linear model without intercept : wrong r-square value?

Question

R linear model function lm looks like have a bug.
with no intercept term.

I want to know this is really a bug or my mistake on something...

library(dplyr)

rm(list=ls())

m2 <- 
  lm(data=iris, Sepal.Length ~ Sepal.Width + Species - 1)

res2 <-
  iris %>%
  mutate(real = Sepal.Length) %>%
  mutate(pred = predict(m2, ., type='response')) %>%
  mutate(error = real - pred) %>%
  mutate(error.sq = error^2) %>%
  mutate(sse = sum(error.sq)) %>%
  mutate(sst = sum((real - mean(real))^2)) %>%
  mutate(r.sq = 1-sse/sst) %>%
  mutate(idx = 1:n())

m2 %>% .$coef
  Sepal.Width     Speciessetosa Speciesversicolor  Speciesvirginica 
    0.8035609         2.2513932         3.7101363         4.1982099 

m2 %>% summary %>% .$r.square
[1] 0.9946393

res2$r.sq %>% unique
[1] 0.7259066

without intercept linear model result shows different r-square value with manual calculation.

m1 <- 
  lm(data=iris, Sepal.Length ~ Sepal.Width + Species)

res1 <-
  iris %>%
  mutate(real = Sepal.Length) %>%
  mutate(pred = predict(m1, ., type='response')) %>%
  mutate(error = real - pred) %>%
  mutate(error.sq = error^2) %>%
  mutate(sse = sum(error.sq)) %>%
  mutate(sst = sum((real - mean(real))^2)) %>%
  mutate(r.sq = 1-sse/sst) %>%
  mutate(idx = 1:n())

m1 %>% .$coef
  (Intercept)       Sepal.Width Speciesversicolor  Speciesvirginica 
    2.2513932         0.8035609         1.4587431         1.9468166 

m1 %>% summary %>% .$r.square
[1] 0.7259066

res1$r.sq %>% unique
[1] 0.7259066

in contrast, with intercept linear model result looks ok

This is not wrong. Some call it the "R0 squared". Make a research on Cross Validated. — Stéphane Laurent, Feb 11 '20 at 07:44
Side note, you can keep all "mutations" inside one *mutate()*. — zx8754, Feb 11 '20 at 07:55
@zx8754 I use R-studio IDE shortcut command + option + down.arrow :D then easier to modify code with multiple mutate line then one — Curycu, Feb 11 '20 at 07:59
If the data is small and efficiency is not a concern, then yeah go with multiple *mutate* calls. — zx8754, Feb 11 '20 at 08:09

Haitao Du · Accepted Answer · 2020-02-11T09:36:10.143

2

R is correct. Without intercept, SST is calculated differently.

Here is the reason and manual calculation:

Why I am getting different $R^2$ from R LM and manual calculation?

edited Feb 11 '20 at 09:36

answered Feb 11 '20 at 08:17

Haitao Du

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linear model without intercept : wrong r-square value?

1 Answers1