The Y = mX + Z correlation model

mu_y = m mu_x + mu_z with mu_x = mu_z = 0, sigma_y = sqrt(m^2 sigma_x^2 + sigma_z^2) and r = m sigma_x / sigma_y. The defaults are the book's worked spread, sigma_y = 13.

Usage

LinModel(m = 1, sigma_x = 7.5, sigma_z = 10.6)

Arguments

m

slope of the underlying relation.

sigma_x

spread of the signal, >= 0.

sigma_z

spread of the independent noise, >= 0.

Value

list(mu_y, sigma_y, r, mu_z, sigma_z).

References

Morin, D. J. (2016). Probability: For the Enthusiastic Beginner. Createspace. Eqs (6.3)-(6.6), (6.17), (6.76).

Examples

LinModel()$sigma_y
#> [1] 12.98499