Assuming linear model y N(X3,021), compute 1) regression coefficients ß = (X'X)-1X'y, 2) standard errors of ß = ôèdiag((

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Assuming Linear Model Y N X3 021 Compute 1 Regression Coefficients Ss X X 1x Y 2 Standard Errors Of Ss Oediag 1 (68.85 KiB) Viewed 17 times

Assuming linear model y N(X3,021), compute 1) regression coefficients ß = (X'X)-1X'y, 2) standard errors of ß = ôèdiag((X'X)–?), and 3) variance estimate ô2 = (y – XB)'(y - XB)/(n - p) using following methods: GE/LU decomposition, Cholesky decomposition, and QR decompo- sition, and compare the computation speed for each method. Please compute them directly us- ing numerical linear algebra functions; you can use the "black-box" function (e.g., Im() in R or sklearn.linear_model.LinearRegression in python) only to check your results. (Hint: chol2inv() func- tion in R computes the inverse of a matrix from its Cholesky factor. In python, you may try cho solve()) a