**MSD** stands for **Mean Squared Deviation**, whereas **MSE** stands for **Mean Squared Error**. Quite often, you will find that they are synonymic. Both **MSD** and **MSE** can be used to compare estimated values and observed values in a model.

The key nuance is on the denominator of both MSD and MSE, as it will lead to biased and unbiased estimates. The following are the formulas of MSD and MSE.

## MSD Formulas

** p** stands for the numbers of parameters you estimate in the model (excluding intercept). If you do not estimate any parameter,

**will be zero.**

*p***Unbiased MSD**

\[ MSD =\frac{SSR}{n-p-1}=\frac{\sum_{i=1}^{n} (\hat{y_i}-y_i)^2 }{n-p-1}\]

**Biased MSD**

\[ MSD =\frac{SSR}{n}=\frac{\sum_{i=1}^{n} (\hat{y_i}-y_i)^2 }{n}\]

## MSE Formulas

**Unbiased MSE**

\[ MSE =\frac{SSR}{n-p-1}=\frac{\sum_{i=1}^{n} (\hat{y_i}-y_i)^2 }{n-p-1}\]

**Biased MSE**

\[ MSE =\frac{SSR}{n}=\frac{\sum_{i=1}^{n} (\hat{y_i}-y_i)^2 }{n}\]