Convert regression line coefficient and intercept of standardised variables back to the original scale

standardised_variables.R

# Standardisation formula
z <- function(x) (x - mean(x)) / sd(x)

#' Convert regression parameters obtained from standardised variables
#' back to the scale of the original data.
#'
#' For a regression y ~ x*, where x* denotes the standardised form of x:
#' Result:      y = m(x*) + c
#' Transformed: y = (m / sd(x))(x) + (c - (m*mean(x)/sd(x))
#'
#' For a regression y* ~ x*, where (x*, y*) are the standardised forms of (x, y):
#' Result:      y* = m(x*) + c
#' Transformed:  y = (m * sd(y) / sd(x))(x) + sd(y)(c - m * mean(x) / sd(x)) + mean(y)
#' 
#' @param m - the slope parameter of the regression
#' @param c - the intercept of the regression
#' @param x - values of x on the original scale. It is assumed that at least the
#'            predictors (x) were standardised. If responses (y) were also standardised,
#'            the original values must be passed through parameter `y`.
#' @param y - values of y on the original scale. If given (not NULL) it is assumed
#'            that both the responses (y) and predictors (x) were standardised
transform <- function(m, c, x, y = NULL) {
    slope <- m / sd(x)
    intercept <- c - m * mean(x) / sd(x)
    if (!is.null(y)) {
        slope <- slope * sd(y)
        intercept <- sd(y) * intercept + mean(y)
    }
    list(m = slope, c = intercept)
}