Bivariate Statistics Functions

Functions to compute bivariate statistics including covariance and the Pearson correlation coefficient.

Covariance: The population covariance is

$$\operatorname{cov}(x, y) = \frac{1}{n}\sum_{i=1}^n (x_i - \bar{x})(y_i - \bar{y})$$

Correlation Coefficient: The Pearson correlation coefficient is

$$\rho_{x,y} = \frac{\operatorname{cov}(x, y)}{\sigma_x \sigma_y}$$

Usage

covariance(x, y)

means_and_covariance(x, y)

correlation_coefficient(x, y)

Arguments

x

A numeric vector.

y

A numeric vector.

Value

A numeric value (or tuple for means_and_covariance) with the computed statistic.

See also

Boost Documentation for more details on the mathematical background.

Examples

# Covariance
covariance(c(1, 2, 3), c(4, 5, 6))
#> [1] 0.6666667
# Means and Covariance
means_and_covariance(c(1, 2, 3), c(4, 5, 6))
#> [1] 2.0000000 5.0000000 0.6666667
# Correlation Coefficient
correlation_coefficient(c(1, 2, 3), c(4, 5, 6))
#> [1] 1