# Is there p-value associated with residual?

I am performing a simple linear regression where y = income and x = education. I was just wondering if there exists p-value associated with the residual e in linear regression model to test its statistical significance. How does one obtain the p-value?

Thank you very much.

• Why do you think you want such a $p$-value? Commented Jul 19, 2018 at 19:28
• I want such a p-value because I want to find some portion of income that's not explained by education. Commented Jul 19, 2018 at 19:29
• Interesting. I suggest thinking about what assumptions must be in place in order for any p-value to be calculated...and then whether such assumptions could be made to apply to your situation. Commented Jul 19, 2018 at 19:31
• In that case you do not want those $p$-values. Instead you are looking for $R^2$: this is the proportion of the variance in income explained by education, so $1-R^2$ is the proportion of the varinace in income not explained by education. Commented Jul 19, 2018 at 19:31
• (Note that in linear regression, the mean of residuals always takes the same value.) If you want to demonstrate that certain residuals exceed the mean residual by >abs(1.96 standard deviations), that should be easy to do. Given N observations, you have N opportunities for that to occur, and in a large data set you'll routinely have residuals out at 3 and 3.5 standard deviations. It's hard to see how these would yield a meaningful p-value tailored to any question. OTOH, you may find it profitable to look into influential points for what they do signify. Commented Jul 19, 2018 at 19:52