Show that the hat matrix is idempotent (i.e. by showing that ?2 = ?) and symmetric.

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Expert Solution

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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orchestra answered 1 year ago

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