Multivariate Linear Regression

Multivariate Linear Regression

Nathaniel E. Helwig Assistant Professor of Psychology and Statistics

University of Minnesota (Twin Cities)

Updated 16-Jan-2017

Nathaniel E. Helwig (U of Minnesota)

Multivariate Linear Regression

Updated 16-Jan-2017 : Slide 1

Copyright

Copyright c 2017 by Nathaniel E. Helwig

Nathaniel E. Helwig (U of Minnesota)

Multivariate Linear Regression

Updated 16-Jan-2017 : Slide 2

Outline of Notes

1) Multiple Linear Regression Model form and assumptions Parameter estimation Inference and prediction

2) Multivariate Linear Regression Model form and assumptions Parameter estimation Inference and prediction

Nathaniel E. Helwig (U of Minnesota)

Multivariate Linear Regression

Updated 16-Jan-2017 : Slide 3

Multiple Linear Regression

Multiple Linear Regression

Nathaniel E. Helwig (U of Minnesota)

Multivariate Linear Regression

Updated 16-Jan-2017 : Slide 4

Multiple Linear Regression Model Form and Assumptions

MLR Model: Scalar Form

The multiple linear regression model has the form

p

yi = b0 + bj xij + ei

j =1

for i {1, . . . , n} where yi R is the real-valued response for the i-th observation b0 R is the regression intercept bj R is the j-th predictor's regression slope xij R is the j-th predictor for the i-th observation ei iid N(0, 2) is a Gaussian error term

Nathaniel E. Helwig (U of Minnesota)

Multivariate Linear Regression

Updated 16-Jan-2017 : Slide 5

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