[solved]-Consider The Linear Regression Model With Design Matrix X3 21 2 Rxp Assume That 2 And 1 For All J 1 P That Is The Columns Of X Are Standardized Centered And Normalized To Unit Em Pirical Var 99412

Consider the linear regression model with design matrix X3 [21 |а2 | ӕз | -..| ] € R*XP. Assume that 2 and = 1, for all j = 1,… ,p, that is, the columns of X are standardized (centered andnormalized to unit em- pirical variance). Here and elsewhere, 1n ER” is the vector of all-ones of length Note that the model does notinclude an intercept Assume that the columns of X are linearlyindependent. We project xp onto the span of the rest of thecolumns: {xi, x2,x3,… , xp-1} and the result turns out to be thefollowing vector: n. р — 0.5 а1. (a) Someone claims that xp – a, isorthogonal to both i and 2. Argue for against this claim or (b)Find R, the coefficient of determination (R2) resulting fromregressing on {ӕ1, 22, 2з, …, 2р-1}. (c) When fitting aregression using this design matrix, what is the variance infla-tion factor (VIF) of the coefficient corresponding to the pthregressor ар?

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