The Gauss-Markov Theorem for Multiple Regression Proves That
A)M_X Is $\sigma _ { u } ^ { 2 }$

question 41

Multiple Choice

The Gauss-Markov theorem for multiple regression proves that

• A)M_X is an idempotent matrix.
• B)the OLS estimator is BLUE.
• C)the OLS residuals and predicted values are orthogonal.
• D)the variance-covariance matrix of the OLS estimator is \(\sigma _ { u } ^ { 2 }\) ( \(X ^ { \prime }\) X)^-1.

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Definitions:

Population Estimate

A value derived from a statistical model or sample that approximates the true characteristic of an entire population.

Positive Correlation

Positive correlation indicates that as one variable increases, the other variable tends to increase as well, demonstrating a direct relationship between the two variables.

Direct Correlation

A positive correlation where the values of both variables change in the same direction.

Two-tailed Test

A statistical hypothesis test in which the area of rejection is on both ends of the sampling distribution, allowing for the investigation of deviations in two opposite directions.