Transcription of Multivariate Regression (Chapter 10)
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Multivariate Regression (Chapter 10)
Multivariate Regression ( chapter 10)This week we ll cover Multivariate Regression and maybe a bit of canonicalcorrelation. Today we ll mostly review univariate Multivariate Multivariate Regression , there are typically multiple dependentvariables as well as multiple independent or explanatory variables. Aspecial case of this is when the explanatory variables are categorical andthe dependent variables are continuous (particularly Multivariate normal),in which case we have MANOVA. For Multivariate Regression , we allow theexplanatory variables to be continuous. This approach generalizes multipleregression much as MANOVA generalizes in Regression , we think of theyvariables as random and thexvariables as fixed. For Multivariate Regression , we ll considerxvariables aseither fixed or random. We ll start with them being treated as 29, 20151 / 35 Multivariate regressionFirst, we ll review multiple (univariate) Regression with this model, we havey1= 0+p j=1 jx1j+ 1y2= 0+p j=1 jx2j+ 0+p j=1 jxnj+ nApril 29, 20152 / 35 Multivariate regressionThe standard assumptions for multiple Regression areE( i) = 0 Var( i) = 2cov( i, j) = 0 Equivalently, you can writeE( ) =0 Cov( ) = 2 IApril 29, 20153 / 35 Multivariate regressionUnder the assumption that thexs are fixed, we haveE(yi) = 0+p j=1 jx1jVar(yi) = 2 Cov(yi,yj) =Cov( i, j) = 0 Equivalently,E(y) =X Cov(y) = 2 IApril 29, 20154 / 35 Multivariate regressionThe Regression model using matrix notation isy=X + When I was an undergrad.
Multivariate Regression (Chapter 10) This week we’ll cover multivariate regression and maybe a bit of canonical correlation. Today we’ll mostly review univariate multivariate regression. With multivariate regression, there are typically multiple dependent variables as well as multiple independent or explanatory variables. A
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