Chapter 5: Matrix Approaches to Simple Linear Regression
Chapter 5: Matrix Approaches to Simple Linear Regression
Chapter 5: Matrix Approaches to Simple Linear Regression
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Sums of Squares and Cross Products● The SSCP matrix contains:Overview<strong>Matrix</strong> AlgebraAlgebraMore MatricesGeneral <strong>Linear</strong>ModelOther <strong>Matrix</strong>Products➤ More Matrices➤ The One➤ Means➤ Fitted Values➤ Residuals➤ SSCP➤ Covariance <strong>Matrix</strong>➤ CorrelationMatrices➤ Sums of Squares➤ SquaredCorrelation➤ b Variance✦ On the diagonal, Sums of Squares for each variable Z k :N∑(Z ik − ¯Z·k ) 2i=1✦ On the off-diagonal the Sum of Cross Products for eachpair of variables, Z k and Z k ′:N∑(Z ik − ¯Z·k )(Z ik ′ − ¯Z·k ′)i=1✦ The matrix expression for the SSCP matrix is:SSCP = (Z − ¯Z) ′ (Z − ¯Z)Wrapping Lecture 17 UpPsychology 790
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