MSE Calculator

This function calculates the mean squared error of a prediction. The Mean Squared Error (MSE) is a statistic that can be used to determine the accuracy of forecasts.

To perform the calculation, enter a series of predicted values X and a series of observation values Y. The individual numbers are separated by semicolons or spaces. To calculate click on the 'Calculate' button.

MSE Formula

\(\displaystyle d_{\mathbf{MSE}} : (x, y) \mapsto \frac{d_{\mathbf{SSD}}}{n} \) \(\displaystyle = \frac{\|x-y\|_2^2}{n} = \frac{1}{n}\sum_{i=1}^{n} (x_i-y_i)^2\)

Example

\(\displaystyle x= 1+2+3+4+5 \)

\(\displaystyle y= 3+5+6+7+7 \)

\(\displaystyle MSE=\frac{(3-1)^2+(5-2)^2+(6-3)^2+(7-4)^2+(7-5)^2}{5}\)

\(\displaystyle \;\;\;\;\;\;\;\;\;\;=\frac{2^2+3^2+3^2+3^2+2^2}{5}\)

\(\displaystyle \;\;\;\;\;\;\;\;\;\;=\frac{4+9+9+9+4}{5} = \frac{35}{5}=7\)