1 a)Describe features of the covariance correlation matrix b) How is a log likelihood ratio...

1 a)Describe features of the covariance correlation matrix

b) How is a log likelihood ratio test is constructed to assess the adequacy of a given model

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Expert Solution

a covariance matrix (also known as dispersionmatrix or variance–covariance matrix) is a matrix whose element in the i, j position is the covariance between the i-th and j-th elements of a random vector. A random vector is a random variable with multiple dimensions.
A measure used to represent how strongly two random variables are related known as correlation. Covariance is nothing but a measure of correlation. On the contrary, correlation refers to the scaled form of covariance. Correlation is dimensionless, i.e. it is a unit-free measure of the relationship betweenvariables.
A correlation matrix is a table showing correlationcoefficients between sets of variables. Each random variable (X_i) in the table is correlated with each of the other values in the table (X_j).

Likelihood Ratio Tests are a powerful, very general method of testing model when unknown parameters are replaced by their maximum likelihood estimates.

For construction refer to:- https://ocw.mit.edu/courses/mathematics/18-443-statistics-for-applications-spring-2015/lecture-notes/MIT18_443S15_LEC10.pdf

orchestra answered 1 year ago

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