Recover the variance from MSE and bias

Question

A pricing model's estimator is known to be biased by 5 units, and its mean squared error is 50.

Mean squared error splits as $\text{MSE} = \text{Variance} + \text{Bias}^2$ .

How much of that error is variance (scatter)?

Accepted Answer

The idea. Total squared error is variance plus squared bias. If you already know the bias, subtract its square to isolate the scatter. Solve. 	ext{Variance} = 	ext{MSE} - 	ext{Bias}^2 = 50 - 5^2 = 50 - 25 = 25. So exactly half of this model's total error, 25 out of 50, is systematic (from the bias), and the other half is random scatter. That split matters for how you fix the model. Bias is a structural problem: it does not shrink by collecting more data, you have to correct the model itself. Variance, by contrast, is a sample-size problem: more or cleaner data pulls it down. Knowing which …

Recover the variance from MSE and bias

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