Tarea.R

# =============================================================
#               Tarea: Analisis de Correlacion y
#                    Visualizacion de Datos
# =============================================================
# Autora: Natalia Valeria Torrico Saavedra
# Fecha: 20 Agosto, 2024
# Descripcion: Tarea de analisis de datos asignada por el
# profesor Boris Branisa.
# Carrera: Negocios Digitales
# =============================================================

# Clean Global Enviroment -------------------------------------

remove(list = ls())

# Cargar Librerias Necesarias ---------------------------------

library(tidyverse) # Conjunto de herramientas

## Warning: package 'tidyverse' was built under R version 4.3.3

## Warning: package 'ggplot2' was built under R version 4.3.3

## Warning: package 'tibble' was built under R version 4.3.3

## Warning: package 'tidyr' was built under R version 4.3.3

## Warning: package 'readr' was built under R version 4.3.3

## Warning: package 'purrr' was built under R version 4.3.3

## Warning: package 'dplyr' was built under R version 4.3.3

## Warning: package 'forcats' was built under R version 4.3.3

## Warning: package 'lubridate' was built under R version 4.3.3

## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr     1.1.4     ✔ readr     2.1.5
## ✔ forcats   1.0.0     ✔ stringr   1.5.1
## ✔ ggplot2   3.5.1     ✔ tibble    3.2.1
## ✔ lubridate 1.9.3     ✔ tidyr     1.3.1
## ✔ purrr     1.0.2     
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag()    masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors

#                    para la ciencia de datos

# Set Working Directory ---------------------------------------

#setwd("C:\Users\natur\Desktop\Proyectos de Estadística")

# 1. Cargar datos necesarios ==================================

load("datos0.RData")
load("datos4.RData")

x0 <- datos0$x #X de datos0
y0 <- datos0$y #Y de datos0

x4 <- datos4$x #X de datos4
y4 <- datos4$y #Y de datos4

n <- length(datos0$x)

# 2. Calculos Estadisticos -------------------------------------

  # Para datos0

    # Media Aritmetica
      meanx0 <- sum(x0)/n #Media segun formula
      meany0 <- sum(y0)/n #Media seguhn formula
      
      mean(x0) == meanx0 # Comprobacion igualdades

## [1] TRUE

      mean(y0) == meany0 # Comprobacion igualdades

## [1] TRUE

    # Desviacion estandar
      sdx0 <- sqrt((sum((x0-meanx0)^2))/(n-1))
      sdy0 <- sqrt((sum((y0-meany0)^2))/(n-1))     
      
      sd(x0) == sdx0

## [1] TRUE

      sd(y0) == sdy0

## [1] TRUE

    # Coeficiente de Correlacion
      cor0 <- (sum((x0-meanx0)*(y0-meany0))/((n-1)*sdx0*sdy0))
      
      
  # Para datos4
      
      # Media Aritmetica
      meanx4 <- sum(x4)/n #Media segun formula
      meany4 <- sum(y4)/n #Media seguhn formula
      
      mean(x4) == meanx4 # Comprobacion igualdades

## [1] FALSE

      mean(y4) == meany4 # Comprobacion igualdades

## [1] TRUE

      # Desviacion estandar
      sdx4 <- sqrt((sum((x4-meanx4)^2))/(n-1))
      sdy4 <- sqrt((sum((y4-meany4)^2))/(n-1))     
      
      sd(x4) == sdx4

## [1] TRUE

      sd(y4) == sdy4

## [1] FALSE

      # Coeficiente de Correlacion
      cor4 <- (sum((x4-meanx4)*(y4-meany4))/((n-1)*sdx4*sdy4))

# 3. Visualizacion de Datos -------------------------------------

scatterplot0 <- ggplot(datos0, aes(x = x0, y = y0)) +
        geom_point() +
        labs(
          title = "Scatterplot of x and y",
          x = "Variable X",
          y = "Variable Y"
        ) +
        theme_minimal() 
plot(scatterplot0)

# Los resultados del scatterplot muestran una grafica de dinosaurio
# la relacion de los puntos x e y son simplemente esteticos visuales
# y a priori no parecen tener ningun tipo de relacion con datos relacionados.


scatterplot4 <- ggplot(datos4, aes(x = x4, y = y4)) +
        geom_point() +
        labs(
          title = "Scatterplot of x and y",
          x = "Variable X",
          y = "Variable Y"
        ) +
        theme_minimal()
plot(scatterplot4)

# Los resultados del scatterplot 4 muestran una X visualmente. Una correclacion
# lineal inexistente y a plena vista una muestra de que no hay relacion entre x e y.


# Lecciones Aprendidas ===========================================

# Se aprende de esta leccion que la correlacion lineal que muestra 
# es el unico elemento de fiarse, hay que aprender a observar graficamente nuyestro datos
# para poder entenderlos.

# ==========================================================
#                     FIN
# ==========================================================