Exercise 3.8.5 (Cosine and sample correlation) Given two samples of observa tions Y = (y1, ,yn)...
Please give the detailed explanation, Thanks!! Denote the sample correlation between x1,...xn and y1,...yn as rx,y. Let wi=a+bi and let zi=c+dyi for i=1,...,n where b>0 and d>0. What is the relationship between rx,y and rw,z?
The (population) correlation coefficient, called p, is discussed in Section 4.5.2 of your text. Given two random variables X and Y with some joint distribution and means ux and uy, p= Corr(X,Y) = Cov(X, Y), where σχσY oſ = Var(x), of = Var(y) and Cov(X,Y) = E[(X - MX)(Y – My)] Given data, we can estimate p. Suppose that (X1,Y1), ..., (Xn, Yn) are independent and iden- tically distributed (i.i.d.) pairs of realizations of the random variables (X, Y). How...