Question

What is explained variance?

Answer 1

We explain this problem by using the variance of the data. The variance is used to estimate the data more perfect to use among some data. We explain the explained variance using this variance among some different group data.
The explained variance used to measure the discrepancy between a model and the actual data.

Complete step-by-step solution:
We are asked to explain about the explained variance.
We know that the variance is used to estimate the more relevant data needed from a group of data so that if the variance is calculated for the different groups of variances then that variance is called as explained variance.
Let us assume an example of making an object. We know that we cannot directly make the object that we require. First we make a model of the required object and test it whether it can be made perfectly using the original material or not. But we know that making one model is not enough to get the perfect result for our product. So, we take some more models by improving the errors.
In this process we find the variance of each model based on its output and try to decrease that variance. When we make an actual product we take the model which is having deviation near to the overall variance to get better results.
This process of finding the variance of the best result out of the group of data is called as explained variance.
Here, we can see that finding this explained variance helps us to decide how much error is there in the actual product. Also we can understand how much we have improved from the first model so that we can try to improve it further more.
We know that explained variance is given as the proportion of variances between group differences and is denoted as ${{\eta }^{2}}$
Mathematically, the explained variance can be given as ratio of sum of squares between the required data to the sum of squares of total variances that is,
$\Rightarrow {{\eta }^{2}}=\dfrac{{{\left( SS \right)}_{\text{Between}}}}{{{\left( SS \right)}_{\text{Total}}}}$

Note: We need to note that this explained variance is calculated among the group of variances to obtain the better understanding of our work in a product.
We cannot tell the explained variance of a data of one group. It should be calculated among the groups of data having different variances due to some errors. Also we do not have any specific formula to calculate the explained variance. We just take the ratio of variance of required data to that to variance of total data to understand the position of that required data among the all groups of data.