010+Correlation

010 Correlation

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: = E [(Z − E (Z ))(X − E (X ))] V ar(Z ) · V ar(X ) , Since E (X ) = 0 we have E (Z ) = E (XY ) = E (X ) · E (Y ) = 0, and in view of E (Y ) = 0 E [(Z − E (Z ))(X − E (X ))] = E (ZX ) = E (X 2 Y = E (X 2 ) · E (Y ) = 0. Thus, ρ = 0, but Z and X are dependent. 4 A. Zhensykbaev Correlation Pearson's empirical or sample correlation coecient. Let us given a sample of n pairs (xi , yi ), which are independent and identically distributed with the probability density function f (x, y ). The estimator of the correlation coecient ρ (the theoretical moment of f (x, y )) is the sample correlation coecient (or empirical moment) ρ= ˆ SSxy . S Sxx SSyy Test of hypothesis about a correlation coecient. Let random vectors (xi , yi ) are normally distributed. Assume that the null hypothesis is H0 = {ρ = 0}, alternative hypothesis is Ha = {ρ = 0}. Test statistic is ρ2 . ˆ Rejection region is RR = ρ2 ≥ ˆ 1 1 + (n − 2)/t2 2 α/ , where t2 2 is dened from the Table VI (McClave and Benson) for the α/ degree of...
View Full Document

This note was uploaded on 02/11/2014 for the course MATH 1390 taught by Professor Christopherstocker during the Spring '13 term at Marquette.

Ask a homework question - tutors are online