Uncorrelated Data = $\displaystyle {\left[\begin{array}{ccc} -{0.39181}&-{1.7147}&-{0.37696}\\-{0.45099}&{0.85022}&{0.91689}\\{0.39831}&{0.81933}&-{0.29081}\\{2.09243}&{0.15376}&{1.67875}\\{0.05969}&{1.34756}&-{0.64612}\\{2.15965}&-{0.53103}&{0.48539}\\-{0.38613}&-{0.48878}&{0.81583}\\-{3.12139}&-{2.66934}&-{1.7007}\\{1.16752}&{2.08137}&{0.75542}\\{0.07225}&-{0.85347}&-{0.54435}\\{0.91308}&-{0.53363}&-{0.30653}\\{1.39042}&-{1.72905}&{2.15451}\\{1.4706}&{0.59536}&{1.56407}\\-{0.90853}&{2.02566}&{0.01705}\\{1.60543}&-{0.22266}&{0.97049}\\-{2.25713}&-{0.61918}&{0.44185}\\{0.19908}&-{2.45726}&{0.37831}\\{0.84592}&-{0.16696}&{0.38829}\\-{0.44572}&-{1.01985}&-{0.72541}\\{0.73654}&-{0.30443}&-{1.36517}\end{array}\right]}$     &     Correlated Data = $\displaystyle {\left[\begin{array}{ccc} -{0.39181}&-{1.7270622622863}&-{0.94714646193245}\\-{0.45099}&{0.83434855153936}&{1.288157736729}\\{0.39831}&{0.83243449918462}&-{0.0098225294701659}\\{2.09243}&{0.22501471544869}&{0.80577717946789}\\{0.05969}&{1.3488116722309}&{0.033669745051615}\\{2.15965}&-{0.45708516166581}&-{0.51839366281348}\\-{0.38613}&-{0.5016614038475}&{0.59194735110853}\\-{3.12139}&-{2.77421576468}&-{1.6047053190129}\\{1.16752}&{2.1199679028854}&{1.1779957768619}\\{0.07225}&-{0.85051029410852}&-{0.85604456967624}\\{0.91308}&-{0.5021870733175}&-{0.78461086297995}\\{1.39042}&-{1.6806364715835}&{0.59867942297767}\\{1.4706}&{0.64515584648829}&{1.1034306746921}\\-{0.90853}&{1.993504673853}&{1.1986799144588}\\{1.60543}&-{0.16779131355626}&{0.20172378657781}\\-{2.25713}&-{0.69577975843526}&{0.81958162540571}\\{0.19908}&-{2.4490433402735}&-{0.83058051250036}\\{0.84592}&-{0.13802018023733}&-{0.01879620303521}\\-{0.44572}&-{1.0344544127977}&-{0.91550243016564}\\{0.73654}&-{0.27913970178451}&-{1.514602162495}\end{array}\right]}$
$\displaystyle {U}={\left[\begin{array}{ccc} {1}&{0}&{0}\\{0.034096298977261}&{0.99941855215723}&{0}\\-{0.32}&{0.44116733146591}&{0.83843388865626}\end{array}\right]}$
$\displaystyle {R}^{{2}}={0.29702861435275}$     &     $\displaystyle {r}_{{{y}{1}}}=-{0.32}$     &     $\displaystyle {r}_{{{y}{2}}}={0.43}$     &     $\displaystyle {r}_{{{12}}}={0.034096298977261}$
$\displaystyle {F}={3.5915305708692}$     &     $\displaystyle {F}^{\cdot}={0.42253300833755}$     &     $\displaystyle {R}^{{2}}={0.29702861435275}$ 54 55
$\displaystyle \alpha={0.05}$     &     $\displaystyle {m}={2}$     &     $\displaystyle {n}={20}$