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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).

Forumula for SSR (or RSS)

$y_i$ 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,

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

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:

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

$RSS = 3$

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statistics

data science

regression

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