MSE Calculator
Online calculator for the Statistics MSE of data series
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.
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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
\(\displaystyle x= 1+2+3+4+5 \)
\(\displaystyle y= 3+5+6+7+7 \)
\(\displaystyle MSE=\frac{(3-1)^2+(5-2)^2+(6-3)^2+(7-4)^2+(7-5)^2}{5}\)
\(\displaystyle \;\;\;\;\;\;\;\;\;\;=\frac{2^2+3^2+3^2+3^2+2^2}{5}\)
\(\displaystyle \;\;\;\;\;\;\;\;\;\;=\frac{4+9+9+9+4}{5} = \frac{35}{5}=7\)
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