If var X > 0 so that X is not trivial, then, by proposition 0.0.1 p.18, we know
ID: 3023617 • Letter: I
Question
If var X > 0 so that X is not trivial, then, by proposition 0.0.1 p.18, we know that there are unique alpha and beta for which Y = alpha + beta X + Z omega, EZ = 0 = rho(X,Z) Suppose that we obtain data y epsilon R^n from Y with corresponding x epsilon R^n so that y= alpha1 + beta x + z Let p(y) = y op(y|1,x) denote the orthogonal projection onto the two-dimensional vector sub-space w =span_R(1,x). Prove that for n sufficiently large (1,x) is linearly independent and thus there will be unique alpha and beta so that y = alpha1 + beta x. Hence prove that both alpha rightarrow alpha and beta rightarrow beta as n rightarrow infinitive.Explanation / Answer
i) 1 is a constant and X is a variable this shows that covariance between 1 and X are zero.
Thus 1 and x is linearly independent