Forcing 0 Intercept Inflates R-squared In R

John Mount has an informative post on how you can trick yourself when running linear regression models in R and forcing the y intercept to be 0:

So far so good. Let’s now remove the “intercept term” by adding the “0+” from the fitting command.

m2 <- lm(y~0+x, data=d)
t(broom::glance(m2))

##                        [,1]
## r.squared      7.524811e-01
## adj.r.squared  7.474297e-01
## sigma          3.028515e-01
## statistic      1.489647e+02
## p.value        1.935559e-30
## df             2.000000e+00
## logLik        -2.143244e+01
## AIC            4.886488e+01
## BIC            5.668039e+01
## deviance       8.988464e+00
## df.residual    9.800000e+01

d$pred2 <- predict(m2, newdata = d)

Uh oh. That appeared to vastly improve the reported R-squared and the significance (“p.value“)!

Read on to learn why this happens and how you can prevent this from tricking you in the future.