1
$\begingroup$

Can a linear regression model with a single input variable x with x not significant but the model has a high R2?

Can this exist? If yes, what are the reasons?

$\endgroup$
2
$\begingroup$

This can happen, but only with very small amounts of data. An example (in R) with three data points:

x <- c(0,1,2)
y <- c(-0.1,0.7,1.2)
summary(lm(y ~ x))

Coefficients:
            Estimate Std. Error t value Pr(>|t|)  
(Intercept)  -0.0500     0.1118  -0.447   0.7323  
x             0.6500     0.0866   7.506   0.0843 .
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.1225 on 1 degrees of freedom
Multiple R-squared:  0.9826,    Adjusted R-squared:  0.9651 
F-statistic: 56.33 on 1 and 1 DF,  p-value: 0.08432

Notice the R-squared is very high, but the x parameter is not 95%-significant.

With lots of data, one cannot have a very high R-squared parameter without the corresponding parameter being significant.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.