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Prove the properties discussed in class for the residual maker, M. We have to prove the properties using matrix notation
The matrix M has the following properties:
1. Symmetric, M = M′.
2. Idempotent, M = MM = M2.
When M is applied twice to any vector, it gives the same result as if it were applied only once. It leaves its image unchanged. Intuitively, the 'shadow of the shadow' is just the shadow itself.
3. MX = 0.
If X is regressed on X instead of y, residuals will be MX instead of My. This model will yield a perfect fit and residuals will be zero.
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Economics thesis undergrad 4th year paper to write. it should be about 22 pages in length, literature review, economic analysis and then data or cost benefit analysis.
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Write a definition for associative property of multiplication.
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