Given a dataset Y=(-11,7,-10,0,-3,7,-1,-1) X X2 - (3,9,4,3,7,9,4,2) (9,3,9,4,5,3,5,4) Consider the multiple regression model Y =...

 

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Given a dataset Y=(-11,7,-10,0,-3,7,-1,-1) X X2 - (3,9,4,3,7,9,4,2) (9,3,9,4,5,3,5,4) Consider the multiple regression model Y = Bo+B1X1+ B2X2+e. i) Draw a 3D-scatter plot and a scatter plot matrix. ii) Find X, X'X. iii) Find the eigenvalues and eigenvectors of X'X. iv) Find (X'X)-1, (X'X)-1/2 and (X'X)1/2 v) Find Z = X(X'X)-1/2, Verify that Z is an orthonormal matrix. vi) Find the regression coefficients. vii) Find R. viii) Find the residuals e. ix) Find the fitted values . x) Find SST, SSR and SSE. xi) Find the partial R of X1 given X2. xii) Find the partial R of X2 given X1. Given a dataset Y=(-11,7,-10,0,-3,7,-1,-1) X X2 - (3,9,4,3,7,9,4,2) (9,3,9,4,5,3,5,4) Consider the multiple regression model Y = Bo+B1X1+ B2X2+e. i) Draw a 3D-scatter plot and a scatter plot matrix. ii) Find X, X'X. iii) Find the eigenvalues and eigenvectors of X'X. iv) Find (X'X)-1, (X'X)-1/2 and (X'X)1/2 v) Find Z = X(X'X)-1/2, Verify that Z is an orthonormal matrix. vi) Find the regression coefficients. vii) Find R. viii) Find the residuals e. ix) Find the fitted values . x) Find SST, SSR and SSE. xi) Find the partial R of X1 given X2. xii) Find the partial R of X2 given X1.