Question: (Multivariate linear regression) Consider the multiple linear regression model discussed in Lecture 23: Y = XB+E where Y ER, X E Rnx(k+1), B e Rk+1

(Multivariate linear regression) Consider the

(Multivariate linear regression) Consider the multiple linear regression model discussed in Lecture 23: Y = XB+E where Y ER", X E Rnx(k+1), B e Rk+1 and R". Suppose that we are given a new vector of covariates (i.e., independent variables) 20 = (1, 201, . . . , 20%) eRk+1. Determine the two-sided 1-a confidence intervals for the following quantities: (a) (2 pts) coefficient Bi-1 for i = 1, ..., k +1; (b) (2 pts) mean response xJB; (c) (2 pts) future response Yo = x 3 + 0 where so ~ N(0,0%). (Multivariate linear regression) Consider the multiple linear regression model discussed in Lecture 23: Y = XB+E where Y ER", X E Rnx(k+1), B e Rk+1 and R". Suppose that we are given a new vector of covariates (i.e., independent variables) 20 = (1, 201, . . . , 20%) eRk+1. Determine the two-sided 1-a confidence intervals for the following quantities: (a) (2 pts) coefficient Bi-1 for i = 1, ..., k +1; (b) (2 pts) mean response xJB; (c) (2 pts) future response Yo = x 3 + 0 where so ~ N(0,0%)

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