Consider the general linear model y = XB+E (where as usual y is an n x...

 

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Consider the general linear model y = XB+E (where as usual y is an n x 1 vector of responses, X is an n xp design matrix and is a vector of zero mean errors uncorrelated with variance o). The regression sum of squares is defined as n SSreg = (i-). i=1 It can be proved that (you are not asked to prove this) that SSreg can also be expressed as the following quadratic form in y: SSreg=yH (-) Y, where H = X(XX)-X is an n x n hat matrix and I is an n x n matrix of ones, i.e., I = i) [2 marks] The ordinary simple linear regression model Yi = Bo+Bxi + Ei, i = 1,...,n, can be written in the form of the general linear model y = XB+ for suitable design matrix X. What is X? What is XTX? Consider the general linear model y = XB+E (where as usual y is an n x 1 vector of responses, X is an n xp design matrix and is a vector of zero mean errors uncorrelated with variance o). The regression sum of squares is defined as n SSreg = (i-). i=1 It can be proved that (you are not asked to prove this) that SSreg can also be expressed as the following quadratic form in y: SSreg=yH (-) Y, where H = X(XX)-X is an n x n hat matrix and I is an n x n matrix of ones, i.e., I = i) [2 marks] The ordinary simple linear regression model Yi = Bo+Bxi + Ei, i = 1,...,n, can be written in the form of the general linear model y = XB+ for suitable design matrix X. What is X? What is XTX?