This can also mean that the lesser the value of the residual standard deviation, the nearer will be the considerable fit for all the groups of data.

Let us consider an example to learn how to calculate residual standard deviation for any linear relation:

**Example:**

Suppose we have two variables 'X' and 'Y' such that they are expected to be in a relation Y = 4X – 3. Then, find the residual standard deviation for this data, if the expected values are given as follows:

X |
Y = 4 X – 3 |
Expected value of Y |

1 | 1 | 2 |

0 | -3 | -2 |

2 | 5 | 4 |

4 | 13 | 12 |

3 | 9 | 11 |

5 | 17 | 16 |

**Solution:**

Here, it is clear that variable 'Y' is dependent and the variable 'X' is independent.

The value of Y varies with the value of 'X' according to the relation: Y = 4X - 3.

Number of observations we have is 6.

The residual standard deviation can be evaluated as follows:

RSD = $(\frac{(1 - 2)^2 + (- 3 + 2)^2 + (5 - 4)^2 + (13 - 12)^2 + (9 - 11)^2 + (17 - 16)^2}{6 - 2})^{\frac{1}{2}}$

RSD =$(\frac{(1)^2 + (1)^2 + (1)^2 + (1)^2 + (2)^2 + (1)^2}{4})^{\frac{1}{2}}$

RSD = $(\frac{1 + 1 + 1 + 1 + 4 + 1}{4})^{\frac{1}{2}}$

RSD = $\frac{9}{2}$ = 3