Lecture 14 Notes from Lena - Lecture 14 Notes Prepared by...

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Lecture 14 Notes Prepared by Dr. Lamb and Lena b 1 1 × SySX1 = ZYi β + 1ZX1i β + 2ZX2i + β nZXni Compare with β 1 and β 2 , if β 1S β 2 , it is meant β 1 is more important than β 2 = + + + yi a b1X1 b2X2 + bnXm a = y - b1X1 - b2X2 -…- bnXm Our goal is minimum Zyi - Zyi2 for Normal Regression Minimum yi - yi2 is good for Estimated Regression Correlation Coefficient r : r1y means Correlation between X1 and Y : r12 means independent X1 and X2 = r21 r1y= 1 β + 1 r12 β + 2 r13 β + 3 + r1m β m r2y=r21β1+ 1 β 2+r 23 β3+…+r 2 mβm r3y=r31β1+r32β2+ 1‧ β3+…+r 3 mβm r m y=r m 1β1+r m 2β2+r m3 β3+…+ 1‧ βm Factor Ryx size is m 1 Rxx m ‧m B m 1
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r1yr2yr3y = 1r12r13 r1m β1 r211r23 r2m β2 r31r321 r3m β3 r m y rm1 rm2 rm3 1 βm Ryx=Rxx B m m m 1 Inverse: Rxx-1 Ryx =Rxx-1 Rxx βm ‧1 m m × m 1 Rxx-1 Ryx = Im m βm ‧ ‧ ‧1 m m × m 1 solution factor =Rxx-1 Ryx
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Lecture 14 Notes from Lena - Lecture 14 Notes Prepared by...

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