Function to Calculate R2 (R-Squared) in R

Question

I have a dataframe with observed and modelled data, and I would like to calculate the R2 value. I expected there to be a function I could call for this, but can't locate one. I know I can write my own and apply it, but am I missing something obvious? I want something like

obs <- 1:5
mod <- c(0.8,2.4,2,3,4.8)
df <- data.frame(obs, mod)

R2 <- rsq(df)
# 0.85

Accepted Answer

You need a little statistical knowledge to see this. R squared between two vectors is just the square of their correlation. So you can define you function as:

rsq <- function (x, y) cor(x, y) ^ 2

Sandipan's answer will return you exactly the same result (see the following proof), but as it stands it appears more readable (due to the evident $r.squared).

Must Read

Let's do the statistics

Basically we fit a linear regression of y over x, and compute the ratio of regression sum of squares to total sum of squares.

lemma 1: a regression y ~ x is equivalent to y - mean(y) ~ x - mean(x)

lemma 2: beta = cov(x, y) / var(x)

lemma 3: R.square = cor(x, y) ^ 2

Function to Calculate R2 (R-Squared) in R

8 Answers

Must Read

Let's do the statistics

Sophia Al-Mansoor