cov cor r-squared in R

covariance_correlation.R

## create example data
x <- 1:20
y <- 35 + 5.5*x

## add some random noise to y
set.seed(99)
y <- y + rnorm(n = 20, mean = 2, sd = 5)

## create a data frame of xy
df <- data.frame(distance = x, fare = y)
summary(df)

## create a scatter plot
plot(x, y, pch=16, type="b", 
     main = "Taxi Fare Prediction", 
     xlab = "Distance (km)", ylab = "Fare (THB)")

abline(coef(lm(fare ~ distance, data = df)), col = "red", lty = "dashed")

## export csv file
write.csv(df, "taxi.csv", row.names = FALSE)

## covariance
cov(x,y)
sum((x - mean(x)) * (y-mean(y))) * 1/(length(x)-1)

## correlation
cor(x,y)
cov(x,y) / (sd(x) * sd(y))

## r-squared
cor(x,y) ** 2
summary(lm(y ~ x, data = df))$r.squared