Consider the simple linear regression model Y = B+ Bx, +, (i = 1,2......). The model...

        

 

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Consider the simple linear regression model Y = B+ Bx, +, (i = 1,2......). The model may be written in matrix notation as Y = X+. (a) Explain the terms Y, X, B and for the model. (b) State the second-order distributional assumptions in matrix notation and then the normal theory assumptions using matrix notations. (c) Show that the error sum of squares 17 may be written as (Y-XB)'(Y-XB) (d) The least squares estimate B of minimize (Y-XB)'(Y-XB) with respect to B. State the normal equations (least squares equations) in matrix form. (e) Suppose the data obtained are as in the table below. X Y -2 0.5 -1 0 2 1.0 1.5 1.5 2.5 For this data write the elements of 5 M6 xx, XY, (XX)-1, (X'X)-x'Y, H = X(XX)-1X, HH, tr (H), HY, (I-H)Y Consider the simple linear regression model Y = B+ Bx, +, (i = 1,2......). The model may be written in matrix notation as Y = X+. (a) Explain the terms Y, X, B and for the model. (b) State the second-order distributional assumptions in matrix notation and then the normal theory assumptions using matrix notations. (c) Show that the error sum of squares 17 may be written as (Y-XB)'(Y-XB) (d) The least squares estimate B of minimize (Y-XB)'(Y-XB) with respect to B. State the normal equations (least squares equations) in matrix form. (e) Suppose the data obtained are as in the table below. X Y -2 0.5 -1 0 2 1.0 1.5 1.5 2.5 For this data write the elements of 5 M6 xx, XY, (XX)-1, (X'X)-x'Y, H = X(XX)-1X, HH, tr (H), HY, (I-H)Y