Per wiki, the mean squared error (MSE) looks like:

$$ \operatorname {MSE} ={\frac {1}{m}}\sum _{i=1}^{m}(y_{i}-{\hat y_{i}})^{2} $$

The professor added a $1\over2$ in front of the formula and explained it a little bit. I am a little bit confused. How does putting a $1\over2$ in front of the squared error make the math easier?

  • $\begingroup$ Just a guess, but it may simplify mathematics involving the derivative. $\endgroup$
    – bradS
    Commented Jun 4, 2019 at 10:02

1 Answer 1


A major reason for using MSE is to optimize the parameters of a regression model. From calculus, you know how to find the minimum of a function by taking the derivative. That puts a "2" out in front, which is irritating to keep writing, so it is reasonable to put a "1/2" at the beginning so the derivative doesn't need a constant out front.

We get away with it because the minima of $f(x)$ and $\frac{f(x)}{2}$ are achieved at the same value(s) of $x$.


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