Mean Square Error (MSE)
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In regression output...
MSE = SSE / DF (Error)
MSE = 96001 / 50
MSE = 1920.02
Okay... but actually explain it to me now.
Mean Square Error (MSE) shows us the average SSE (resembling variability left unexplained by the model) in our model, adjusting for the number of predictor variables used.
Scenario: Crammer Nation University wants to develop a regression equation to predict the "Number of Recruits" a given fraternity will receive this rush season given the "Parties Thrown" by the fraternity the previous year. They take a sample of 6 fraternities on campus, resulting in the following scatterplot with line of best fit.
SSE = (-1.2)2 + (+2.0)2 + (-2.6)2 + (+1.9)2 + (+2.3)2 + (-2.4)2
SSE = (1.44) + (4.00) + (6.76) + (3.61) + (5.29) + (5.76)
SSE = 26.86
Degrees of freedom for Error equals...
df = n - k - 1
...and since we have one predictor variable of "Parties", we can calculate the following df:
df = 6 - 1 - 1
df = 4
MSE = 26.86 / 4
MSE = 6.715
The closer MSE is to zero, the better our model fits our data.
That's because there's less SSE per degree of freedom not accounted for in our model!