Statistical degrees of freedom - What are they REALLY?

When degrees of freedom are introduced in intro stats classes, students often get confused. However, there is a quite easy way to understand them using the geometry behind statistics. This video builds upon an earlier video about variance estimation, but it is not necessary to have watched it:

   • Variance: Why n-1? Intuitive explanat...  



Timeline:
0:55 Usual explanation
3:24 Introduction to geometry of statistics
6:02 Data partition into mean and residual vectors
8:48 Degrees of freedom as possible vector movement
13:30 Differences due to sample mean vs. population mean
15:37 Residuals vector and variance
17:38 Why underestimation can be compensated by "sample size reduction"