For the OLS Estimator = ( X)-1

question 15

Essay

For the OLS estimator = ( X)-1 Y to exist,X'X must be invertible.This is the case when X has full rank.What is the rank of a matrix? What is the rank of the product of two matrices? Is it possible that X could have rank n? What would be the rank of X'X in the case n<(k+1)? Explain intuitively why the OLS estimator does not exist in that situation.

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Definitions:

Gamma Ray Emission

A type of radioactive decay where an unstable nucleus emits a gamma ray to become more stable.

Beta Particle Emission

A radioactive decay process where an unstable atomic nucleus emits a beta particle, which is a high-speed electron or positron, as part of the transformation to a stable state.

Alpha Particle Emission

A type of radioactive decay in which an atomic nucleus releases an alpha particle (2 protons and 2 neutrons) and transforms into an atom with a mass number 4 units less and atomic number 2 units less.

Beta Particle Emission

A radioactive decay process where a beta particle (electron or positron) is emitted from an atomic nucleus.