Covarianza y Correlación

rm(list=ls()) #Limpiar entorno de trabajo

set.seed(1999)

x <- rnorm(1000, 0, 1)
y <- rnorm(1000, 0,1)

plot(x,y, xlim = c(-4,4), ylim = c(-4,4))
abline(v = mean(y), col="red", lwd=3, lty=2)
abline(h = mean(x), col="red", lwd=3, lty=2)
text(3, 3, "Cuadrante 1")
text(-3, 3, "Cuadrante 2")
text(3, -3, "Cuadrante 4")
text(-3, -3, "Cuadrante 3")

x <- rnorm(1000, 0, 1)
mu <- rnorm(1000, 2,1)
y <- x+mu

plot(x,y, main= "Asociación lineal positiva", xlab = "Eje x", ylab = "Eje y")

cov(x,y)

## [1] 0.9896691

cor(x,y)

## [1] 0.7117343

x <- rnorm(1000, 0, 1)
mu <- rnorm(1000, 2,1)
y <- -1*x+mu

plot(x,y, main= "Asociación lineal negativa", xlab = "Eje x", ylab = "Eje y")

cov(x,y)

## [1] -0.9992439

cor(x,y)

## [1] -0.7090518

x <- rnorm(1000, 0, 1)
y <- rnorm(1000, 2,1)

plot(x,y, main= "Ausencia de asociación", xlab = "Eje x", ylab = "Eje y")

cov(x,y)

## [1] 0.0210465

cor(x,y)

## [1] 0.02170317

x <- rnorm(1000, 0, 1)
mu <- rnorm(1000, 2,1)
y <- x^2+mu

plot(x,y, main= "Asociación no lineal", xlab = "Eje x", ylab = "Eje y")

cov(x,y)

## [1] 0.05079409

cor(x,y)

## [1] 0.02970539