I am very new to statistics and am currently using the Introduction to Statistical Learning with R book.
I am having some issues understanding the difference between RSS and RSE. From my understanding, RSS is the sum of all the residual errors, that is to say it is a measure of how "off" our model is from the true relation. However, according to the book, RSE is the average amount that our response will deviate from the true regression line.
What is the difference exactly or what am I misunderstanding? I have tried to reading online but most of the links I have found simply explain that you use the RSS to calculate the RSE.
Any help is appreciated, Thanks!
Best Answer
Residual sum of squares (RSS) is defined as $ \sum_{i=1}^{n} e_i^2 $, where $e_i$ is the residual. Residual Standard Error (RSE) is derived from RSS, and is defined as $\sqrt{RSS/(n-2)}$ where $n$ is the sample size. RSS shows the aggregate squared deviation around the fitted line, and since it is squared it is not on the same scale as your dependent variable. RSE, on the other hand is on the same scale as your dependent variable. It serves as an estimate of the standard deviation of the dependent variable.