Estimating Principal Components
{"Image DocumentName": "Estimating Principal Components", "Image ImageDescription": "The first PC is the linear combination with maximum variance, PC 1 = F 1 = a 11 X 1 + a 12 X 2 +\u2026+ a 1p X p. That is, it finds \ud835\udc4e 11 , \ud835\udc4e 12 ,\u2026, \ud835\udc4e 1\ud835\udc5d = \ud835\udc82 \ud835\udfcf to maximize. Var(F1) = \ud835\udc49\ud835\udc4e\ud835\udc5f \ud835\udc4e 11 \ud835\udc4b 1 +\u2026+ \ud835\udc4e 1\ud835\udc5d \ud835\udc4b \ud835\udc5d =\ud835\udc49\ud835\udc4e\ud835\udc5f \ud835\udc82 \ud835\udfcf \ud835\udc7b \ud835\udc4b. constrained such that \ud835\udc57=1 \ud835\udc5d \ud835\udc4e 1\ud835\udc57 2 =1. First PC: linear combination \ud835\udc82 \ud835\udfcf \ud835\udc7b \ud835\udc4b that maximizes Var(a1TX) such that \ud835\udc57=1 \ud835\udc5d \ud835\udc4e 1\ud835\udc57 2 =1. Second PC: PC 2 = F 2 = a 21 X 1 + a 22 X 2 +\u2026+ a 2p X p Linear combination that maximizes Var(a2TX) such that \ud835\udc57=1 \ud835\udc5d \ud835\udc4e 2\ud835\udc57 2 =1 AND Corr(F1,F2)=0. And so on\u2026..", "Image XResolution": "37", "Image YResolution": "37", "Image ResolutionUnit": "Pixels/Centimeter", "Image Software": "SlidePlayer", "Image YCbCrPositioning": "Centered"}