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How to Calculate Residual Standard Deviation?

TopResidual Standard Deviation value is calculated to show how the linear plots are consistent throughout groups. For instance, suppose you have a group of data and you wish to find out whether a single linear plot is considerable for all the groups or we need to consider distinct fits for each of the group of data. Therefore, we can define the residual standard deviation as goodness-of-fit amount.

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