rq v - paos.colorado.edupaos.colorado.edu/~sala7581/14_pca.pdf · fig. 3. the pcs of 6-yr (hp) (lp)...

13
6DOO\ /DQJIRUG 6SDWLDO $QDO\VLV (2) 3&$ &RUUHODWLRQ

Upload: vodieu

Post on 26-Apr-2019

212 views

Category:

Documents


0 download

TRANSCRIPT

6DOO\�/DQJIRUG

6SDWLDO�$QDO\VLV���

(2)��3&

$��&

RUUHODWLRQ

+RZ

�FDQ�ZH�GHILQH�FOLP

DWH"�

)RU�D�JOREDO�GDWD�VHW�RU�PRGHO�RXWSXW���

���ODW�[�����ORQ�[����OHYHOV����IRU�MXVW�WKH�DWP

RVSKHUH�DW�RQH�WLPH�VWHS�

+RZ

�FDQ�ZH�VLP

SOLI\�WKH�DPRXQW�RI�GDWD"

+RZ

�FDQ�ZH�ILQG�UHODWLRQVKLSV�LQ�P

DSV"

,V�&RORUDGR�SUHFLSLWDWLRQ�UHODWHG�WR�JOREDO�SDWWHUQV"

'DWD�'

HFRPSRVLWLRQ

&RQVLGHU�D�VSHFWUDO�P

RGHO���4�[��\��W�� �Ȉ�T

P �W��<P �[��\�

0RUH�JHQHUDOO\���;

�[��\��W�� �Ȉ�D�W��(�[��\�

&KRRVH�EDVLV�VWDWHV�(�[��\��VXFK�WKDW�WKH�P

D[LPXP

�DP

RXQW�RI�YDULDELOLW\�DFFRXQWHG�IRU���WKHQ�GHWHUPLQH�

DPSOLWXGHV�D��

(�DUH�WKH�(PSLULFDO�2

UWKRJRQDO�)XQFWLRQV��(2)V��DQG�D�

DUH�WKH�3ULQFLSDO�&RP

SRQHQWV��3&V�

)RU�D�VFDWWHU�SORW�UHSUHVHQWDWLRQ�RI�WKH�GDWD�

��ZH�Z

DQW�WR�FKRRVH�YHFWRUV�DV�WKH�QHZ

�FRRUGLQDWH�V\VWHP

��ZKHUH�WKH�

PD[LP

XP�YDULDQFH�OLHV�

DORQJ�WKH�SULPDU\�D[LV��

7KHVH�DUH�WKH�HLJHQYHFWRUV�RI�WKH�FRUUHODWLRQ�PDWUL[���

$Y� �ȜY

ZKHUH�$

� �;7;

Y�DUH�WKH�HLJHQYHFWRUV��(2)V��DQG�Ȝ�WKH�HLJHQYDOXHV�RU�WKH�

FRUUHODWLRQ�PDWUL[�$

��RI�WKH�GDWD�;��

$�QRWH�RQ�SXWWLQJ�GDWD�LQWR�P

DWULFHV���

��GLPHQVLRQDO�GDWD�FDQ�EH�SXW�LQWR�D���GLP

HQVLRQDO�PDWUL[�

E\�OLVWLQJ�WKH�ORFDWLRQV�UDWKHU�WKDQ�[��\�FRRUGLQDWHV��

(LJHQYHFWRU�0HWKRG

;�LV�WKH�RULJLQDO�GDWD�Z

LWK�WKH�WLPH�P

HDQ�UHPRYHG��

&DOFXODWH�WKH�FRUUHODWLRQ�P

DWUL[���ZKHUH�$

� �;7;

6ROYH�IRU�Ȝ���GHW��$

���Ȝ,�� ��

6XEVWLWXWH�EDFN�WR�VROYH�IRU�HLJHQYHFWRUV���$Y� �ȜY

3URMHFW�HLJHQYHFWRU�RQWR�WKH�GDWD�WR�JHW�WKH�3&�WLP

H�VHULHV��

Y7;

� �D

6LQJOH�9DOXH�'

HFRPSRVLWLRQ�

(TXLYDOHQW�WR�HLJHQYHFWRU�PHWKRG���EXW�P

RUH�JHQHUDO�DQG�RIWHQ�XVHG�WR�REWDLQ�3&

�DQG�(2)�SDWWHUQ�LQ�RQH�VWHS��

$� �8

Ȉ97

ZKHUH�8

��9�DUH�RUWKRQRUP

DO��DQG�Ȉ�LV�GLDJRQDO�ZLWK�

ȈL�M � �į

L�M �ȖL�L ��7KH�HLJHQYDOXHV�RI�$

�DUH�ȖL�L ���WKH�FROXP

QV�RI�9�FRQWDLQ�WKH�HLJHQYHFWRUV�RI�$

��WKH�FROXPQV�RI�8

�FRQWDLQ�WKH�SULQFLSDO�FRP

SRQHQWV��

:H�Z

LOO�EH�XVLQJ�WKH�,'/�SDFNDJH�VYGF�

+RZ

�WR�UHDG�GDWD�LQ�,'/

1HW&

')�ILOHV�DUH�ELQDU\��DQG�XVH�³,'

´�FRGHV�WR�ORFDWH�WKH�GDWD��

2SHQ�WKH�ILOH��DQG�UHWXUQ�ILOH�,'QFLG� �QFGIBRSHQ�aVDOD�����(2)�GDWD�PRQ�PHDQ�QF�

*HW�WKH�,'

�RI�WKH�YDULDEOHYDULG� �QFGIBYDULG�QFLG��µ=µ�

5HDG�WKH�GDWDQFGIBJHWYDU�QFLG��YDULG��]J�

&ORVH�ILOHQFGIBFORVH�QFLG

+LQW��\RX�QHHG�WR�NQRZ

�WKH�YDULDEOH�QDPH�µ=¶�ILUVW��

*HW�WKLV�IURP

�QFGXPS�

1HW&

')�ILOHV

$�XQL[�SURJUDP

�QFGXPS�VKRZV�³FRQWHQWV´�RI�D�1

HW&')�ILOH��JLYH�

±K�RSWLRQ�WR�VHH�RQO\�KHDGHU���QFGXPS�°K�(2)�GDWD�PRQ�PHDQ�QF

QHWFGI�(2)�GDWD�PRQ�PHDQ�^GLPHQVLRQV�

WLPH� �81/,0,7('����������FXUUHQWO\�OHY� ����

'LPHQVLRQV�RI�GDWD

ODW� �����ORQ� �����

YDULDEOHV�IORDW�ORQ�ORQ���

&RRUGLQDWHV

ORQ�ORQJBQDPH� ��/RQJLWXGH���ORQ�XQLWV� ��GHJUHHVBHDVW���

IORDW�ODW�ODW���ODW�ORQJBQDPH� ��/DWLWXGH���ODW�XQLWV� ��GHJUHHVBQRUWK���

GRXEOH�WLPH�WLPH���WLPH�ORQJBQDPH� ��7LPH���

IORDW�]J�WLPH��OHY��ODW��ORQ���9DULDEOHV

]J�ORQJBQDPH� ��*HRSRWHQWLDO�KHLJKW���]J�XQLWV� ��P���

025(�9$5,$%/(6�+(5(`

/DE�$VVLJQP

HQW

3HUIRUP�(2

)�DQDO\VLV�IRU�PRQWKO\�P

HDQ�GDWD�RYHU�VSHFLILF�UHJLRQ�IRU����������0DNH�SORWV�RI�)LUVW�WZ

R�(2)�SDWWHUQV�DV�P

DSV3HUFHQWDJH�YDULDQFH�H[SODLQHG�RI�ILUVW����(2

)V$PSOLWXGH�YV�WLP

H�IRU�WKH�ILUVW�WZR�3&

V&RUUHODWH�HDFK�RI�WKH�WLP

H�VHULHV�ZLWK�SUHFLSLWDWLRQ�RYHU�

1RUWK�$

PHULFD��!�Z

KDW�LV�WKH�FRUUHODWLRQ�RYHU�&RORUDGR�IRU�

WKH�ILUVW�WZR�3&

V"�

3&$�URXWLQH�DQG�³VWXE´��SFDQDO�SUR��SFDVWXE�SUR��LQ��KRPH�DWRF�VDOD�����

(162

�SDWWHUQ�LQ�667V

=KDQJ�HW�DO��-RXUQDO�RI�&OLP

DWH����������������������

(2)�RI�WURSLFDO�VHD�VXUIDFH�WHP

SHUDWXUH