SLOPE
MARTIN SARMIENTO
2025-12-01
1 Configuración y Carga de Datos
##### UNIVERSIDAD CENTRAL DEL ECUADOR #####
#### AUTOR: MARTIN SARMIENTO ####
### CARRERA: INGENIERÍA EN PETRÓLEOS #####
#### VARIABLE PENDIENTE ####
## DATASET ##
setwd("~/R/SLOPE")
# Cargar dataset
Datos <- read.csv("DataSet_prov.csv", sep = ";", dec = ",", fileEncoding = "latin1")
# Estructura de los datos
str(Datos)## 'data.frame': 5075 obs. of 30 variables:
## $ FID_ : int 0 2 3 4 5 6 10 11 12 13 ...
## $ OBJECTID : int 127 129 130 131 132 133 137 138 139 140 ...
## $ code : chr "00127-ARG-P" "00129-ARG-G" "00130-ARG-P" "00131-ARG-P" ...
## $ plant_name : chr "Aconcagua solar farm" "Altiplano 200 Solar Power Plant" "Altiplano 200 Solar Power Plant" "Anchoris solar farm" ...
## $ country : chr "Argentina" "Argentina" "Argentina" "Argentina" ...
## $ operational_status : chr "announced" "operating" "operating" "construction" ...
## $ longitude : num -68.9 -66.9 -66.9 -68.9 -70.3 ...
## $ latitude : num -33 -24.1 -24.1 -33.3 -37.4 ...
## $ elevation : int 929 4000 4000 937 865 858 570 1612 665 3989 ...
## $ area : num 250 4397290 5774 645 241 ...
## $ size : chr "Pequeña" "Grande" "Pequeña" "Pequeña" ...
## $ slope : num 0.574 1.603 6.243 0.903 1.791 ...
## $ slope_type : chr "Plano o casi plano" "Plano o casi plano" "Moderado" "Plano o casi plano" ...
## $ curvature : num 0.000795 -0.002781 -0.043699 0.002781 -0.002384 ...
## $ curvature_type : chr "Superficies planas o intermedias" "Superficies planas o intermedias" "Superficies cóncavas / Valles" "Superficies planas o intermedias" ...
## $ aspect : num 55.1 188.7 270.9 108.4 239.3 ...
## $ aspect_type : chr "Northeast" "South" "West" "East" ...
## $ dist_to_road : num 127 56015 52697 336 34 ...
## $ ambient_temperature : num 12.6 6.8 6.8 13.1 11.4 ...
## $ ghi : num 6.11 8.01 7.88 6.12 6.22 ...
## $ humidity : num 53.7 53.7 53.7 53.7 53.7 ...
## $ wind_speed : num 3.78 7.02 8.33 3.87 6.56 ...
## $ wind_direction : num 55.1 55.1 55.1 55.1 55.1 ...
## $ dt_wind : chr "Northeast" "Northeast" "Northeast" "Northeast" ...
## $ solar_aptitude : num 0.746 0.8 0.727 0.595 0.657 ...
## $ solar_aptitude_rounded: int 7 8 7 6 7 7 7 8 7 8 ...
## $ solar_aptittude_class : chr "Alta" "Alta" "Alta" "Media" ...
## $ capacity : num 25 101 107 180 20 ...
## $ optimal_tilt : int 31 26 26 31 33 30 31 29 31 27 ...
## $ pv_potential : num 4.98 6.39 6.39 4.97 5 ...##
## Adjuntando el paquete: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union2 Cálculo de Intervalos y Frecuencias
# Extraer variable
Variable <- na.omit(Datos$slope)
N <- length(Variable)
# CÁLCULO LÍMITES DECIMALES
min_dec <- min(Variable)
max_dec <- max(Variable)
k_dec <- floor(1 + 3.322 * log10(N))
rango_dec <- max(Variable) - min(Variable)
amplitud_dec <- rango_dec / k_dec
# Cortes exactos
cortes_dec <- seq(min(Variable), max(Variable), length.out = k_dec + 1)
cortes_dec[length(cortes_dec)] <- max(Variable) + 0.0001
# Frecuencias
inter_dec <- cut(Variable, breaks = cortes_dec, include.lowest = TRUE, right = FALSE)
ni_dec <- as.vector(table(inter_dec))
# CÁLCULOS MATEMÁTICOS
hi_dec <- (ni_dec / N) * 100
Ni_asc_dec <- cumsum(ni_dec)
Hi_asc_dec <- cumsum(hi_dec)
Ni_desc_dec <- rev(cumsum(rev(ni_dec)))
Hi_desc_dec <- rev(cumsum(rev(hi_dec)))
# Dataframe Decimal
TDF_Decimal <- data.frame(
Li = cortes_dec[1:k_dec],
Ls = cortes_dec[2:(k_dec+1)],
MC = (cortes_dec[1:k_dec] + cortes_dec[2:(k_dec+1)]) / 2,
ni = ni_dec,
hi = hi_dec,
Ni_asc = Ni_asc_dec,
Ni_desc = Ni_desc_dec,
Hi_asc = Hi_asc_dec,
Hi_desc = Hi_desc_dec)
# CÁLCULO LÍMITES ENTEROS
BASE <- 10
min_int <- floor(min(Variable) / BASE) * BASE
max_int <- ceiling(max(Variable) / BASE) * BASE
k_int_sug <- floor(1 + 3.322 * log10(N))
Rango_int <- max_int - min_int
Amplitud_raw <- Rango_int / k_int_sug
Amplitud_int <- ceiling(Amplitud_raw / 10) * 10
if(Amplitud_int == 0) Amplitud_int <- 10
cortes_int <- seq(from = min_int, by = Amplitud_int, length.out = k_int_sug + 2)
cortes_int <- cortes_int[cortes_int <= (max_int + Amplitud_int)]
while(max(cortes_int) < max(Variable)) {
cortes_int <- c(cortes_int, max(cortes_int) + Amplitud_int)
}
K_real <- length(cortes_int) - 1
lim_inf_int <- cortes_int[1:K_real]
lim_sup_int <- cortes_int[2:(K_real+1)]
# Frecuencias
inter_int <- cut(Variable, breaks = cortes_int, include.lowest = TRUE, right = FALSE)
ni_int <- as.vector(table(inter_int))
# CÁLCULOS MATEMÁTICOS
hi_int <- (ni_int / N) * 100
Ni_asc_int <- cumsum(ni_int)
Hi_asc_int <- cumsum(hi_int)
Ni_desc_int <- rev(cumsum(rev(ni_int)))
Hi_desc_int <- rev(cumsum(rev(hi_int)))
# Dataframe Entero
TDF_Enteros <- data.frame(
Li = lim_inf_int,
Ls = lim_sup_int,
MC = (lim_inf_int + lim_sup_int) / 2,
ni = ni_int,
hi = hi_int,
Ni_asc = Ni_asc_int,
Ni_desc = Ni_desc_int,
Hi_asc = Hi_asc_int,
Hi_desc = Hi_desc_int)3 Tabla de Distribución de Frecuencias
3.1 Tabla con Límites Decimales
# Crear Dataframe
TDF_Dec_Final <- data.frame(
Li = as.character(round(TDF_Decimal$Li, 2)),
Ls = as.character(round(TDF_Decimal$Ls, 2)),
MC = as.character(round(TDF_Decimal$MC, 2)),
ni = as.character(TDF_Decimal$ni),
hi = as.character(round(TDF_Decimal$hi, 2)),
Ni_asc = as.character(TDF_Decimal$Ni_asc),
Ni_desc = as.character(TDF_Decimal$Ni_desc),
Hi_asc = as.character(round(TDF_Decimal$Hi_asc, 2)),
Hi_desc = as.character(round(TDF_Decimal$Hi_desc, 2))
)
# Calcular Totales
totales_dec <- c("TOTAL", "-", "-", sum(TDF_Decimal$ni), round(sum(TDF_Decimal$hi), 2), "-", "-", "-", "-")
TDF_Dec_Final <- rbind(TDF_Dec_Final, totales_dec)
# Generar GT
TDF_Dec_Final %>%
gt() %>%
tab_header(title = md("**Tabla N°1 de Distribución de Frecuencias de la Pendiente (°) de las Plantas Solares**")) %>%
cols_label(
Li = "Lim. Inf",
Ls = "Lim. Sup",
MC = "Marca Clase",
ni = "Frec. Abs (ni)",
hi = "Frec. Rel (%)",
Ni_asc = "Ni (Asc)",
Ni_desc = "Ni (Desc)",
Hi_asc = "Hi Asc (%)",
Hi_desc = "Hi Desc (%)"
) %>%
cols_align(align = "center", columns = everything()) %>%
tab_options(heading.title.font.size = px(14), column_labels.background.color = "#F0F0F0")| Tabla N°1 de Distribución de Frecuencias de la Pendiente (°) de las Plantas Solares | ||||||||
| Lim. Inf | Lim. Sup | Marca Clase | Frec. Abs (ni) | Frec. Rel (%) | Ni (Asc) | Ni (Desc) | Hi Asc (%) | Hi Desc (%) |
|---|---|---|---|---|---|---|---|---|
| 0 | 2.59 | 1.29 | 4688 | 92.37 | 4688 | 5075 | 92.37 | 100 |
| 2.59 | 5.17 | 3.88 | 273 | 5.38 | 4961 | 387 | 97.75 | 7.63 |
| 5.17 | 7.76 | 6.47 | 65 | 1.28 | 5026 | 114 | 99.03 | 2.25 |
| 7.76 | 10.35 | 9.06 | 23 | 0.45 | 5049 | 49 | 99.49 | 0.97 |
| 10.35 | 12.94 | 11.64 | 18 | 0.35 | 5067 | 26 | 99.84 | 0.51 |
| 12.94 | 15.52 | 14.23 | 2 | 0.04 | 5069 | 8 | 99.88 | 0.16 |
| 15.52 | 18.11 | 16.82 | 0 | 0 | 5069 | 6 | 99.88 | 0.12 |
| 18.11 | 20.7 | 19.41 | 1 | 0.02 | 5070 | 6 | 99.9 | 0.12 |
| 20.7 | 23.29 | 21.99 | 3 | 0.06 | 5073 | 5 | 99.96 | 0.1 |
| 23.29 | 25.87 | 24.58 | 0 | 0 | 5073 | 2 | 99.96 | 0.04 |
| 25.87 | 28.46 | 27.17 | 1 | 0.02 | 5074 | 2 | 99.98 | 0.04 |
| 28.46 | 31.05 | 29.75 | 0 | 0 | 5074 | 1 | 99.98 | 0.02 |
| 31.05 | 33.64 | 32.34 | 1 | 0.02 | 5075 | 1 | 100 | 0.02 |
| TOTAL | - | - | 5075 | 100 | - | - | - | - |
3.2 Tabla con Límites Enteros
# Crear Dataframe Visual
TDF_Int_Final <- data.frame(
Li = as.character(TDF_Enteros$Li),
Ls = as.character(TDF_Enteros$Ls),
MC = as.character(TDF_Enteros$MC),
ni = as.character(TDF_Enteros$ni),
hi = as.character(round(TDF_Enteros$hi, 2)),
Ni_asc = as.character(TDF_Enteros$Ni_asc),
Ni_desc = as.character(TDF_Enteros$Ni_desc),
Hi_asc = as.character(round(TDF_Enteros$Hi_asc, 2)),
Hi_desc = as.character(round(TDF_Enteros$Hi_desc, 2))
)
# Calcular Totales
totales_int <- c("TOTAL", "-", "-", sum(TDF_Enteros$ni), round(sum(TDF_Enteros$hi), 2), "-", "-", "-", "-")
TDF_Int_Final <- rbind(TDF_Int_Final, totales_int)
# Generar GT
TDF_Int_Final %>%
gt() %>%
tab_header(title = md("**Tabla N°2 de Distribución de Frecuencias de la Pendiente (°) de las Plantas Solares**")) %>%
cols_label(
Li = "Lim. Inf",
Ls = "Lim. Sup",
MC = "Marca Clase",
ni = "Frec. Abs (ni)",
hi = "Frec. Rel (%)",
Ni_asc = "Ni (Asc)",
Ni_desc = "Ni (Desc)",
Hi_asc = "Hi Asc (%)",
Hi_desc = "Hi Desc (%)"
) %>%
cols_align(align = "center", columns = everything()) %>%
tab_options(heading.title.font.size = px(14), column_labels.background.color = "#F0F0F0")| Tabla N°2 de Distribución de Frecuencias de la Pendiente (°) de las Plantas Solares | ||||||||
| Lim. Inf | Lim. Sup | Marca Clase | Frec. Abs (ni) | Frec. Rel (%) | Ni (Asc) | Ni (Desc) | Hi Asc (%) | Hi Desc (%) |
|---|---|---|---|---|---|---|---|---|
| 0 | 10 | 5 | 5046 | 99.43 | 5046 | 5075 | 99.43 | 100 |
| 10 | 20 | 15 | 24 | 0.47 | 5070 | 29 | 99.9 | 0.57 |
| 20 | 30 | 25 | 4 | 0.08 | 5074 | 5 | 99.98 | 0.1 |
| 30 | 40 | 35 | 1 | 0.02 | 5075 | 1 | 100 | 0.02 |
| 40 | 50 | 45 | 0 | 0 | 5075 | 0 | 100 | 0 |
| TOTAL | - | - | 5075 | 100 | - | - | - | - |
4 Análisis Gráfico
4.1 Histogramas de Cantidad
par(mar = c(8, 5, 5, 2))
barplot(TDF_Enteros$ni,
names.arg = TDF_Enteros$MC,
main = "",
xlab = "",
ylab = "Cantidad",
col = "#C1E1C1",
space = 0,
las = 2,
cex.names = 0.7)
mtext("Pendiente (°)", side = 1, line = 4)
mtext("Gráfica N°1: Distribución de Cantidad de Plantas Solares por Pendiente",
side = 3,
line = 2,
adj = 0.5,
cex = 0.9,
font = 2)
par(mar = c(8, 5, 5, 2))
barplot(TDF_Enteros$ni,
main = "",
xlab = "",
ylab = "Cantidad",
names.arg = TDF_Enteros$MC,
col = "#C1E1C1",
space = 0,
cex.names = 0.7,
las = 2,
ylim = c(0, sum(TDF_Enteros$ni)))
mtext("Pendiente (°)", side = 1, line = 4)
mtext("Gráfica N°2: Distribución de Cantidad de Plantas Solares por Pendiente",
side = 3,
line = 2,
adj = 0.5,
cex = 0.9,
font = 2)
4.2 Histogramas Porcentuales
par(mar = c(8, 5, 5, 2))
bp3 <- barplot(TDF_Enteros$hi,
main = "",
xlab = "",
ylab = "Porcentaje (%)",
col = "#C1E1C1",
space = 0,
names.arg = TDF_Enteros$MC,
cex.names = 0.7,
las = 2,
ylim = c(0, max(TDF_Enteros$hi) * 1.2))
mtext("Pendiente (°)", side = 1, line = 4)
mtext("Gráfica N°3: Distribución Porcentual de las Plantas Solares por Pendiente",
side = 3,
line = 2,
adj = 0.5,
cex = 0.9,
font = 2)
text(x = bp3,
y = TDF_Enteros$hi,
labels = paste0(round(TDF_Enteros$hi, 1), "%"),
pos = 3, cex = 0.6, col = "black")
par(mar = c(8, 5, 5, 2))
bp4 <- barplot(TDF_Enteros$hi,
main = "",
xlab = "",
ylab = "Porcentaje (%)",
col = "#C1E1C1",
space = 0,
names.arg = TDF_Enteros$MC,
las = 2,
cex.names = 0.7,
ylim = c(0, 110))
mtext("Pendiente (°)", side = 1, line = 4)
mtext("Gráfica N°4: Distribución Porcentual de las Plantas Solares por Pendiente",
side = 3,
line = 2,
adj = 0.5,
cex = 0.9,
font = 2)
text(x = bp4,
y = TDF_Enteros$hi,
labels = paste0(round(TDF_Enteros$hi, 1), "%"),
pos = 3, cex = 0.6, col = "black")
4.3 Diagrama de Cajas (Boxplot)
par(mar = c(5, 5, 4, 2))
boxplot(Variable,
horizontal = TRUE,
col = "#C1E1C1",
xlab = "Pendiente (°)",
cex.main = 0.9,
main = "Gráfica N°5: Distribución de la Pendiente en las Plantas Solares")
4.4 Ojivas
par(mar = c(5, 5, 7, 10), xpd = TRUE)
# Coordenadas
x_asc <- TDF_Enteros$Ls
x_desc <- TDF_Enteros$Li
y_asc <- TDF_Enteros$Ni_asc
y_desc <- TDF_Enteros$Ni_desc
# 1. Dibujar la Ascendente
plot(x_asc, y_asc,
type = "b",
main = "",
xlab = "Pendiente (°)",
ylab = "Frecuencia acumulada",
col = "black",
pch = 19,
xlim = c(min(TDF_Enteros$Li), max(x_asc)),
ylim = c(0, sum(TDF_Enteros$ni)),
bty = "l"
)
# 2. Agregar la Descendente
lines(x_desc, y_desc, col = "green", type = "b", pch = 19)
grid()
mtext("Gráfica N°6: Ojivas Ascendentes y Descendentes de la\nDistribución de la Pendiente en las Plantas Solares",
side = 3,
line = 3,
adj = 0.5,
cex = 0.9,
font = 2)
legend("right",
legend = c("Ascendente", "Descendente"),
col = c("black", "green"),
lty = 1,
pch = 1,
cex = 0.6,
inset = c(0.05, 0.05),
bty = "n")
5 Indicadores Estadísticos
## INDICADORES DE TENDENCIA CENTRAL
# Media aritmética
media <- round(mean(Variable), 2)
# Mediana
mediana <- round(median(Variable), 2)
# Moda
max_frecuencia <- max(TDF_Enteros$ni)
moda_vals <- TDF_Enteros$MC[TDF_Enteros$ni == max_frecuencia]
moda_txt <- paste(round(moda_vals, 2), collapse = ", ")
## INDICADORES DE DISPERSIÓN
# Varianza
varianza <- var(Variable)
# Desviación Estándar
sd_val <- sd(Variable)
# Coeficiente de Variación
cv <- round((sd_val / abs(media)) * 100, 2)
## INDICADORES DE FORMA
# Coeficiente de Asimetría
asimetria <- skewness(Variable, type = 2)
# Curtosis
curtosis <- kurtosis(Variable)
# Outliers
Q1 <- quantile(Variable, 0.25)
Q3 <- quantile(Variable, 0.75)
IQR_val <- Q3 - Q1
lim_inf <- Q1 - 1.5 * IQR_val
lim_sup <- Q3 + 1.5 * IQR_val
outliers_data <- Variable[Variable < lim_inf | Variable > lim_sup]
num_outliers <- length(outliers_data)
if(num_outliers > 0){
rango_outliers <- paste0(num_outliers, " [", round(min(outliers_data), 2), "; ", round(max(outliers_data), 2), "]")
} else {
rango_outliers <- "0 [Sin Outliers]"
}
tabla_indicadores <- data.frame(
"Variable" = c("Pendiente (°)"),
"Rango_MinMax" = paste0("[", round(min(Variable), 2), "; ", round(max(Variable), 2), "]"),
"X" = c(media),
"Me" = c(mediana),
"Mo" = c(moda_txt),
"V" = c(varianza),
"Sd" = c(sd_val),
"Cv" = c(cv),
"As" = c(asimetria),
"K" = c(curtosis),
"Outliers" = rango_outliers)
# Generar Tabla GT
tabla_conclusiones_gt <- tabla_indicadores %>%
gt() %>%
tab_header(title = md("**Tabla N°3 de Conclusiones de Pendiente de las Plantas Solares**")) %>%
tab_source_note(source_note = "Autor: Martin Sarmiento") %>%
cols_label(
Variable = "Variable",
Rango_MinMax = "Rango",
X = "Media (X)",
Me = "Mediana (Me)",
Mo = "Moda (Mo)",
V = "Varianza (V)",
Sd = "Desv. Est. (Sd)",
Cv = "C.V. (%)",
As = "Asimetría (As)",
K = "Curtosis (K)",
Outliers = "Outliers [Intervalo]"
) %>%
tab_options(
heading.title.font.size = px(16),
column_labels.background.color = "#f0f0f0"
)
tabla_conclusiones_gt| Tabla N°3 de Conclusiones de Pendiente de las Plantas Solares | ||||||||||
| Variable | Rango | Media (X) | Mediana (Me) | Moda (Mo) | Varianza (V) | Desv. Est. (Sd) | C.V. (%) | Asimetría (As) | Curtosis (K) | Outliers [Intervalo] |
|---|---|---|---|---|---|---|---|---|---|---|
| Pendiente (°) | [0; 33.64] | 1.12 | 0.71 | 5 | 2.421539 | 1.55613 | 138.94 | 6.812875 | 84.32038 | 355 [2.7; 33.64] |
| Autor: Martin Sarmiento | ||||||||||
6 Conclusiones
La variable “Pendiente” fluctúa entre 0° y 33.64° y sus valores se encuentran alrededor de 0.71°, con una desviación estándar de 1.55613, siendo una variable muy heterogénea, cuyos valores se concentran en la parte media baja de la variable con la agregación de presencia de valores atípicos de 355 outliers; por todo lo anterior, el comportamiento de la variable es muy perjudicial.