standardized-regression.R

library(magrittr)
# as pearson's correlation
cor <- anscombe %$% cor(y1, x1)
cor

## [1] 0.8164205

# as a linear model
fit <- anscombe %$% lm(y1 ~ x1)
fit

## 
## Call:
## lm(formula = y1 ~ x1)
## 
## Coefficients:
## (Intercept)           x1  
##      3.0001       0.5001

# as a linear model with standardized parameters
fit.scaled <- anscombe %$% lm(scale(y1) ~ scale(x1))
fit.scaled

## 
## Call:
## lm(formula = scale(y1) ~ scale(x1))
## 
## Coefficients:
## (Intercept)    scale(x1)  
##  -1.674e-17    8.164e-01

# is the standardized parameter for x1 equal to pearson's correlation?
coef(fit.scaled) == cor

## (Intercept)   scale(x1) 
##       FALSE        TRUE