A **residual sum of squares (RSS)**, also known as the sum of squared residuals (SSR), is a statistical technique used to measure the amount of variance in a data set that is not explained by a regression model. It is the sum of the squared values of the residuals (deviations of predicted from actual empirical values of data).

$y_i$ is the $i^{th}$ actual value from data, $\hat{y_i}$ is the $i^{th}$ predicted value using regression, and $a$ and $b$ are constants.

In the graph shown, #key# residual: the difference between the predicted and actual value #key# is represented by the yellow lines. 

**SSR** is the total sum of the squares of these residuals (yellow lines).

# Example

Given the set of values:

| $X$ | $Y$ |
|:---:|:---:|
| 0   | 1   |
| 1   | 2   |
| 2   | 6   |
| 3   | 7   |
| 4   | 8   |

and with $a=1$ and $b=2$, we will get the following result:

>$RSS = (1-(1+(2*0)))^2+ (2-(1+(2*1)))^2 + (6-(1+(2*2)))^2 + (7-(1+(2*3)))^2 + (8-(1+(2*4)))^2$
<br/><br/>$RSS = 3$

The residual sum of squares

Measures unexplained variance in data by summing the squared residuals. RSS is 3 for given example.