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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Squared CorrelationOverview● Recall that the Squared Multiple Correlation Coefficient, orR 2 , is found from:<strong>Matrix</strong> AlgebraAlgebraR 2 =SS reg∑ Ni=1 (Y i − Ȳ ) 2More 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● This is also obtainable by matrix calculations:R 2 = b′ X ′ Y − 1 N (Y′ 1) 2Y ′ Y − 1 N (Y′ 1) 2Wrapping Lecture 17 UpPsychology 790