In: Statistics and Probability
Show that the hat matrix is idempotent (i.e. by showing that ?2 = ?) and symmetric.
In linear regression, the formula for the hat matrix is given
by:
where is the matrix of independent variables; and
is the transpose of the matrix .
Now, consider:
Thus, the hat matrix is idempotent.
Now, we show that the hat matrix is symmetric, consider:
Thus, the hat matrix is symmetric.
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