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#EJERCICIO EN CLASE (Análisis de Datos de Toros, ej.1.26)
#Parte (a): Cálculo de estadísticos y correlaciones
bull_data <- read.table("C:/Users/dell/Documents/rmarkdown/T1-10.dat", header = FALSE)
nombres_columnas <- c("V1", "V2", "V3","V4", "V5", "V6","V7", "V8", "V9")
colnames(bull_data) <- nombres_columnas
# Seleccionar solo las variables numéricas para el análisis
numeric_data <- bull_data[, c("V3", "V4", "V5", "V6", "V7", "V8", "V9")]
# Calcular vector de medias
mean_vector <- colMeans(numeric_data);mean_vector
## V3 V4 V5 V6 V7 V8
## 50.5223684 995.9473684 70.8815789 6.3157895 0.1967105 54.1263158
## V9
## 1555.2894737
# Calcular matriz de covarianza
cov_matrix <- cov(numeric_data);cov_matrix
## V3 V4 V5 V6 V7 V8
## V3 2.99802632 100.130526 2.9600175 1.50884211 -0.053392105 2.98313684
## V4 100.13052632 8594.343860 209.5043509 51.95017544 -1.398175439 129.94007018
## V5 2.96001754 209.504351 10.6916561 1.45922807 -0.142994737 3.41422456
## V6 1.50884211 51.950175 1.4592281 0.85894737 -0.021614035 1.48757895
## V7 -0.05339211 -1.398175 -0.1429947 -0.02161404 0.008022368 -0.05064561
## V8 2.98313684 129.940070 3.4142246 1.48757895 -0.050645614 4.01796491
## V9 82.81077193 6680.308772 83.9254035 44.32070175 2.412964912 147.28961404
## V9
## V3 82.810772
## V4 6680.308772
## V5 83.925404
## V6 44.320702
## V7 2.412965
## V8 147.289614
## V9 16850.661754
# Calcular matriz de correlación
cor_matrix <- cor(numeric_data);cor_matrix
## V3 V4 V5 V6 V7 V8 V9
## V3 1.0000000 0.6237958 0.5228223 0.9402488 -0.3442770 0.8595129 0.3684348
## V4 0.6237958 1.0000000 0.6911371 0.6046407 -0.1683852 0.6992519 0.5551134
## V5 0.5228223 0.6911371 1.0000000 0.4815234 -0.4882545 0.5209146 0.1977254
## V6 0.9402488 0.6046407 0.4815234 1.0000000 -0.2603762 0.8007440 0.3683960
## V7 -0.3442770 -0.1683852 -0.4882545 -0.2603762 1.0000000 -0.2820899 0.2075349
## V8 0.8595129 0.6992519 0.5209146 0.8007440 -0.2820899 1.0000000 0.5660575
## V9 0.3684348 0.5551134 0.1977254 0.3683960 0.2075349 0.5660575 1.0000000
# Interpretación de correlaciones
# Podemos visualizar la matriz de correlación
library(corrplot)
## corrplot 0.92 loaded
corrplot(cor_matrix, method = "ellipse", type = "upper")
# Análisis por raza
# Calcular medias por raza
media_V1 <- aggregate(numeric_data, by = list(V1 = bull_data$V1), FUN = mean);media_V1
## V1 V3 V4 V5 V6 V7 V8 V9
## 1 1 49.88750 969.2188 69.80938 6.062500 0.2500000 53.55000 1551.719
## 2 5 49.15294 940.0588 68.53529 5.588235 0.2147059 52.19412 1501.941
## 3 8 52.13704 1062.8148 73.62963 7.074074 0.1222222 56.02593 1593.111
##Parte (b): Visualización 3D (Breed, Frame, BkFat)
library(plotly)
## Loading required package: ggplot2
## Warning: package 'ggplot2' was built under R version 4.2.3
##
## Attaching package: 'plotly'
## The following object is masked from 'package:ggplot2':
##
## last_plot
## The following object is masked from 'package:stats':
##
## filter
## The following object is masked from 'package:graphics':
##
## layout
library(RColorBrewer)
# Paleta de colores
colors <- brewer.pal(length(unique(bull_data$Breed)), "Set1")
## Warning in brewer.pal(length(unique(bull_data$Breed)), "Set1"): minimal value for n is 3, returning requested palette with 3 different levels
# Gráfico 3D
plot_ly(bull_data,
x = ~V6,
y = ~V7,
z = ~V1,
color = ~as.factor(V1),
colors = colors,
type = "scatter3d",
mode = "markers",
marker = list(size = 5),
text = ~paste("Breed:", V1, "<br>Frame:", V6, "<br>BkFat:", V7),
hoverinfo = "text") %>%
layout(scene = list(
xaxis = list(title = "Frame"),
yaxis = list(title = "BkFat (inches)"),
zaxis = list(title = "Breed"),
title = "Visualización 3D: Breed vs Frame vs BkFat"
))
#EJERCICIO 2.30
# Datos del problema
#Vector de medias
mu <- c(4, 3, 2, 1)
Sigma <- matrix(c(3, 0, 2, 2,
0, 1, 1, 0,
2, 1, 9, -2,
2, 0, -2, 4), nrow = 4)
# Particiones
mu1 <- c(1, 2)
mu2 <- c(3, 4)
# Matrices A y B
A <- matrix(c(1, 2), nrow = 1)
B <- matrix(c(1, -2, 2, -1), nrow = 2,byrow = TRUE)
#Inciso (a)
#E(X^(1))
E_X1 <- mu[mu1];E_X1
## [1] 4 3
#Inciso (b) E(AX^(1))
E_AX1 <- A %*% E_X1;E_AX1
## [,1]
## [1,] 10
#Inciso (c) Cov(X^(1))
Cov_X1 <- Sigma[mu1, mu1];Cov_X1
## [,1] [,2]
## [1,] 3 0
## [2,] 0 1
#Inciso (d) Cov(AX^(1))
Cov_AX1 <- A %*% Cov_X1 %*% t(A);Cov_AX1
## [,1]
## [1,] 7
#Inciso (e) E(X^(2))
E_X2 <- mu[mu2];E_X2
## [1] 2 1
#Inciso (f) E(BX^(2))
E_BX2 <- B %*% E_X2;E_BX2
## [,1]
## [1,] 0
## [2,] 3
#Inciso (g) Cov(X^(2))
Cov_X2 <- Sigma[mu2, mu2];Cov_X2
## [,1] [,2]
## [1,] 9 -2
## [2,] -2 4
#Inciso (h) Cov(BX^(2))
Cov_BX2 <- B %*% Cov_X2 %*% t(B);Cov_BX2
## [,1] [,2]
## [1,] 33 36
## [2,] 36 48
#Inciso (i) Cov(X^(1), X^(2))
Cov_X1_X2 <- Sigma[mu1, mu2];Cov_X1_X2
## [,1] [,2]
## [1,] 2 2
## [2,] 1 0
#Inciso (j) Cov(AX^(1), BX^(2))
Cov_AX1_BX2 <- A %*% Cov_X1_X2 %*% t(B);Cov_AX1_BX2
## [,1] [,2]
## [1,] 0 6
#Resultados
E_X1
## [1] 4 3
E_AX1
## [,1]
## [1,] 10
Cov_X1
## [,1] [,2]
## [1,] 3 0
## [2,] 0 1
Cov_AX1
## [,1]
## [1,] 7
E_X2
## [1] 2 1
E_BX2
## [,1]
## [1,] 0
## [2,] 3
Cov_X2
## [,1] [,2]
## [1,] 9 -2
## [2,] -2 4
Cov_BX2
## [,1] [,2]
## [1,] 33 36
## [2,] 36 48
Cov_X1_X2
## [,1] [,2]
## [1,] 2 2
## [2,] 1 0
Cov_AX1_BX2
## [,1] [,2]
## [1,] 0 6