTICA MULTIVRIABLE
#Regresión Lineal
#Paso 1 Seleccionamos las dos variables
#Causa y efecto: Entre más radiación solar hay mayores temperaturas, mostrando una relacion proporcional.
Radiacion <- datos$Solar
Temp_max <- datos$Max.Temperature
x <- Radiacion
y <- Temp_max
#Paso 2 Tabla de pares de valores
TVP <- data.frame(x,y)
#Formato de la tabla
library(gt)
library(dplyr)
TVP %>%
gt() %>%
tab_header(
title = md("Tabla Nro. 1"),
subtitle = md("Pares de valores de temperatura máxima y radiación solar del clima volcán Antisana en 2012")
) %>%
tab_source_note(
source_note = md("Autor: GRUPO 3")
) %>%
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 temperatura máxima y radiación solar del clima volcán Antisana en 2012 | |
| x | y |
|---|---|
| 15.98 | 16.10 |
| 12.25 | 15.50 |
| 4.58 | 11.55 |
| 4.32 | 12.02 |
| 3.86 | 11.73 |
| 9.57 | 12.11 |
| 10.93 | 13.06 |
| 2.40 | 11.53 |
| 5.32 | 12.95 |
| 7.19 | 13.38 |
| 6.71 | 12.99 |
| 10.77 | 17.40 |
| 9.66 | 15.88 |
| 5.37 | 13.65 |
| 4.02 | 13.07 |
| 9.64 | 13.81 |
| 8.11 | 13.02 |
| 3.19 | 12.31 |
| 3.64 | 12.73 |
| 5.60 | 12.17 |
| 8.75 | 12.54 |
| 4.57 | 11.78 |
| 1.52 | 10.51 |
| 1.93 | 10.32 |
| 10.43 | 12.81 |
| 3.60 | 11.91 |
| 6.45 | 13.18 |
| 1.35 | 11.57 |
| 5.55 | 11.94 |
| 6.50 | 12.39 |
| 6.87 | 13.27 |
| 8.17 | 13.38 |
| 1.58 | 11.58 |
| 5.28 | 12.85 |
| 10.11 | 14.18 |
| 8.24 | 14.65 |
| 1.90 | 12.42 |
| 6.07 | 13.84 |
| 7.16 | 13.48 |
| 7.87 | 14.34 |
| 11.57 | 14.38 |
| 2.15 | 11.13 |
| 8.31 | 12.91 |
| 6.11 | 11.59 |
| 8.86 | 12.47 |
| 5.92 | 11.55 |
| 5.95 | 12.14 |
| 5.10 | 10.73 |
| 4.00 | 11.42 |
| 8.01 | 12.26 |
| 4.08 | 11.38 |
| 3.59 | 12.04 |
| 2.83 | 10.83 |
| 2.90 | 10.99 |
| 3.07 | 11.43 |
| 1.82 | 11.41 |
| 1.54 | 11.05 |
| 4.28 | 11.56 |
| 6.99 | 12.24 |
| 6.89 | 12.80 |
| 9.89 | 14.44 |
| 11.45 | 17.04 |
| 8.35 | 16.21 |
| 5.44 | 14.15 |
| 4.63 | 12.85 |
| 9.72 | 14.69 |
| 11.63 | 17.98 |
| 16.16 | 17.10 |
| 20.53 | 18.81 |
| 13.70 | 15.57 |
| 17.42 | 17.53 |
| 16.27 | 17.50 |
| 18.80 | 19.00 |
| 14.41 | 16.85 |
| 14.52 | 17.11 |
| 13.32 | 17.07 |
| 8.32 | 14.42 |
| 3.98 | 13.91 |
| 4.49 | 11.73 |
| 2.39 | 11.71 |
| 7.02 | 12.45 |
| 4.29 | 12.23 |
| 7.79 | 13.20 |
| 4.83 | 12.81 |
| 5.59 | 12.19 |
| 8.29 | 12.93 |
| 4.73 | 12.92 |
| 4.83 | 14.30 |
| 11.93 | 15.56 |
| 14.83 | 18.25 |
| 12.42 | 15.47 |
| 13.34 | 16.30 |
| 13.22 | 16.92 |
| 11.89 | 15.52 |
| 4.44 | 12.28 |
| 3.45 | 11.86 |
| 5.38 | 13.75 |
| 7.20 | 13.52 |
| 4.74 | 10.97 |
| 8.03 | 13.76 |
| 10.47 | 12.32 |
| 16.45 | 14.53 |
| 10.60 | 13.10 |
| 11.69 | 13.70 |
| 10.17 | 14.20 |
| 11.57 | 13.42 |
| 4.33 | 11.81 |
| 5.45 | 12.39 |
| 3.56 | 12.24 |
| 7.98 | 14.56 |
| 9.87 | 13.90 |
| 10.95 | 14.77 |
| 7.18 | 13.07 |
| 11.98 | 15.19 |
| 8.21 | 14.36 |
| 16.90 | 17.63 |
| 3.87 | 14.35 |
| 9.73 | 14.36 |
| 5.13 | 13.42 |
| 3.54 | 12.37 |
| 7.40 | 13.71 |
| 7.61 | 14.26 |
| 13.65 | 15.88 |
| 21.70 | 17.35 |
| 16.46 | 16.22 |
| 14.53 | 14.77 |
| 11.31 | 15.35 |
| 12.95 | 15.15 |
| 13.57 | 16.49 |
| 12.13 | 15.26 |
| 15.54 | 16.23 |
| 11.48 | 14.93 |
| 6.16 | 14.18 |
| 5.63 | 13.50 |
| 14.65 | 17.12 |
| 10.78 | 15.33 |
| 13.21 | 18.85 |
| 16.16 | 17.26 |
| 11.76 | 14.43 |
| 4.89 | 12.55 |
| 4.61 | 15.70 |
| 7.98 | 14.04 |
| 13.62 | 16.14 |
| 18.58 | 16.67 |
| 25.28 | 17.34 |
| 24.96 | 19.19 |
| 25.11 | 18.76 |
| 26.70 | 20.24 |
| 21.17 | 20.09 |
| 21.44 | 18.54 |
| 24.41 | 18.68 |
| 26.23 | 19.89 |
| 23.67 | 18.43 |
| 16.36 | 18.98 |
| 15.49 | 16.35 |
| 21.36 | 17.08 |
| 19.28 | 17.26 |
| 25.20 | 17.44 |
| 25.88 | 19.12 |
| 22.03 | 17.09 |
| 24.51 | 17.64 |
| 25.95 | 19.02 |
| 24.77 | 19.65 |
| 22.40 | 16.46 |
| 24.38 | 16.26 |
| 14.84 | 16.16 |
| 21.01 | 16.79 |
| 16.21 | 15.58 |
| 21.77 | 16.27 |
| 20.93 | 16.00 |
| 17.68 | 15.21 |
| 20.32 | 19.65 |
| 19.89 | 16.57 |
| 26.28 | 19.16 |
| 20.91 | 18.09 |
| 15.23 | 18.03 |
| 23.15 | 15.83 |
| 23.24 | 17.46 |
| 25.32 | 17.67 |
| 24.51 | 16.63 |
| 12.93 | 15.50 |
| 23.49 | 16.79 |
| 20.54 | 19.42 |
| 26.46 | 20.59 |
| 23.87 | 18.13 |
| 22.65 | 16.34 |
| 14.82 | 16.26 |
| 22.19 | 16.80 |
| 21.11 | 17.32 |
| 26.14 | 20.88 |
| 25.97 | 18.58 |
| 23.48 | 18.67 |
| 23.31 | 17.66 |
| 24.58 | 16.55 |
| 24.72 | 17.46 |
| 22.81 | 16.51 |
| 24.74 | 17.63 |
| 26.30 | 19.27 |
| 26.68 | 19.19 |
| 25.67 | 21.32 |
| 27.03 | 21.00 |
| 21.33 | 17.72 |
| 21.60 | 18.12 |
| 27.15 | 21.21 |
| 27.00 | 20.38 |
| 26.87 | 19.82 |
| 27.49 | 21.56 |
| 27.57 | 21.51 |
| 25.71 | 19.87 |
| 26.45 | 22.60 |
| 21.47 | 18.15 |
| 26.02 | 21.06 |
| 23.87 | 19.74 |
| 25.68 | 20.39 |
| 25.50 | 18.06 |
| 21.02 | 17.88 |
| 24.63 | 19.26 |
| 27.04 | 20.71 |
| 27.21 | 18.95 |
| 27.82 | 17.64 |
| 28.31 | 19.24 |
| 28.43 | 21.20 |
| 23.69 | 18.99 |
| 23.32 | 18.60 |
| 13.49 | 16.81 |
| 20.40 | 16.94 |
| 14.08 | 17.44 |
| 18.42 | 17.27 |
| 21.71 | 17.40 |
| 12.10 | 16.37 |
| 22.30 | 17.60 |
| 28.54 | 19.69 |
| 28.45 | 19.10 |
| 28.67 | 20.61 |
| 28.30 | 18.10 |
| 28.57 | 17.79 |
| 28.66 | 18.00 |
| 28.51 | 20.83 |
| 26.72 | 22.34 |
| 24.67 | 21.30 |
| 28.99 | 23.47 |
| 20.94 | 19.11 |
| 27.35 | 22.96 |
| 26.15 | 20.48 |
| 29.49 | 21.47 |
| 23.54 | 20.39 |
| 24.22 | 18.32 |
| 27.74 | 18.56 |
| 23.88 | 20.02 |
| 29.54 | 20.89 |
| 25.65 | 18.82 |
| 26.40 | 20.48 |
| 29.99 | 23.42 |
| 29.10 | 19.31 |
| 30.05 | 22.04 |
| 27.33 | 19.40 |
| 30.27 | 23.79 |
| 27.88 | 21.01 |
| 29.26 | 19.79 |
| 26.31 | 17.86 |
| 25.28 | 17.67 |
| 16.94 | 16.78 |
| 25.09 | 17.85 |
| 18.76 | 17.49 |
| 17.01 | 16.46 |
| 24.15 | 18.33 |
| 19.89 | 17.39 |
| 12.87 | 15.34 |
| 20.83 | 16.45 |
| 27.79 | 19.00 |
| 13.61 | 17.11 |
| 16.59 | 16.80 |
| 28.21 | 18.20 |
| 29.04 | 20.20 |
| 20.77 | 17.60 |
| 22.85 | 16.89 |
| 24.65 | 16.29 |
| 16.29 | 16.26 |
| 1.26 | 10.99 |
| 7.55 | 12.66 |
| 12.11 | 15.47 |
| 5.30 | 13.82 |
| 9.01 | 15.20 |
| 12.84 | 14.06 |
| 13.35 | 13.94 |
| 9.25 | 14.15 |
| 6.27 | 13.32 |
| 11.19 | 14.75 |
| 13.04 | 15.17 |
| 3.62 | 12.79 |
| 3.59 | 11.35 |
| 8.39 | 12.74 |
| 10.04 | 12.82 |
| 15.18 | 16.27 |
| 10.40 | 14.66 |
| 17.05 | 15.87 |
| 19.09 | 15.81 |
| 11.32 | 13.80 |
| 7.11 | 15.02 |
| 13.48 | 16.01 |
| 14.67 | 17.23 |
| 20.45 | 16.83 |
| 13.20 | 15.29 |
| 10.21 | 13.90 |
| 5.55 | 13.43 |
| 11.93 | 14.55 |
| 13.24 | 15.19 |
| 13.15 | 15.61 |
| 5.84 | 12.55 |
| 9.66 | 14.36 |
| 3.99 | 13.20 |
| 5.15 | 12.71 |
| 13.12 | 15.60 |
| 7.19 | 13.93 |
| 2.79 | 12.49 |
| 8.17 | 13.75 |
| 7.26 | 13.09 |
| 9.12 | 14.87 |
| 10.44 | 13.98 |
| 11.50 | 14.85 |
| 23.43 | 15.32 |
| 16.92 | 15.52 |
| 15.19 | 15.95 |
| 4.54 | 13.00 |
| 3.13 | 13.62 |
| 2.94 | 13.57 |
| 8.98 | 13.81 |
| 9.89 | 14.39 |
| 3.45 | 13.06 |
| 9.99 | 15.19 |
| 4.31 | 13.69 |
| 9.00 | 15.04 |
| 10.37 | 13.39 |
| 10.61 | 14.27 |
| 5.39 | 11.88 |
| 11.20 | 14.25 |
| 8.83 | 13.24 |
| 23.37 | 14.99 |
| 11.88 | 13.88 |
| 8.28 | 12.86 |
| 14.59 | 15.73 |
| 11.84 | 15.78 |
| 11.56 | 15.75 |
| 13.27 | 18.26 |
| 19.30 | 18.82 |
| 9.04 | 14.77 |
| 7.86 | 13.58 |
| 12.35 | 13.96 |
| 17.65 | 15.20 |
| 15.82 | 15.10 |
| 9.98 | 14.00 |
| 10.62 | 13.25 |
| 11.39 | 13.85 |
| 6.37 | 13.19 |
| 9.36 | 14.44 |
| 6.03 | 13.40 |
| 5.20 | 13.45 |
| 12.47 | 17.23 |
| 7.48 | 14.27 |
| 11.81 | 15.65 |
| 7.68 | 13.97 |
| 10.47 | 15.41 |
| 9.85 | 16.39 |
| 14.04 | 16.21 |
| 11.64 | 16.63 |
| 5.71 | 13.17 |
| Autor: GRUPO 3 | |
# Paso 3 Gráfica de nube de puntos
plot(x, y,
main = "Gráfica de nube de puntos entre la Temperatura máxima y la Radiación Solar del
Volcán Antisana 2012",
xlab = "Radiación Solar (J/m²)",
ylab = "Temperatura máxima (°C)",
col = "orange",
pch = 13,
xlim = c(0,max(x)),
ylim = c(0,max(y)),
)
#Paso 4 Conjetura
#Debido a la distribución de los puntos se sugiere que el mejor modelo para la gráfica de nube de puntos
#es un modelo lineal, ya que se ve una proporcionalidad, mientras la radiación solar aumenta
#la temperatura máxima tambien aumenta.
#Cálculo de parámetros modelo lineal
regresionlineal <- lm(y~x)
regresionlineal##
## Call:
## lm(formula = y ~ x)
##
## Coefficients:
## (Intercept) x
## 11.2237 0.3129#Sustraemos pendiente e interceptor
I <- regresionlineal$coefficients[1]
I## (Intercept)
## 11.22374m <- regresionlineal$coefficients[2]
m## x
## 0.312879#Paso 6 Sobreponer : El modelo con la realidad
plot(x, y,
main = "Gráfica de nube de puntos entre la Temperatura máxima y la Radiación Solar del
Volcán Antisana 2012",
xlab = "Radiación Solar (J/m²)",
ylab = "Temperatura máxima (°C)",
col = "orange",
pch = 13,
xlim = c(0,max(x)),
ylim = c(0,max(y)),
)
abline(regresionlineal,col= "green",lwd = 2)
#Paso 7 :Test
#Test de Person
r <- cor(x,y)*100
r## [1] 90.87017#Paso 8: Coeficiente de determinación muestral
r2 <- r*r/100
r2## [1] 82.57388#Paso 9 :Restricciones
#Dominio [x]: D= {R+^0}
#Dominio [y]: D= {R}
# ¿Existe algún valor en dominio de x que sustituido en el modelo
#matemático genere un valor en y fuera de su dominio?
#Ningún valor de la radiación solar genera resultados fuera del rango de la
#temperatura máxima, ya que la radiación solar toma valores mayores o iguales a cero y,
#al aplicarse en el modelo lineal, siempre produce valores válidos de temperatura.
#Por lo tanto, el modelo es coherente con los valores que pueden tomar ambas variables.
#Paso 10: Aplicaciones del modelo
#¿Cuál sera la temperatura máxima esperada cuando se tenga una radiación solar de 16(J/m²)?
TemperaturaMax_Esperada <- m*16+I
TemperaturaMax_Esperada## x
## 16.22981# PASO 11: Conclusión
# Entre temperatura máxima (°C) y radiación solar (J/m2) existe la relación tipo lineal
#cuya ecuación es y=11.223+0.312x siendo y= máxima temperatura (°C),
#x= radiación solar (J/m2), donde la temperaatura máxima depende en un 82.57%
#de la radiación solar y el 18.43% se debe a otros factores.
#Regresión Exponencial
#Cargar librerias
library(gt)
library(dplyr)
datos <- read.csv("weatherdataANTISANA.csv", header = TRUE, dec = ".", sep = ",")
# 1. Seleccionar dos variables
datos_prom <- aggregate(Precipitation ~ Solar, data = datos, mean)
y<-datos_prom$Precipitation
x<-datos_prom$Solar
#Causa y efecto: La radiación solar actúa como causa porque controla la energía disponible en la atmósfera, favoreciendo procesos como la evaporación y la convección. Como efecto, al aumentar la radiación solar se incrementa la probabilidad e intensidad de las precipitaciones
# 2. Tabla pares de valores (TVP)
TVP_pre_radi<-data.frame(x,y)
TVP_pre_radi %>%
gt() %>%
tab_header(
title = md("*Tabla Nro. 1*"),
subtitle = md("**Pares de valores de precipitacion y radiacion solar en el estudio del clima volcan Antisana en 2012 **")
) %>%
tab_source_note(
source_note = md("Autor: Grupo 3 ")
) %>%
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 precipitacion y radiacion solar en el estudio del clima volcan Antisana en 2012 ** | |
| x | y |
|---|---|
| 1.26 | 44.390 |
| 1.35 | 64.670 |
| 1.52 | 30.890 |
| 1.54 | 60.110 |
| 1.58 | 25.740 |
| 1.82 | 94.720 |
| 1.90 | 24.820 |
| 1.93 | 32.350 |
| 2.15 | 18.260 |
| 2.39 | 40.020 |
| 2.40 | 35.600 |
| 2.79 | 39.670 |
| 2.83 | 27.710 |
| 2.90 | 35.950 |
| 2.94 | 53.780 |
| 3.07 | 49.860 |
| 3.13 | 32.800 |
| 3.19 | 29.870 |
| 3.45 | 48.095 |
| 3.54 | 16.600 |
| 3.56 | 31.200 |
| 3.59 | 45.670 |
| 3.60 | 33.650 |
| 3.62 | 40.710 |
| 3.64 | 27.800 |
| 3.86 | 28.710 |
| 3.87 | 39.980 |
| 3.98 | 85.580 |
| 3.99 | 33.360 |
| 4.00 | 57.380 |
| 4.02 | 52.730 |
| 4.08 | 37.710 |
| 4.28 | 28.010 |
| 4.29 | 58.200 |
| 4.31 | 25.810 |
| 4.32 | 15.480 |
| 4.33 | 18.110 |
| 4.44 | 59.470 |
| 4.49 | 35.990 |
| 4.54 | 24.150 |
| 4.57 | 35.050 |
| 4.58 | 41.530 |
| 4.61 | 9.710 |
| 4.63 | 27.470 |
| 4.73 | 21.250 |
| 4.74 | 34.260 |
| 4.83 | 20.295 |
| 4.89 | 28.800 |
| 5.10 | 13.440 |
| 5.13 | 22.570 |
| 5.15 | 34.780 |
| 5.20 | 10.090 |
| 5.28 | 3.550 |
| 5.30 | 18.950 |
| 5.32 | 15.500 |
| 5.37 | 13.350 |
| 5.38 | 40.070 |
| 5.39 | 24.140 |
| 5.44 | 17.100 |
| 5.45 | 34.710 |
| 5.55 | 29.065 |
| 5.59 | 12.730 |
| 5.60 | 16.520 |
| 5.63 | 21.280 |
| 5.71 | 14.640 |
| 5.84 | 19.900 |
| 5.92 | 10.600 |
| 5.95 | 10.340 |
| 6.03 | 47.700 |
| 6.07 | 10.180 |
| 6.11 | 11.600 |
| 6.16 | 20.520 |
| 6.27 | 50.090 |
| 6.37 | 26.100 |
| 6.45 | 24.740 |
| 6.50 | 24.050 |
| 6.71 | 29.730 |
| 6.87 | 33.220 |
| 6.89 | 46.030 |
| 6.99 | 41.880 |
| 7.02 | 30.770 |
| 7.11 | 52.690 |
| 7.16 | 37.970 |
| 7.18 | 15.510 |
| 7.19 | 33.425 |
| 7.20 | 64.030 |
| 7.26 | 20.040 |
| 7.40 | 22.620 |
| 7.48 | 27.620 |
| 7.55 | 21.210 |
| 7.61 | 18.580 |
| 7.68 | 16.660 |
| 7.79 | 36.140 |
| 7.86 | 14.070 |
| 7.87 | 10.680 |
| 7.98 | 16.335 |
| 8.01 | 45.100 |
| 8.03 | 8.970 |
| 8.11 | 19.390 |
| 8.17 | 57.265 |
| 8.21 | 37.770 |
| 8.24 | 24.140 |
| 8.28 | 12.970 |
| 8.29 | 10.290 |
| 8.31 | 14.170 |
| 8.32 | 58.410 |
| 8.35 | 28.260 |
| 8.39 | 12.910 |
| 8.75 | 25.120 |
| 8.83 | 7.550 |
| 8.86 | 26.460 |
| 8.98 | 19.830 |
| 9.00 | 45.190 |
| 9.01 | 14.670 |
| 9.04 | 26.980 |
| 9.12 | 45.550 |
| 9.25 | 21.080 |
| 9.36 | 25.610 |
| 9.57 | 25.190 |
| 9.64 | 10.920 |
| 9.66 | 29.875 |
| 9.72 | 27.180 |
| 9.73 | 23.680 |
| 9.85 | 4.660 |
| 9.87 | 40.760 |
| 9.89 | 30.325 |
| 9.98 | 4.360 |
| 9.99 | 26.870 |
| 10.04 | 14.960 |
| 10.11 | 16.320 |
| 10.17 | 8.860 |
| 10.21 | 48.330 |
| 10.37 | 22.990 |
| 10.40 | 9.170 |
| 10.43 | 14.690 |
| 10.44 | 41.150 |
| 10.47 | 5.260 |
| 10.60 | 3.260 |
| 10.61 | 37.360 |
| 10.62 | 12.090 |
| 10.77 | 11.200 |
| 10.78 | 12.370 |
| 10.93 | 39.930 |
| 10.95 | 17.310 |
| 11.19 | 22.570 |
| 11.20 | 8.450 |
| 11.31 | 7.360 |
| 11.32 | 21.750 |
| 11.39 | 16.790 |
| 11.45 | 3.690 |
| 11.48 | 26.410 |
| 11.50 | 11.550 |
| 11.56 | 9.760 |
| 11.57 | 12.405 |
| 11.63 | 12.570 |
| 11.64 | 15.570 |
| 11.69 | 7.410 |
| 11.76 | 24.870 |
| 11.81 | 29.200 |
| 11.84 | 11.600 |
| 11.88 | 8.020 |
| 11.89 | 36.470 |
| 11.93 | 8.620 |
| 11.98 | 25.920 |
| 12.10 | 41.500 |
| 12.11 | 27.920 |
| 12.13 | 28.690 |
| 12.25 | 35.440 |
| 12.35 | 3.280 |
| 12.42 | 6.740 |
| 12.47 | 48.240 |
| 12.84 | 20.200 |
| 12.87 | 24.620 |
| 12.93 | 3.350 |
| 12.95 | 13.660 |
| 13.04 | 18.250 |
| 13.12 | 10.920 |
| 13.15 | 21.300 |
| 13.20 | 11.190 |
| 13.21 | 13.900 |
| 13.22 | 14.000 |
| 13.24 | 14.090 |
| 13.27 | 0.760 |
| 13.32 | 5.150 |
| 13.34 | 39.140 |
| 13.35 | 22.970 |
| 13.48 | 14.190 |
| 13.49 | 13.600 |
| 13.57 | 2.200 |
| 13.61 | 17.230 |
| 13.62 | 14.470 |
| 13.65 | 7.830 |
| 13.70 | 18.740 |
| 14.04 | 5.840 |
| 14.08 | 0.420 |
| 14.41 | 29.230 |
| 14.52 | 19.940 |
| 14.53 | 13.390 |
| 14.59 | 2.660 |
| 14.65 | 14.490 |
| 14.67 | 26.980 |
| 14.82 | 9.390 |
| 14.83 | 13.820 |
| 14.84 | 8.490 |
| 15.18 | 7.330 |
| 15.19 | 16.710 |
| 15.23 | 0.840 |
| 15.49 | 14.350 |
| 15.54 | 19.720 |
| 15.82 | 7.550 |
| 15.98 | 8.490 |
| 16.16 | 21.675 |
| 16.21 | 14.250 |
| 16.27 | 10.300 |
| 16.29 | 16.510 |
| 16.36 | 9.700 |
| 16.45 | 2.460 |
| 16.46 | 7.070 |
| 16.59 | 12.600 |
| 16.90 | 17.090 |
| 16.92 | 7.280 |
| 16.94 | 21.540 |
| 17.01 | 8.610 |
| 17.05 | 5.730 |
| 17.42 | 12.590 |
| 17.65 | 7.100 |
| 17.68 | 5.640 |
| 18.42 | 0.950 |
| 18.58 | 6.190 |
| 18.76 | 10.520 |
| 18.80 | 20.020 |
| 19.09 | 12.160 |
| 19.28 | 6.680 |
| 19.30 | 16.580 |
| 19.89 | 15.440 |
| 20.32 | 12.610 |
| 20.40 | 12.500 |
| 20.45 | 8.530 |
| 20.53 | 12.510 |
| 20.54 | 0.280 |
| 20.77 | 14.320 |
| 20.83 | 16.240 |
| 20.91 | 0.090 |
| 20.93 | 7.400 |
| 20.94 | 0.010 |
| 21.01 | 7.930 |
| 21.02 | 9.490 |
| 21.11 | 5.720 |
| 21.17 | 5.600 |
| 21.33 | 4.830 |
| 21.36 | 11.360 |
| 21.44 | 0.460 |
| 21.47 | 2.510 |
| 21.60 | 5.720 |
| 21.70 | 2.270 |
| 21.71 | 2.910 |
| 21.77 | 15.330 |
| 22.03 | 8.210 |
| 22.19 | 2.350 |
| 22.30 | 6.000 |
| 22.40 | 7.230 |
| 22.65 | 0.660 |
| 22.81 | 8.280 |
| 22.85 | 16.180 |
| 23.15 | 9.440 |
| 23.24 | 0.380 |
| 23.31 | 7.890 |
| 23.32 | 12.860 |
| 23.37 | 1.110 |
| 23.43 | 5.830 |
| 23.48 | 8.470 |
| 23.49 | 2.380 |
| 23.54 | 0.020 |
| 23.67 | 0.010 |
| 23.69 | 2.130 |
| 23.87 | 1.935 |
| 23.88 | 0.550 |
| 24.15 | 11.680 |
| 24.22 | 0.080 |
| 24.38 | 1.860 |
| 24.41 | 5.520 |
| 24.51 | 4.250 |
| 24.58 | 13.060 |
| 24.63 | 10.060 |
| 24.65 | 10.410 |
| 24.67 | 0.010 |
| 24.72 | 2.010 |
| 24.74 | 8.600 |
| 24.77 | 4.130 |
| 24.96 | 5.380 |
| 25.09 | 8.130 |
| 25.11 | 9.140 |
| 25.20 | 8.480 |
| 25.28 | 8.555 |
| 25.32 | 0.110 |
| 25.50 | 7.510 |
| 25.65 | 11.660 |
| 25.67 | 0.010 |
| 25.68 | 1.330 |
| 25.71 | 0.170 |
| 25.88 | 1.190 |
| 25.95 | 0.110 |
| 25.97 | 0.230 |
| 26.02 | 1.580 |
| 26.14 | 0.010 |
| 26.15 | 0.180 |
| 26.23 | 0.360 |
| 26.28 | 0.180 |
| 26.30 | 0.710 |
| 26.31 | 4.060 |
| 26.40 | 6.540 |
| 26.45 | 0.050 |
| 26.46 | 0.010 |
| 26.68 | 0.440 |
| 26.70 | 0.040 |
| 26.72 | 0.010 |
| 26.87 | 0.230 |
| 27.00 | 0.010 |
| 27.03 | 0.010 |
| 27.04 | 0.030 |
| 27.15 | 0.060 |
| 27.21 | 0.010 |
| 27.33 | 0.060 |
| 27.35 | 0.280 |
| 27.49 | 0.010 |
| 27.57 | 0.010 |
| 27.74 | 1.790 |
| 27.79 | 0.670 |
| 27.82 | 1.020 |
| 27.88 | 2.750 |
| 28.21 | 3.130 |
| 28.30 | 0.140 |
| 28.31 | 0.010 |
| 28.43 | 0.010 |
| 28.45 | 1.050 |
| 28.51 | 0.010 |
| 28.54 | 0.010 |
| 28.57 | 1.040 |
| 28.66 | 0.050 |
| 28.67 | 0.010 |
| 28.99 | 0.010 |
| 29.04 | 6.380 |
| 29.10 | 0.040 |
| 29.26 | 1.530 |
| 29.49 | 0.010 |
| 29.54 | 1.940 |
| 29.99 | 0.010 |
| 30.05 | 0.030 |
| 30.27 | 0.010 |
| Autor: Grupo 3 | |
# 3. Gráfica de dispersión
plot(x, y,
main = "Grafica No1:Diagrama de dispersion entre Precipitaciones y Radiacion solar\n
en el estudio clima en el volcan Antisana en 2012",
xlab = "Radiacion solar (J/m2)", #
ylab = "Precipitacion (mm)",
col = "brown2",
pch = 16,
cex = 1.2,
cex.main = 1,
cex.lab = 1,
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 sugiere un modelo con curva, a medida que aumenta la radiación solar, la precipitación disminuye de forma cada vez más rápida, lo que sugiere un modelo exponencial decreciente para describir el comportamiento entre ambas variables.
# 5. Cálculo de parámetros modelo exponencial
y1<-log(y)
regresionexponencial<- lm(y1~x)
beta0<- regresionexponencial$coefficients[1]
beta1<- regresionexponencial$coefficients[2]
b<- beta1
b## x
## -0.200551a<-exp(beta0)
a## (Intercept)
## 111.7808# 6. Gráfica de dispersión modelo-realidad
plot(x, y,
main = " Grafica N.-2: Regresion lineal entre la precipitacion y radiacion solar
en el volcan Antisana en 2012 ",
xlab = "Radiacion solar (J/m2)",
ylab = "Precipitacion (mm)",
col = "brown2",
pch = 16,
cex = 1.2,
cex.main = 1,
cex.lab = 1,
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="blue4",add = TRUE)
# 7. Test de bondad
#Test de Pearson, coeficiente de correlación (relacion inversa)
r<- cor(x,y1)*100
r## [1] -74.26949# 8. Coeficiente de determinación muestral
r2<- r^2/100
r2## [1] 55.15957# 9. Restricciones
#Dominio [x]: D= {R+^0}
#Dominio [y]: D= {R+^0}
# ¿Existe algún valor en 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 tanto la radiación solar como la precipitación toman valores no negativos y el modelo, genera siempre valores positivos de precipitación. Además, al ser un modelo exponencial decreciente, la precipitación disminuye con el aumento de la radiación solar sin salirse de su dominio físico.
# 10. Aplicaciones del modelo
# La precipitación esperada cuando la radiación solar es de 20 (J/m2)
Precipitacion_esperada<- 112 * exp(-0.200551 * 20)
Precipitacion_esperada## [1] 2.02887# 11. Conclusión
# Entre la radición solar en (J/m2) y precipitación en (mm) existe ralación tipo exponencial cuya ecuación o modelo es y= 112*e^-0.200551x donde x es la radiación solar, y es la precipitación, donde la precpitación depende en un 67.76% de la radiación solar y el 32.24% se debe a otros factores.
#Modelo logaritmico
# 1. Seleccionar dos variables
#y=a+bln(x)
datos_prom <- aggregate(Precipitation ~ Solar, data = datos, mean)
y<-datos_prom$Solar
x<-datos_prom$Precipitation
#Causa y efecto: La radiación solar es la causa porque regula la energía atmosférica, y la precipitación es el efecto, ya que varía en respuesta a los cambios en la radiación solar.
# 2. Tabla pares de valores (TVP)
TVP_radi_prec<-data.frame(x,y)
TVP_radi_prec %>%
gt() %>%
tab_header(
title = md("*Tabla Nro. 1*"),
subtitle = md("**Pares de valores de precipitacion y radiacion solar, estudio del clima volcan Antisana en 2012 **")
) %>%
tab_source_note(
source_note = md("Autor: Grupo 3")
) %>%
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 precipitacion y radiacion solar, estudio del clima volcan Antisana en 2012 ** | |
| x | y |
|---|---|
| 44.390 | 1.26 |
| 64.670 | 1.35 |
| 30.890 | 1.52 |
| 60.110 | 1.54 |
| 25.740 | 1.58 |
| 94.720 | 1.82 |
| 24.820 | 1.90 |
| 32.350 | 1.93 |
| 18.260 | 2.15 |
| 40.020 | 2.39 |
| 35.600 | 2.40 |
| 39.670 | 2.79 |
| 27.710 | 2.83 |
| 35.950 | 2.90 |
| 53.780 | 2.94 |
| 49.860 | 3.07 |
| 32.800 | 3.13 |
| 29.870 | 3.19 |
| 48.095 | 3.45 |
| 16.600 | 3.54 |
| 31.200 | 3.56 |
| 45.670 | 3.59 |
| 33.650 | 3.60 |
| 40.710 | 3.62 |
| 27.800 | 3.64 |
| 28.710 | 3.86 |
| 39.980 | 3.87 |
| 85.580 | 3.98 |
| 33.360 | 3.99 |
| 57.380 | 4.00 |
| 52.730 | 4.02 |
| 37.710 | 4.08 |
| 28.010 | 4.28 |
| 58.200 | 4.29 |
| 25.810 | 4.31 |
| 15.480 | 4.32 |
| 18.110 | 4.33 |
| 59.470 | 4.44 |
| 35.990 | 4.49 |
| 24.150 | 4.54 |
| 35.050 | 4.57 |
| 41.530 | 4.58 |
| 9.710 | 4.61 |
| 27.470 | 4.63 |
| 21.250 | 4.73 |
| 34.260 | 4.74 |
| 20.295 | 4.83 |
| 28.800 | 4.89 |
| 13.440 | 5.10 |
| 22.570 | 5.13 |
| 34.780 | 5.15 |
| 10.090 | 5.20 |
| 3.550 | 5.28 |
| 18.950 | 5.30 |
| 15.500 | 5.32 |
| 13.350 | 5.37 |
| 40.070 | 5.38 |
| 24.140 | 5.39 |
| 17.100 | 5.44 |
| 34.710 | 5.45 |
| 29.065 | 5.55 |
| 12.730 | 5.59 |
| 16.520 | 5.60 |
| 21.280 | 5.63 |
| 14.640 | 5.71 |
| 19.900 | 5.84 |
| 10.600 | 5.92 |
| 10.340 | 5.95 |
| 47.700 | 6.03 |
| 10.180 | 6.07 |
| 11.600 | 6.11 |
| 20.520 | 6.16 |
| 50.090 | 6.27 |
| 26.100 | 6.37 |
| 24.740 | 6.45 |
| 24.050 | 6.50 |
| 29.730 | 6.71 |
| 33.220 | 6.87 |
| 46.030 | 6.89 |
| 41.880 | 6.99 |
| 30.770 | 7.02 |
| 52.690 | 7.11 |
| 37.970 | 7.16 |
| 15.510 | 7.18 |
| 33.425 | 7.19 |
| 64.030 | 7.20 |
| 20.040 | 7.26 |
| 22.620 | 7.40 |
| 27.620 | 7.48 |
| 21.210 | 7.55 |
| 18.580 | 7.61 |
| 16.660 | 7.68 |
| 36.140 | 7.79 |
| 14.070 | 7.86 |
| 10.680 | 7.87 |
| 16.335 | 7.98 |
| 45.100 | 8.01 |
| 8.970 | 8.03 |
| 19.390 | 8.11 |
| 57.265 | 8.17 |
| 37.770 | 8.21 |
| 24.140 | 8.24 |
| 12.970 | 8.28 |
| 10.290 | 8.29 |
| 14.170 | 8.31 |
| 58.410 | 8.32 |
| 28.260 | 8.35 |
| 12.910 | 8.39 |
| 25.120 | 8.75 |
| 7.550 | 8.83 |
| 26.460 | 8.86 |
| 19.830 | 8.98 |
| 45.190 | 9.00 |
| 14.670 | 9.01 |
| 26.980 | 9.04 |
| 45.550 | 9.12 |
| 21.080 | 9.25 |
| 25.610 | 9.36 |
| 25.190 | 9.57 |
| 10.920 | 9.64 |
| 29.875 | 9.66 |
| 27.180 | 9.72 |
| 23.680 | 9.73 |
| 4.660 | 9.85 |
| 40.760 | 9.87 |
| 30.325 | 9.89 |
| 4.360 | 9.98 |
| 26.870 | 9.99 |
| 14.960 | 10.04 |
| 16.320 | 10.11 |
| 8.860 | 10.17 |
| 48.330 | 10.21 |
| 22.990 | 10.37 |
| 9.170 | 10.40 |
| 14.690 | 10.43 |
| 41.150 | 10.44 |
| 5.260 | 10.47 |
| 3.260 | 10.60 |
| 37.360 | 10.61 |
| 12.090 | 10.62 |
| 11.200 | 10.77 |
| 12.370 | 10.78 |
| 39.930 | 10.93 |
| 17.310 | 10.95 |
| 22.570 | 11.19 |
| 8.450 | 11.20 |
| 7.360 | 11.31 |
| 21.750 | 11.32 |
| 16.790 | 11.39 |
| 3.690 | 11.45 |
| 26.410 | 11.48 |
| 11.550 | 11.50 |
| 9.760 | 11.56 |
| 12.405 | 11.57 |
| 12.570 | 11.63 |
| 15.570 | 11.64 |
| 7.410 | 11.69 |
| 24.870 | 11.76 |
| 29.200 | 11.81 |
| 11.600 | 11.84 |
| 8.020 | 11.88 |
| 36.470 | 11.89 |
| 8.620 | 11.93 |
| 25.920 | 11.98 |
| 41.500 | 12.10 |
| 27.920 | 12.11 |
| 28.690 | 12.13 |
| 35.440 | 12.25 |
| 3.280 | 12.35 |
| 6.740 | 12.42 |
| 48.240 | 12.47 |
| 20.200 | 12.84 |
| 24.620 | 12.87 |
| 3.350 | 12.93 |
| 13.660 | 12.95 |
| 18.250 | 13.04 |
| 10.920 | 13.12 |
| 21.300 | 13.15 |
| 11.190 | 13.20 |
| 13.900 | 13.21 |
| 14.000 | 13.22 |
| 14.090 | 13.24 |
| 0.760 | 13.27 |
| 5.150 | 13.32 |
| 39.140 | 13.34 |
| 22.970 | 13.35 |
| 14.190 | 13.48 |
| 13.600 | 13.49 |
| 2.200 | 13.57 |
| 17.230 | 13.61 |
| 14.470 | 13.62 |
| 7.830 | 13.65 |
| 18.740 | 13.70 |
| 5.840 | 14.04 |
| 0.420 | 14.08 |
| 29.230 | 14.41 |
| 19.940 | 14.52 |
| 13.390 | 14.53 |
| 2.660 | 14.59 |
| 14.490 | 14.65 |
| 26.980 | 14.67 |
| 9.390 | 14.82 |
| 13.820 | 14.83 |
| 8.490 | 14.84 |
| 7.330 | 15.18 |
| 16.710 | 15.19 |
| 0.840 | 15.23 |
| 14.350 | 15.49 |
| 19.720 | 15.54 |
| 7.550 | 15.82 |
| 8.490 | 15.98 |
| 21.675 | 16.16 |
| 14.250 | 16.21 |
| 10.300 | 16.27 |
| 16.510 | 16.29 |
| 9.700 | 16.36 |
| 2.460 | 16.45 |
| 7.070 | 16.46 |
| 12.600 | 16.59 |
| 17.090 | 16.90 |
| 7.280 | 16.92 |
| 21.540 | 16.94 |
| 8.610 | 17.01 |
| 5.730 | 17.05 |
| 12.590 | 17.42 |
| 7.100 | 17.65 |
| 5.640 | 17.68 |
| 0.950 | 18.42 |
| 6.190 | 18.58 |
| 10.520 | 18.76 |
| 20.020 | 18.80 |
| 12.160 | 19.09 |
| 6.680 | 19.28 |
| 16.580 | 19.30 |
| 15.440 | 19.89 |
| 12.610 | 20.32 |
| 12.500 | 20.40 |
| 8.530 | 20.45 |
| 12.510 | 20.53 |
| 0.280 | 20.54 |
| 14.320 | 20.77 |
| 16.240 | 20.83 |
| 0.090 | 20.91 |
| 7.400 | 20.93 |
| 0.010 | 20.94 |
| 7.930 | 21.01 |
| 9.490 | 21.02 |
| 5.720 | 21.11 |
| 5.600 | 21.17 |
| 4.830 | 21.33 |
| 11.360 | 21.36 |
| 0.460 | 21.44 |
| 2.510 | 21.47 |
| 5.720 | 21.60 |
| 2.270 | 21.70 |
| 2.910 | 21.71 |
| 15.330 | 21.77 |
| 8.210 | 22.03 |
| 2.350 | 22.19 |
| 6.000 | 22.30 |
| 7.230 | 22.40 |
| 0.660 | 22.65 |
| 8.280 | 22.81 |
| 16.180 | 22.85 |
| 9.440 | 23.15 |
| 0.380 | 23.24 |
| 7.890 | 23.31 |
| 12.860 | 23.32 |
| 1.110 | 23.37 |
| 5.830 | 23.43 |
| 8.470 | 23.48 |
| 2.380 | 23.49 |
| 0.020 | 23.54 |
| 0.010 | 23.67 |
| 2.130 | 23.69 |
| 1.935 | 23.87 |
| 0.550 | 23.88 |
| 11.680 | 24.15 |
| 0.080 | 24.22 |
| 1.860 | 24.38 |
| 5.520 | 24.41 |
| 4.250 | 24.51 |
| 13.060 | 24.58 |
| 10.060 | 24.63 |
| 10.410 | 24.65 |
| 0.010 | 24.67 |
| 2.010 | 24.72 |
| 8.600 | 24.74 |
| 4.130 | 24.77 |
| 5.380 | 24.96 |
| 8.130 | 25.09 |
| 9.140 | 25.11 |
| 8.480 | 25.20 |
| 8.555 | 25.28 |
| 0.110 | 25.32 |
| 7.510 | 25.50 |
| 11.660 | 25.65 |
| 0.010 | 25.67 |
| 1.330 | 25.68 |
| 0.170 | 25.71 |
| 1.190 | 25.88 |
| 0.110 | 25.95 |
| 0.230 | 25.97 |
| 1.580 | 26.02 |
| 0.010 | 26.14 |
| 0.180 | 26.15 |
| 0.360 | 26.23 |
| 0.180 | 26.28 |
| 0.710 | 26.30 |
| 4.060 | 26.31 |
| 6.540 | 26.40 |
| 0.050 | 26.45 |
| 0.010 | 26.46 |
| 0.440 | 26.68 |
| 0.040 | 26.70 |
| 0.010 | 26.72 |
| 0.230 | 26.87 |
| 0.010 | 27.00 |
| 0.010 | 27.03 |
| 0.030 | 27.04 |
| 0.060 | 27.15 |
| 0.010 | 27.21 |
| 0.060 | 27.33 |
| 0.280 | 27.35 |
| 0.010 | 27.49 |
| 0.010 | 27.57 |
| 1.790 | 27.74 |
| 0.670 | 27.79 |
| 1.020 | 27.82 |
| 2.750 | 27.88 |
| 3.130 | 28.21 |
| 0.140 | 28.30 |
| 0.010 | 28.31 |
| 0.010 | 28.43 |
| 1.050 | 28.45 |
| 0.010 | 28.51 |
| 0.010 | 28.54 |
| 1.040 | 28.57 |
| 0.050 | 28.66 |
| 0.010 | 28.67 |
| 0.010 | 28.99 |
| 6.380 | 29.04 |
| 0.040 | 29.10 |
| 1.530 | 29.26 |
| 0.010 | 29.49 |
| 1.940 | 29.54 |
| 0.010 | 29.99 |
| 0.030 | 30.05 |
| 0.010 | 30.27 |
| Autor: Grupo 3 | |
# 3. Gráfica de dispersión
plot(x, y,
main = "Grafica No1:Diagrama de dispersion entre Precipitacion y Radiacion solar
en el estudio clima en el volcan Antisana en 2012",
xlab = "Precipitacion (mm)", # Nombre eje X
ylab = "Radiacion solar (J/m2)",
col = "cyan",
pch = 16,
cex = 1.2,
cex.main = 1,
cex.lab = 1,
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 evidencia una curva decreciente, los datos sugiere un modelo logarítmico debido a que la precipitación muestra un descenso abrupto inicial que se estabiliza gradualmente conforme aumenta la radiación solar, formando una curva asintótica.
# 5. Cálculo de parámetros modelo logaritmico
x1<- log(x)
regresionlogaritmica<- lm(y~x1)
# Ver los coeficientes (a,b)
a<- regresionlogaritmica$coefficients[1]
a## (Intercept)
## 19.4988b<-regresionlogaritmica$coefficients[2]
b## x1
## -2.750401# 6. Gráfica de dispersión modelo-realidad
plot(x, y,
main = " Grafica No2: Regresion lineal entre la Precipitacion y Radiacion solar
en el volcan Antisana en 2012 ",
xlab = "Precipitacion (mm)",
ylab = "Radiacion solar (J/m2)",
col = "cyan",
pch = 16,
cex = 1.2,
cex.main = 1,
cex.lab = 1,
cex.axis = 0.9,
xlim = c(0, max(x)*1.05),
ylim = c(0, max(y)*1.05))
curve(a + b * log(x),
n = 500,
add = TRUE,
col = "orange4",
lwd = 2)
# 7. Test de bondad
#Test de Pearson, coeficiente de correlación
r<- cor(x1,y)*100
r## [1] -74.26949# 8. Coeficiente de determinación muestral
r2<- r^2/100
r2## [1] 55.15957# 9. Restricciones
#Dominio [x]: D= {R+^0}
#Dominio [y]: D= {R+^0}
# ¿Existe algún valor en dominio de x que sustituido en el modelo matemático genere un valor en y fuera de su dominio?
# El modelo es válido únicamente para valores de radiación en el intervalo 0 < x <= 1201,2. Las restricciones principales son que (x) no puede ser 0 porque el logaritmo natural de cero no existe (indeterminado), y (x) no puede ser mayor a 1201.2 porque el modelo empezaría a predecir valores de precipitación negativos (y < 0), lo cual es físicamente imposible en este contexto meteorológico.
# 10. Aplicaciones del modelo
# La radiación esperada cuando la precipitación es de 55 (mm)
Radiación_esperada<- 19.4988-2.750401*log(55)
Radiación_esperada## [1] 8.477027# 11. Conclusión
# Entre radiación solar (J/m2) y precipitación (mm) existe una relación tipo logaritmica cuya ecuación o modelo es 19.4988 - 2.750401 * log(x), siendo y= Radiación molar y x= Precipitación, donde la radiación solar depende en un 74.26% de las precipitaciones y el 25.74% se debe a otros factores. El modelo presenta restricciones y funciona con precipitaciones > 0 mm de agua y para valores menores o iguales a 1201.2 mm de agua
# Regresión Multiple
#Carga de paquetes
library(scatterplot3d)
#Cargar los datos y seleccionar variables
y <- datos$Precipitation
x1 <- datos$Relative.Humidity
x2 <-datos$Solar
# 2. Tabla de tripleta de valores (TTP)
TTP<-data.frame(x1,x2,y)
TTP %>%
gt() %>%
tab_header(
title = md("*Tabla Nro. 1*"),
subtitle = md("**Tripleta de valores de la Humedad, radicion solar y Precipitación en un estudio del clima volcán Antisana en 2012 **")
) %>%
tab_source_note(
source_note = md("Autor: Grupo 3")
) %>%
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 | ||
| **Tripleta de valores de la Humedad, radicion solar y Precipitación en un estudio del clima volcán Antisana en 2012 ** | ||
| x1 | x2 | y |
|---|---|---|
| 0.93 | 15.98 | 8.49 |
| 0.96 | 12.25 | 35.44 |
| 0.98 | 4.58 | 41.53 |
| 0.99 | 4.32 | 15.48 |
| 0.98 | 3.86 | 28.71 |
| 0.97 | 9.57 | 25.19 |
| 0.98 | 10.93 | 39.93 |
| 0.99 | 2.40 | 35.60 |
| 0.99 | 5.32 | 15.50 |
| 0.98 | 7.19 | 45.68 |
| 0.98 | 6.71 | 29.73 |
| 0.96 | 10.77 | 11.20 |
| 0.96 | 9.66 | 16.77 |
| 0.98 | 5.37 | 13.35 |
| 0.99 | 4.02 | 52.73 |
| 0.97 | 9.64 | 10.92 |
| 0.98 | 8.11 | 19.39 |
| 0.99 | 3.19 | 29.87 |
| 0.99 | 3.64 | 27.80 |
| 0.98 | 5.60 | 16.52 |
| 0.97 | 8.75 | 25.12 |
| 0.99 | 4.57 | 35.05 |
| 0.99 | 1.52 | 30.89 |
| 0.99 | 1.93 | 32.35 |
| 0.97 | 10.43 | 14.69 |
| 0.99 | 3.60 | 33.65 |
| 0.98 | 6.45 | 24.74 |
| 0.99 | 1.35 | 64.67 |
| 0.98 | 5.55 | 17.45 |
| 0.99 | 6.50 | 24.05 |
| 0.98 | 6.87 | 33.22 |
| 0.98 | 8.17 | 50.27 |
| 0.99 | 1.58 | 25.74 |
| 0.98 | 5.28 | 3.55 |
| 0.97 | 10.11 | 16.32 |
| 0.98 | 8.24 | 24.14 |
| 0.99 | 1.90 | 24.82 |
| 0.97 | 6.07 | 10.18 |
| 0.98 | 7.16 | 37.97 |
| 0.97 | 7.87 | 10.68 |
| 0.96 | 11.57 | 20.89 |
| 0.99 | 2.15 | 18.26 |
| 0.97 | 8.31 | 14.17 |
| 0.98 | 6.11 | 11.60 |
| 0.97 | 8.86 | 26.46 |
| 0.98 | 5.92 | 10.60 |
| 0.97 | 5.95 | 10.34 |
| 0.98 | 5.10 | 13.44 |
| 0.98 | 4.00 | 57.38 |
| 0.97 | 8.01 | 45.10 |
| 0.99 | 4.08 | 37.71 |
| 0.99 | 3.59 | 42.52 |
| 0.99 | 2.83 | 27.71 |
| 0.99 | 2.90 | 35.95 |
| 0.99 | 3.07 | 49.86 |
| 0.99 | 1.82 | 94.72 |
| 0.99 | 1.54 | 60.11 |
| 0.98 | 4.28 | 28.01 |
| 0.99 | 6.99 | 41.88 |
| 0.98 | 6.89 | 46.03 |
| 0.97 | 9.89 | 43.64 |
| 0.95 | 11.45 | 3.69 |
| 0.94 | 8.35 | 28.26 |
| 0.95 | 5.44 | 17.10 |
| 0.98 | 4.63 | 27.47 |
| 0.96 | 9.72 | 27.18 |
| 0.95 | 11.63 | 12.57 |
| 0.92 | 16.16 | 18.83 |
| 0.90 | 20.53 | 12.51 |
| 0.90 | 13.70 | 18.74 |
| 0.90 | 17.42 | 12.59 |
| 0.90 | 16.27 | 10.30 |
| 0.92 | 18.80 | 20.02 |
| 0.94 | 14.41 | 29.23 |
| 0.94 | 14.52 | 19.94 |
| 0.94 | 13.32 | 5.15 |
| 0.97 | 8.32 | 58.41 |
| 0.99 | 3.98 | 85.58 |
| 0.99 | 4.49 | 35.99 |
| 0.99 | 2.39 | 40.02 |
| 0.99 | 7.02 | 30.77 |
| 0.99 | 4.29 | 58.20 |
| 0.99 | 7.79 | 36.14 |
| 0.99 | 4.83 | 16.34 |
| 0.99 | 5.59 | 12.73 |
| 0.98 | 8.29 | 10.29 |
| 0.98 | 4.73 | 21.25 |
| 0.98 | 4.83 | 24.25 |
| 0.96 | 11.93 | 11.50 |
| 0.92 | 14.83 | 13.82 |
| 0.93 | 12.42 | 6.74 |
| 0.94 | 13.34 | 39.14 |
| 0.94 | 13.22 | 14.00 |
| 0.94 | 11.89 | 36.47 |
| 0.99 | 4.44 | 59.47 |
| 0.99 | 3.45 | 57.83 |
| 0.98 | 5.38 | 40.07 |
| 0.98 | 7.20 | 64.03 |
| 0.98 | 4.74 | 34.26 |
| 0.95 | 8.03 | 8.97 |
| 0.95 | 10.47 | 1.36 |
| 0.90 | 16.45 | 2.46 |
| 0.91 | 10.60 | 3.26 |
| 0.96 | 11.69 | 7.41 |
| 0.95 | 10.17 | 8.86 |
| 0.92 | 11.57 | 3.92 |
| 0.99 | 4.33 | 18.11 |
| 0.99 | 5.45 | 34.71 |
| 0.99 | 3.56 | 31.20 |
| 0.97 | 7.98 | 29.70 |
| 0.97 | 9.87 | 40.76 |
| 0.98 | 10.95 | 17.31 |
| 0.98 | 7.18 | 15.51 |
| 0.95 | 11.98 | 25.92 |
| 0.99 | 8.21 | 37.77 |
| 0.93 | 16.90 | 17.09 |
| 0.98 | 3.87 | 39.98 |
| 0.98 | 9.73 | 23.68 |
| 0.98 | 5.13 | 22.57 |
| 0.99 | 3.54 | 16.60 |
| 0.98 | 7.40 | 22.62 |
| 0.97 | 7.61 | 18.58 |
| 0.92 | 13.65 | 7.83 |
| 0.87 | 21.70 | 2.27 |
| 0.89 | 16.46 | 7.07 |
| 0.92 | 14.53 | 13.39 |
| 0.94 | 11.31 | 7.36 |
| 0.92 | 12.95 | 13.66 |
| 0.90 | 13.57 | 2.20 |
| 0.91 | 12.13 | 28.69 |
| 0.92 | 15.54 | 19.72 |
| 0.96 | 11.48 | 26.41 |
| 0.98 | 6.16 | 20.52 |
| 0.98 | 5.63 | 21.28 |
| 0.93 | 14.65 | 14.49 |
| 0.94 | 10.78 | 12.37 |
| 0.94 | 13.21 | 13.90 |
| 0.93 | 16.16 | 24.52 |
| 0.97 | 11.76 | 24.87 |
| 0.99 | 4.89 | 28.80 |
| 0.97 | 4.61 | 9.71 |
| 0.96 | 7.98 | 2.97 |
| 0.93 | 13.62 | 14.47 |
| 0.91 | 18.58 | 6.19 |
| 0.88 | 25.28 | 3.46 |
| 0.87 | 24.96 | 5.38 |
| 0.88 | 25.11 | 9.14 |
| 0.83 | 26.70 | 0.04 |
| 0.85 | 21.17 | 5.60 |
| 0.84 | 21.44 | 0.46 |
| 0.81 | 24.41 | 5.52 |
| 0.78 | 26.23 | 0.36 |
| 0.81 | 23.67 | 0.01 |
| 0.85 | 16.36 | 9.70 |
| 0.90 | 15.49 | 14.35 |
| 0.88 | 21.36 | 11.36 |
| 0.92 | 19.28 | 6.68 |
| 0.85 | 25.20 | 8.48 |
| 0.82 | 25.88 | 1.19 |
| 0.85 | 22.03 | 8.21 |
| 0.84 | 24.51 | 6.08 |
| 0.77 | 25.95 | 0.11 |
| 0.80 | 24.77 | 4.13 |
| 0.86 | 22.40 | 7.23 |
| 0.83 | 24.38 | 1.86 |
| 0.84 | 14.84 | 8.49 |
| 0.84 | 21.01 | 7.93 |
| 0.89 | 16.21 | 14.25 |
| 0.88 | 21.77 | 15.33 |
| 0.90 | 20.93 | 7.40 |
| 0.89 | 17.68 | 5.64 |
| 0.87 | 20.32 | 12.61 |
| 0.90 | 19.89 | 4.48 |
| 0.79 | 26.28 | 0.18 |
| 0.75 | 20.91 | 0.09 |
| 0.81 | 15.23 | 0.84 |
| 0.85 | 23.15 | 9.44 |
| 0.79 | 23.24 | 0.38 |
| 0.72 | 25.32 | 0.11 |
| 0.77 | 24.51 | 2.42 |
| 0.88 | 12.93 | 3.35 |
| 0.85 | 23.49 | 2.38 |
| 0.76 | 20.54 | 0.28 |
| 0.73 | 26.46 | 0.01 |
| 0.76 | 23.87 | 0.58 |
| 0.81 | 22.65 | 0.66 |
| 0.87 | 14.82 | 9.39 |
| 0.86 | 22.19 | 2.35 |
| 0.81 | 21.11 | 5.72 |
| 0.73 | 26.14 | 0.01 |
| 0.77 | 25.97 | 0.23 |
| 0.78 | 23.48 | 8.47 |
| 0.86 | 23.31 | 7.89 |
| 0.84 | 24.58 | 13.06 |
| 0.78 | 24.72 | 2.01 |
| 0.81 | 22.81 | 8.28 |
| 0.80 | 24.74 | 8.60 |
| 0.77 | 26.30 | 0.71 |
| 0.71 | 26.68 | 0.44 |
| 0.66 | 25.67 | 0.01 |
| 0.67 | 27.03 | 0.01 |
| 0.72 | 21.33 | 4.83 |
| 0.71 | 21.60 | 5.72 |
| 0.68 | 27.15 | 0.06 |
| 0.63 | 27.00 | 0.01 |
| 0.69 | 26.87 | 0.23 |
| 0.64 | 27.49 | 0.01 |
| 0.63 | 27.57 | 0.01 |
| 0.68 | 25.71 | 0.17 |
| 0.70 | 26.45 | 0.05 |
| 0.73 | 21.47 | 2.51 |
| 0.74 | 26.02 | 1.58 |
| 0.74 | 23.87 | 3.29 |
| 0.68 | 25.68 | 1.33 |
| 0.71 | 25.50 | 7.51 |
| 0.78 | 21.02 | 9.49 |
| 0.84 | 24.63 | 10.06 |
| 0.72 | 27.04 | 0.03 |
| 0.56 | 27.21 | 0.01 |
| 0.62 | 27.82 | 1.02 |
| 0.62 | 28.31 | 0.01 |
| 0.58 | 28.43 | 0.01 |
| 0.71 | 23.69 | 2.13 |
| 0.79 | 23.32 | 12.86 |
| 0.89 | 13.49 | 13.60 |
| 0.89 | 20.40 | 12.50 |
| 0.86 | 14.08 | 0.42 |
| 0.84 | 18.42 | 0.95 |
| 0.82 | 21.71 | 2.91 |
| 0.91 | 12.10 | 41.50 |
| 0.86 | 22.30 | 6.00 |
| 0.75 | 28.54 | 0.01 |
| 0.72 | 28.45 | 1.05 |
| 0.68 | 28.67 | 0.01 |
| 0.74 | 28.30 | 0.14 |
| 0.73 | 28.57 | 1.04 |
| 0.72 | 28.66 | 0.05 |
| 0.67 | 28.51 | 0.01 |
| 0.65 | 26.72 | 0.01 |
| 0.68 | 24.67 | 0.01 |
| 0.67 | 28.99 | 0.01 |
| 0.72 | 20.94 | 0.01 |
| 0.66 | 27.35 | 0.28 |
| 0.63 | 26.15 | 0.18 |
| 0.62 | 29.49 | 0.01 |
| 0.63 | 23.54 | 0.02 |
| 0.66 | 24.22 | 0.08 |
| 0.64 | 27.74 | 1.79 |
| 0.65 | 23.88 | 0.55 |
| 0.63 | 29.54 | 1.94 |
| 0.74 | 25.65 | 11.66 |
| 0.75 | 26.40 | 6.54 |
| 0.64 | 29.99 | 0.01 |
| 0.64 | 29.10 | 0.04 |
| 0.66 | 30.05 | 0.03 |
| 0.69 | 27.33 | 0.06 |
| 0.64 | 30.27 | 0.01 |
| 0.70 | 27.88 | 2.75 |
| 0.69 | 29.26 | 1.53 |
| 0.69 | 26.31 | 4.06 |
| 0.78 | 25.28 | 13.65 |
| 0.90 | 16.94 | 21.54 |
| 0.87 | 25.09 | 8.13 |
| 0.90 | 18.76 | 10.52 |
| 0.92 | 17.01 | 8.61 |
| 0.88 | 24.15 | 11.68 |
| 0.86 | 19.89 | 26.40 |
| 0.93 | 12.87 | 24.62 |
| 0.92 | 20.83 | 16.24 |
| 0.77 | 27.79 | 0.67 |
| 0.87 | 13.61 | 17.23 |
| 0.89 | 16.59 | 12.60 |
| 0.82 | 28.21 | 3.13 |
| 0.78 | 29.04 | 6.38 |
| 0.85 | 20.77 | 14.32 |
| 0.87 | 22.85 | 16.18 |
| 0.89 | 24.65 | 10.41 |
| 0.88 | 16.29 | 16.51 |
| 0.99 | 1.26 | 44.39 |
| 0.97 | 7.55 | 21.21 |
| 0.96 | 12.11 | 27.92 |
| 0.98 | 5.30 | 18.95 |
| 0.97 | 9.01 | 14.67 |
| 0.98 | 12.84 | 20.20 |
| 0.98 | 13.35 | 22.97 |
| 0.98 | 9.25 | 21.08 |
| 0.99 | 6.27 | 50.09 |
| 0.96 | 11.19 | 22.57 |
| 0.97 | 13.04 | 18.25 |
| 0.99 | 3.62 | 40.71 |
| 0.99 | 3.59 | 48.82 |
| 0.98 | 8.39 | 12.91 |
| 0.98 | 10.04 | 14.96 |
| 0.90 | 15.18 | 7.33 |
| 0.97 | 10.40 | 9.17 |
| 0.94 | 17.05 | 5.73 |
| 0.93 | 19.09 | 12.16 |
| 0.97 | 11.32 | 21.75 |
| 0.97 | 7.11 | 52.69 |
| 0.96 | 13.48 | 14.19 |
| 0.92 | 14.67 | 26.98 |
| 0.92 | 20.45 | 8.53 |
| 0.96 | 13.20 | 11.19 |
| 0.98 | 10.21 | 48.33 |
| 0.99 | 5.55 | 40.68 |
| 0.97 | 11.93 | 5.74 |
| 0.96 | 13.24 | 14.09 |
| 0.97 | 13.15 | 21.30 |
| 0.99 | 5.84 | 19.90 |
| 0.97 | 9.66 | 42.98 |
| 0.98 | 3.99 | 33.36 |
| 0.99 | 5.15 | 34.78 |
| 0.95 | 13.12 | 10.92 |
| 0.99 | 7.19 | 21.17 |
| 0.99 | 2.79 | 39.67 |
| 0.98 | 8.17 | 64.26 |
| 0.98 | 7.26 | 20.04 |
| 0.97 | 9.12 | 45.55 |
| 0.99 | 10.44 | 41.15 |
| 0.97 | 11.50 | 11.55 |
| 0.93 | 23.43 | 5.83 |
| 0.91 | 16.92 | 7.28 |
| 0.94 | 15.19 | 16.71 |
| 0.99 | 4.54 | 24.15 |
| 0.99 | 3.13 | 32.80 |
| 0.99 | 2.94 | 53.78 |
| 0.99 | 8.98 | 19.83 |
| 0.98 | 9.89 | 17.01 |
| 0.99 | 3.45 | 38.36 |
| 0.98 | 9.99 | 26.87 |
| 0.98 | 4.31 | 25.81 |
| 0.97 | 9.00 | 45.19 |
| 0.98 | 10.37 | 22.99 |
| 0.96 | 10.61 | 37.36 |
| 0.97 | 5.39 | 24.14 |
| 0.96 | 11.20 | 8.45 |
| 0.96 | 8.83 | 7.55 |
| 0.90 | 23.37 | 1.11 |
| 0.94 | 11.88 | 8.02 |
| 0.97 | 8.28 | 12.97 |
| 0.91 | 14.59 | 2.66 |
| 0.92 | 11.84 | 11.60 |
| 0.96 | 11.56 | 9.76 |
| 0.91 | 13.27 | 0.76 |
| 0.88 | 19.30 | 16.58 |
| 0.98 | 9.04 | 26.98 |
| 0.98 | 7.86 | 14.07 |
| 0.95 | 12.35 | 3.28 |
| 0.91 | 17.65 | 7.10 |
| 0.93 | 15.82 | 7.55 |
| 0.95 | 9.98 | 4.36 |
| 0.96 | 10.62 | 12.09 |
| 0.96 | 11.39 | 16.79 |
| 0.97 | 6.37 | 26.10 |
| 0.98 | 9.36 | 25.61 |
| 0.98 | 6.03 | 47.70 |
| 0.98 | 5.20 | 10.09 |
| 0.95 | 12.47 | 48.24 |
| 0.98 | 7.48 | 27.62 |
| 0.97 | 11.81 | 29.20 |
| 0.98 | 7.68 | 16.66 |
| 0.96 | 10.47 | 9.16 |
| 0.95 | 9.85 | 4.66 |
| 0.93 | 14.04 | 5.84 |
| 0.94 | 11.64 | 15.57 |
| 0.97 | 5.71 | 14.64 |
| Autor: Grupo 3 | ||
# 3. Gráfica de dispersión
regresion<- scatterplot3d(x1,x2,y, main = "Gráfica No1: Diagrama de disperción entre la Humedad, radicion solar y Precipitación en el estudio del clima en el volcán Antisana en 2012",
xlab = "Humendad (%)",ylab = "Radiación solar (J/m2)",zlab = "Precipitación (mm)",
color = "cyan4",pch = 7 ,angle = 225) 
# 4. Conjetura
#La distribución de los puntos sugiere un comportamiento tipo plano inclinado, ya que la precipitación depende simultáneamente de la radiación solar y de la humedad relativa. Se observa una tendencia creciente de la precipitación conforme aumenta la humedad, mientras que valores elevados de radiación solar se asocian con menores niveles de precipitación, evidenciando una relación inversa entre estas variables. Este patrón indica la influencia conjunta de la humedad y la radiación solar en la variabilidad de la precipitación.
# 5. Ajuste del modelo
regresionmultiple<- lm(y~x1+x2)
regresionmultiple##
## Call:
## lm(formula = y ~ x1 + x2)
##
## Coefficients:
## (Intercept) x1 x2
## 29.416 6.899 -1.281#Coeficientes
a<-regresionmultiple$coefficients[2]
a## x1
## 6.899352b<-regresionmultiple$coefficients[3]
b## x2
## -1.280549c<- regresionmultiple$coefficients[1]
c## (Intercept)
## 29.41579# 6. Gráfica de dispersión modelo-realidad
regresion<- scatterplot3d(x1,x2,y,angle = 225, main = "Gráfica No2: Regresión lineal entre la humedad, radiación solar y
máxima temperatura en el estudio del clima en el volcán Antisana en 2012",
xlab = "Humendad (%)",ylab = "Radiación solar (J/m2)",zlab = "Precipitacion (mm))",
color = "cyan4",pch = 7)
regresion$plane3d(regresionmultiple)
# 7. Test de bondad
#Test de Pearson, coeficiente de correlación
r<- cor(y,x1+x2)*100
r## [1] -70.31012# 8. Coeficiente de determinación muestral
r2<- r^2/100
r2## [1] 49.43513# 9. Restricciones
#Dominio [x1]: D= {0,1}
#Dominio [y]: D= {R+^0}
#Dominio [x2]: D= {R+^0}
# ¿Existe algún valor en dominio de x1,x2 que sustituido en el modelo matemático genere un valor en y fuera de su dominio?
#Restriccion: No existen valores negativos para la variable Precipitacion.
# 10. Aplicaciones del modelo
# Que Precipitacion espero cuando tenemos un radiación solar de 14(J/m2) y una humedad de 0.8 (%)
Temperatura_esperada<- 29.41579-1.280549*14+6.899352*0.8
Temperatura_esperada## [1] 17.00759# 11. Conclusión
# Entre humedad (%), Radiación solar (J/m2) y Precipitacion (mm) existe la relación tipo lineal cuya ecuación es
#y= 29.41579-1.280549x2+6.899352x1 siendo y= Precipitacion (mm), x2= radiación solar (J/m2) y x1= humedad (%),donde no existe restricciones y podemos afirmar que la
#temperatura mínima esta influenciada en un 70.31% de la radiación solar y la humedad, el 29.69% se debe a otros factores.
#Por ejemplo cuando la radiación vale 14 (J/m2) y la humedad de 0.8 (%) obtenemos una Precipitación de 17.007 (mm).
#Machine Learning
library(magick)
library(cowplot)
setwd("C:/Users/JOSUE/Downloads/ESTADISTICA")
img1 <- image_read("Pasos del Machine Learning Parte 1.jpeg")
img2 <- image_read("Pasos del Machine Learning Parte 2.jpeg")
plot_grid(
ggdraw() + draw_image(img1),
ggdraw() + draw_image(img2),
ncol = 1
)
#Problema de Regresión:
#Prompt:
#Eres un experto en Machine Lerning, programación en lenguaje Python, IA y conoces sobre las redes neuronales soy estudiante de la carrera de Ingeniería Ambiental,
#actualmente cursando la materia de Estadística y Probabilidad. Genera un modelo de machine learning basado en una red neuronal artificial para predecir la Precipitacion
#a partir de máxima temperatura, mínima temperatura , humedad relativa , velocidad de viento, radiación solar. usando los datos que se encuentran en /content/drive/MyDrive/weatherdataANTISANA.csv.
#Debes generar el código en lenguaje Pyhton, cada etapa debe estar en una única celda, la variable cualitativa conviértela en variable cuantitativa usando codificación binaria,
#y normaliza las variables para que todas se encuentren en la misma escala entre 0 y 1, Los comentarios que generes ponlos en idioma Español,
#presenta la gráfica del error con respecto a las iteraciones o épocas, y haz predicciones finales, descargas todas las librerías que necesites y las que puedas necesitar desde el inicio,
#la precipitación no puede ser negativa.La predicción de la precipitación se realizó mediante una red neuronal artificial.
El notebook completo puede consultarse en Google Colab en el siguiente enlace:
https://colab.research.google.com/drive/1vjYlOXZ_g9gcFYR8oLe64TnST8lI8qIS?usp=sharing