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Nathaniel E. Helwig

Multivariate Linear RegressionNathaniel E. HelwigAssistant Professor of Psychology and StatisticsUniversity of Minnesota (Twin Cities)Updated 16-Jan-2017 Nathaniel E. Helwig (U of Minnesota)Multivariate Linear RegressionUpdated 16-Jan-2017 : Slide 1 CopyrightCopyrightc 2017 by Nathaniel E. HelwigNathaniel E. Helwig (U of Minnesota)Multivariate Linear RegressionUpdated 16-Jan-2017 : Slide 2 Outline of Notes1) Multiple Linear RegressionModel form and assumptionsParameter estimationInference and prediction2) Multivariate Linear RegressionModel form and assumptionsParameter estimationInference and predictionNathaniel E. Helwig (U of Minnesota)Multivariate Linear RegressionUpdated 16-Jan-2017 : Slide 3 Multiple Linear RegressionMultiple Linear RegressionNathaniel E. Helwig (U of Minnesota)Multivariate Linear RegressionUpdated 16-Jan-2017 : Slide 4 Multiple Linear RegressionModel Form and AssumptionsMLR Model: Scalar FormThe multiple linear regression model has the formyi=b0+p j=1bjxij+eifori {1.}

Xn i=1 (yi y )2 = y0[In (1=n)J]y SSR = Xn i=1 (y^ i y )2 = y0[H (1=n)J]y SSE = Xn i=1 (yi ^yi) 2 = y0[In H]y Note: J is an n n matrix of ones Nathaniel E. Helwig (U of Minnesota) Multivariate Linear Regression Updated 16-Jan-2017 : Slide 16

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