Mean Squared Error

Mean Squared Error (MSE) measures the average squared difference between estimated values and the actual value. MSE is:

always a zero or positive value
better for values closer to zero

In the diagram below, a Linear Regression line is used to predict Y values based on various X values.

The Mean Squared Error calculates a total error based on the difference between observed and predicted Y values as shown in the equation below:

$\\M=\frac{1}{n}\sum_{i=1}^{n}\left( Y_{i}-\hat{Y}_{i}\right )^{2} \\\\\mathrm{\textup{where:}} \\\\M\,\,\,\mathrm{\textup{mean squared error}} \\n\,\,\,\,\,\,\mathrm{\textup{number of values}} \\Y\,\,\,\,\,\mathrm{\textup{vector of observed values}} \\\hat{Y}\,\,\,\,\,\mathrm{\textup{vector of predicted values}}$

References

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