Write Down, in General, the Variance-Covariance Matrix for the Multiple $\sigma _ { \mathrm { u } } ^ { 2 }$

question 17

Essay

Write down, in general, the variance-covariance matrix for the multiple regression error term U. Using the assumptions cov(ui,uj|XiXj)= 0 and var(ui|Xi)= $\sigma _ { \mathrm { u } } ^ { 2 }$ Show that the variance-covariance matrix can be written as $\sigma _ { \mathrm { u } } ^ { 2 }$ I_n.

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Definitions:

Coefficient Of Determination

A measure, usually represented as R^2, that shows the proportion of the variance in the dependent variable that is predictable from the independent variable(s).

Variance

A measurement of the spread between numbers in a data set, signaling how far each number in the set is from the mean.

MSE

Mean Squared Error, a measure of the average squared differences between the estimated values and the actual value, indicating the quality of an estimator.

SSE

Sum of Squares due to Error, a measure used in statistical analysis to quantify the discrepancy between the observed and predicted data values.