Statistik mit Excel: Beschreibende Statistik für jedermann, 3. Auflage

Wolf-Gert Matthäus, Jörg Schulze Statistik mit Excel Wolf-Gert Matthäus, Jörg Schulze Statistik mit Excel Beschreibe...

Author: Wolf-Gert Matthäus | Jörg Schulze

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Wolf-Gert Matthäus, Jörg Schulze

Statistik mit Excel

Wolf-Gert Matthäus, Jörg Schulze

Statistik mit Excel Beschreibende Statistik für jedermann 3., überarbeitete und erweiterte Auflage

Bibliografische Information der Deutschen Nationalbibliothek Die Deutsche Nationalbibliothek verzeichnet diese Publikation in der Deutschen Nationalbibliografie; detaillierte bibliografische Daten sind im Internet über abrufbar.

1. Auflage 2003 2. Auflage 2005 3., überarbeitete und erweiterte Auflage 2008 Alle Rechte vorbehalten © B.G. Teubner Verlag / GWV Fachverlage GmbH, Wiesbaden 2008 Lektorat: Ulrich Sandten / Kerstin Hoffmann

Der B.G. Teubner Verlag ist ein Unternehmen von Springer Science+Business Media. www.teubner.de Das Werk einschließlich aller seiner Teile ist urheberrechtlich geschützt. Jede Verwertung außerhalb der engen Grenzen des Urheberrechtsgesetzes ist ohne Zustimmung des Verlags unzulässig und strafbar. Das gilt insbesondere für Vervielfältigungen, Übersetzungen, Mikroverfilmungen und die Einspeicherung und Verarbeitung in elektronischen Systemen. Die Wiedergabe von Gebrauchsnamen, Handelsnamen, Warenbezeichnungen usw. in diesem Werk berechtigt auch ohne besondere Kennzeichnung nicht zu der Annahme, dass solche Namen im Sinne der Warenzeichen- und Markenschutz-Gesetzgebung als frei zu betrachten wären und daher von jedermann benutzt werden dürften. Umschlaggestaltung: Ulrike Weigel, www.CorporateDesignGroup.de Druck und buchbinderische Verarbeitung: Strauss Offsetdruck, Mörlenbach Gedruckt auf säurefreiem und chlorfrei gebleichtem Papier. Printed in Germany

ISBN 978-3-8351-0159-3

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báåÑ~ÅÜÉë=^Äò®ÜäÉå=ãáí=ZÄHLENWENN KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKPV=

PKO=

hä~ëëÉåÄáäÇìåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKQS=

PKOKN= = hä~ëëÉåòìçêÇåìåÖ=ãáí=ÇÉê=cìåâíáçå=WENNKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKQT= PKOKO= = aáÉ=cìåâíáçå=VERWEIS KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKQV= PKOKP= = aáÉ=cìåâíáçå=HÄUFIGKEIT KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKRM= PKOKQ= = a~ë=tÉêâòÉìÖ=HISTOGRAMM KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKRM=

U===================================================================================================fåÜ~äíëîÉêòÉáÅÜåáë= PKP=

jçÇ~äïÉêí KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKRO=

PKQ=

e®ìÑáÖâÉáíÉå=îçå=m~~êÉåW=máîçíJq~ÄÉääÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKRQ=

PKQKN= = ^ìÑÖ~ÄÉåëíÉääìåÖ=ìåÇ=_ÉòÉáÅÜåìåÖÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKRQ= PKQKO= = eÉêëíÉääìåÖ=ÉáåÉê=ÉáåÑ~ÅÜÉå=máîçíJq~ÄÉääÉKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKRQ= PKQKP= = cÉäÇÉáåëíÉääìåÖÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKRT= PKQKQ= = mê®ëÉåí~íáçå=îçå=máîçíJq~ÄÉääÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKRV= PKQKR= = ^Äò®ÜäÉå=ãáííÉäë=máîçíJq~ÄÉääÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK RV= PKQKS= = s~êá~ÄäÉ=máîçíJq~ÄÉääÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKSN= PKQKT= = máîçíJq~ÄÉääÉå=ãáí=a~íìãë~åÖ~ÄÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK SO= PKR=

^ÄëçäìíÉ=pìããÉåÜ®ìÑáÖâÉáíÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ST=

= = Q=

dê~ÑáëÅÜÉ=a~êëíÉääìåÖÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK SV=

= QKN=

eáëíçÖê~ããÉW=tÉêâòÉìÖ=HISTOGRAMM KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKSV=

QKO=

aáÉ= F11 JjÉíÜçÇÉ=òìê=eÉêëíÉääìåÖ=îçå=dê~ÑáâÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK TO=

QKOKN= = wìë~ããÉåÜ®åÖÉåÇÉ=a~íÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKTO= QKOKO= = káÅÜí=òìë~ããÉåÜ®åÖÉåÇÉ=a~íÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKTS= QKP=

wÉáíêÉáÜÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKTS=

QKQ=

pâ~äáÉêìåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKUM=

QKQKN= = _ÉÇÉìíìåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK UM= QKQKO= = içÖ~êáíÜãáëÅÜÉ=pâ~äáÉêìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK UO= QKR=

dê~ÑáëÅÜÉ=a~êëíÉääìåÖ=îçå=máîçíJq~ÄÉääÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK UQ=

QKS=

a~êëíÉääìåÖ=îçå=~ÄëçäìíÉå=pìããÉåÜ®ìÑáÖâÉáíÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKUS=

QKSKN= = _ÉêÉáíë=ÄÉêÉÅÜåÉíÉ=pìããÉåÜ®ìÑáÖâÉáíÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK US= QKSKO= = NMMJmêçòÉåíJaá~Öê~ããÉKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKUT= QKSKP= = NMMJmêçòÉåíJaá~Öê~ããÉ=áã=wÉáí~Ää~ìÑ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKUU= = = R=

oÉä~íáîÉ=e®ìÑáÖâÉáíÉåI=ÉãéáêáëÅÜÉ=sÉêíÉáäìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK VN=

= RKN=

_ÉêÉÅÜåìåÖ=êÉä~íáîÉê=e®ìÑáÖâÉáíÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKVN=

RKO=

bñÅÉä=êÉÅÜåÉí=Ñ~äëÅÜ=>\ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK VP=

RKP=

hìãìäáÉêíÉ=êÉä~íáîÉ=e®ìÑáÖâÉáíÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKVU=

=

fåÜ~äíëîÉêòÉáÅÜåáë= S=

V

pí~íáëíáëÅÜÉ=j~≈ò~ÜäÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NMP=

= SKN=

jáííÉäïÉêíÉKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NMP=

SKNKN= = jÉÇá~å=ìåÇ=~êáíÜãÉíáëÅÜÉë=jáííÉä=EaìêÅÜëÅÜåáííF KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NMP= SKNKO= = tÉáíÉêÉ=jáííÉäïÉêíÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NMT= SKO=

píêÉììåÖëã~≈ÉKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NMT=

SKOKN= = pé~ååïÉáíÉKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NMT= SKOKO= = jáííäÉêÉ=~ÄëçäìíÉ=^ÄïÉáÅÜìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NMT= SKOKP= = bãéáêáëÅÜÉ=pí~åÇ~êÇ~ÄïÉáÅÜìåÖ=ìåÇ=s~êá~åò KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NMU= SKOKQ= = báåëÅÜìÄW=kçêã~äîÉêíÉáäìåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NMV= SKP=

pÅÜáÉÑÉ=ìåÇ=t∏äÄìåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NNP=

SKQ=

aáÉ=sÉêÑΩÜêìåÖW=mçéìä~íáçåëâÉååÖê∏≈Éå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NNQ=

= = T=

hçêêÉä~íáçå=ìåÇ=oÉÖêÉëëáçåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NNV=

= TKN=

aÉê=hçêêÉä~íáçåëâçÉÑÑáòáÉåí=îçå=_ê~î~áëJmÉ~êëçåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NNV=

TKNKN= = _ÉÖêáÑÑI=_ÉÇÉìíìåÖI=_ÉêÉÅÜåìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NNV= TKNKO= = eÉêëíÉääìåÖ=ÇÉê=mìåâíïçäâÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NOM= TKO=

oÉÖêÉëëáçå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NOP=

TKOKN= = _ÉêÉÅÜåìåÖ=ÇÉê=oÉÖêÉëëáçåëâçåëí~åíÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NOP= TKOKO= = oÉÅÜåìåÖ=ãáí=ÇÉã=tÉêâòÉìÖ=REGRESSION KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NOS= TKP=

jìäíáéäÉ=äáåÉ~êÉ=oÉÖêÉëëáçåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NOV=

TKQ=

káÅÜíäáåÉ~êÉ=wìë~ããÉåÜ®åÖÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NPN=

TKQKN= = dêìåÇä~ÖÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NPN= TKQKO= = qê~åëÑçêã~íáçåÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NPR= = = U=

wÉáíêÉáÜÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NPT=

= UKN=

_ÉÖêáÑÑ=ìåÇ=bêÑ~ëëìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NPT=

UKO=

bñéÉêáãÉåíÉääJîáëìÉääÉ=qêÉåÇÉêãáííäìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NPU=

UKP=

iáåÉ~êÉ=wÉáíêÉáÜÉå=ìåÇ=ÇáÉ=TRENDJcìåâíáçåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NQN=

UKQ=

däÉáíÉåÇÉê=aìêÅÜëÅÜåáíí KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NQQ=

===================================================================================================fåÜ~äíëîÉêòÉáÅÜåáë= NM UKR=

dêìåÇä~ÖÉå=ÇÉê=wÉáíêÉáÜÉå~å~äóëÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NQT=

UKRKN= = ^ìÑÄ~ì=ÇÉë=~ÇÇáíáîÉå=wÉáíêÉáÜÉåãçÇÉääë KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NQU= UKRKO= = däÉáíÉåÇÉ=aìêÅÜëÅÜåáííÉ=ìåÇ=Ç~ë=~ÇÇáíáîÉ=wÉáíêÉáÜÉåãçÇÉääKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NRM= UKRKP= = i~åÖÑêáëíáÖÉ=qêÉåÇë=ÉêâÉååÄ~ê=ã~ÅÜÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NRN= UKRKQ= = jçå~íëíóéáëÅÜÉ=^ÄïÉáÅÜìåÖÉå=ÄÉêÉÅÜåÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NRO= UKRKR= = p~áëçåÄÉêÉáåáÖíÉ=wÉáíêÉáÜÉ=ÄÉêÉÅÜåÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NRS= UKRKS= = ^ìëÄäáÅâKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NRT= = = V=

fãéçêí=îçå=a~íÉå=~ìë=a~íÉåÄ~åâÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NRV=

= VKN=

dêìåÇë®íòäáÅÜÉëKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NRV=

VKO=

fãéçêí=~ìë=jpJ^ÅÅÉëë KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NRV=

VKP=

báåêáÅÜíìåÖ=ÉáåÉë=la_`JqêÉáÄÉêë KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NSN=

VKQ=

wìÖêáÑÑ=~ìÑ=âçåâêÉíÉ=a~íÉåÄ~åâÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NSP=

VKQKN= = jáÅêçëçÑí=pniJpÉêîÉê KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NSP= VKQKO= = lê~ÅäÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NSP= VKR=

bñÅÉäJwìÖêáÑÑ=~ìÑ=lê~ÅäÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NSR=

VKRKN= = a~íÉå=áãéçêíáÉêÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NSR= VKRKO= = a~íÉå=îáëì~äáëáÉêÉå=ìåÇ=~âíìÉää=Ü~äíÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NSV= = = ^åÜ~åÖ=NW=sçã=mêçÄäÉã=òìê=bñÅÉäJi∏ëìåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NTN= = = ^åÜ~åÖ=OW=_Éá=bñÅÉä=OMMT=áëí=ã~åÅÜÉë=~åÇÉêëKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NTV= = = iáíÉê~íìê= = KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OMN= = = p~ÅÜïçêíîÉêòÉáÅÜåáë KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OMP= = = =

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Grundlagen

1.1

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q~ÄK=N~W=_ÉáëéáÉäÉ=ÑΩê=èì~äáí~íáîÉ=jÉêâã~äÉ= _Éëáíòí=Ç~ÖÉÖÉå=Ç~ë=jÉêâã~ä=ÉáåÉ=ãÉëëÄ~êÉ=aáãÉåëáçå=çÇÉê=â~åå=Éë=áå=jÉåÖÉåÉáåÜÉáJ íÉå=~ìëÖÉÇêΩÅâí=ïÉêÇÉåI=ëç=ëéêáÅÜí=ã~å=îçå=ÉáåÉã=èì~åíáí~íáîÉå=jÉêâã~äK= = Merkmal


^äíÉê=Eg~ÜêÉF=

ÁI=RI=NUI=ÁI=UVI=Á=

_ÉåòáåîÉêÄê~ìÅÜ=EiáíÉêLNMM=âãF=

PIRX=Á=X=QIU=X=Á=X=TIP=X=Á=X=NOIR=X=Á=

q~ÄK=NÄW=_ÉáëéáÉäÉ=ÑΩê=èì~åíáí~íáîÉ=jÉêâã~äÉ=

=

káããí=Éáå=èì~åíáí~íáîÉë=jÉêâã~ä=åìê=ÉáåáÖÉ=îÉêëÅÜáÉÇÉåÉ=tÉêíÉ=~åI=ëç=ëéêáÅÜí=ã~å=îçå= ÉáåÉã=ÇáëâêÉíÉå=jÉêâã~ä=EòK=_K=jáí~êÄÉáíÉêò~ÜäI=e~ìëÜ~äíëÖê∏≈ÉI=hÑòJ_Éëí~åÇFK==== h~åå=Éáå=jÉêâã~ä=Ç~ÖÉÖÉå=EíÜÉçêÉíáëÅÜF=ìåÉåÇäáÅÜ=îáÉäÉ=tÉêíÉ=~ååÉÜãÉåI=ëç=ÜÉá≈í=Ç~ë= jÉêâã~ä=ëíÉíáÖ=EòK=_K=h∏êéÉêÖê∏≈ÉI=dÉëÅÜïáåÇáÖâÉáíI=aìêÅÜãÉëëÉê=ÉáåÉë=_~ìíÉáäëFK==

1.2

Datenniveau, Skalierung der Merkmale

aáÉ=bêãáííäìåÖ=îçå=jÉêâã~äëïÉêíÉå=ÉêÑçäÖí=ÇìêÅÜ=ÉáåÉå=w®ÜäîçêÖ~åÖ=çÇÉê=ÇìêÅÜ=jÉëëìåÖI= _ÉÑê~ÖìåÖI=_ÉçÄ~ÅÜíìåÖK= aáÉ= bêÖÉÄåáëëÉ= ïÉêÇÉå= ÉåíïÉÇÉê= ìåãáííÉäÄ~ê= çÇÉê= ãáí= eáäÑÉ= ÉáJ åÉë=pâ~äáÉêìåÖëîÉêÑ~ÜêÉåë=áå=ÉáåÉ=pâ~ä~=~ÄÖÉÄáäÇÉíK==

=

=NU

=

N==dêìåÇä~ÖÉå=

aáÉëÉ=Eëí~íáëíáëÅÜÉF=jÉëëJpâ~ä~=áëí=Ç~åå=Ç~ë=fåëíêìãÉåíI=ãáí=ÇÉã=ÇáÉ=jÉêâã~äëïÉêíÉ=ÉêãáíJ íÉäí=ïÉêÇÉåK=^ìÑ=ÇÉê=pâ~ä~=ïÉêÇÉå=ÇáÉ=ã∏ÖäáÅÜÉå=jÉêâã~äëïÉêíÉI=Ñ~ääë=ã∏ÖäáÅÜI=å~ÅÜ=ÄÉJ ëíáããíÉã=lêÇåìåÖëéêáåòáé=~äë=pâ~äÉåïÉêíÉ=~ÄÖÉíê~ÖÉåK== aáÉ=pâ~äÉå=ïÉêÇÉå=ÖÉï∏ÜåäáÅÜ=áå== J=h~êÇáå~äëâ~äÉå= J=lêÇáå~äëâ~äÉå= J=kçãáå~äëâ~äÉå= ìåíÉêÖäáÉÇÉêíK== gÉ=å~ÅÜ=^êí=ÇÉê=pâ~ä~=ëéêáÅÜí=ã~å=Ç~åå=~ìÅÜ=îçå=ÇÉã=òìÖÉÜ∏êáÖÉå=káîÉ~ì=ÇÉê=a~íÉå=Ea~J íÉååáîÉ~ìFK=

1.2.1

Kardinalskala (metrische Skala)

tÉåå=ÇáÉ=a~íÉå=áåíÉêî~ääJ=çÇÉê=Ç~êΩÄÉê=Üáå~ìë=ëçÖ~ê=åçÅÜ=ê~íáçå~ä=ëâ~äáÉêí=ëáåÇI=Ç~åå= ëéêáÅÜí=ã~å=îçå=â~êÇáå~ä=ëâ~äáÉêíÉå=a~íÉå=EçÇÉê=ãÉíêáëÅÜ=ëâ~äáÉêíÉå=a~íÉåFK=aáÉëÉ=a~íÉå= Ü~ÄÉå=Ç~ë=Ü∏ÅÜëíÉ=a~íÉååáîÉ~ìK==

Intervallskala j~å= ëéêáÅÜí= îçå= áåíÉêî~ääëâ~äáÉêíÉå= a~íÉåI= ïÉåå= ÇáÉ= ^ìëéê®ÖìåÖÉå= ÉáåÉë= jÉêâã~äë= áå= ÉáåÉ=o~åÖçêÇåìåÖ=ÖÉÄê~ÅÜí=ïÉêÇÉå=â∏ååÉå=ìåÇ=ïÉåå=òìë®íòäáÅÜ=åçÅÜ=ÄÉëíáããí=ïÉêJ ÇÉå= â~ååI= áå= ïÉäÅÜÉã= ^ìëã~≈= ëáÅÜ= òïÉá= îÉêëÅÜáÉÇÉåÉ= jÉêâã~äë~ìëéê®ÖìåÖÉå= ìåíÉêJ ëÅÜÉáÇÉåK== = Merkmal


rÜêòÉáí=

QWMMWMMI=UWNTWRSI=NOWRVWOOI=Á=

qÉãéÉê~íìê=Eáå=dê~Ç=`ÉäëáìëF=

JPQI=JNOI=RSI=OMMI=Á=

h~äÉåÇÉêòÉáí=

NKNKOMMMI=ONKNOKOMMOI=UKNKOMPRI=Á=

q~ÄK=NKOW=_ÉáëéáÉäÉ=ÑΩê=áåíÉêî~ääëâ~äáÉêíÉ=a~íÉå= fåíÉêî~ääëâ~äáÉêíÉ=a~íÉå=äáÉÖÉå=~äë=w~ÜäÉåïÉêíÉ=EåìãÉêáëÅÜÉ=tÉêíÉF=îçêK=t®ÜêÉåÇ=Éë=çÑÑÉåJ ëáÅÜíäáÅÜ=ìåëáååáÖ=áëíI=ÇáÉ=rÜêòÉáíÉå=Q=rÜê=ìåÇ=NO=rÜê=Ç~ÜáåÖÉÜÉåÇ=òì=áåíÉêéêÉíáÉêÉåI=Ç~ëë= Éë=łìã=NO=rÜê=ÇêÉáã~ä=ëç=ëé®í=áëí=ïáÉ=ìã=Q=rÜêI=áëí=ÇáÉ=^ìëë~ÖÉ=çÑÑÉåÄ~ê=ëáååîçääI=Ç~ëë= łîçå=Q=rÜê=Äáë=U=rÜê=ÖÉå~ìëç=îáÉä=wÉáí=îÉêÖÉÜí=ïáÉ=îçå=R=rÜê=Äáë=V=rÜêK== páååîçää=ëáåÇ=~ìÅÜ=ÇáÉ=^åÖ~ÄÉå=ÇÉê=ãáííäÉêÉå=qÉãéÉê~íìê=EaìêÅÜëÅÜåáííëïÉêíF=ëçïáÉ=ïÉáíÉJ êÉê=ëí~íáëíáëÅÜÉê=j~≈ò~ÜäÉå=EëáÉÜÉ=^ÄëÅÜåáíí=S=~ìÑ=pÉáíÉ=NMPFK=

Verhältnisskala (Ratioskala) j~å= ëéêáÅÜí= Ç~êΩÄÉê= Üáå~ìë= ëçÖ~ê= îçå= ê~íáçå~ä=ëâ~äáÉêíÉå=a~íÉåI= ïÉåå= ÇÉê= pâ~äÉåïÉêí= kìää=ÇÉã=å~íΩêäáÅÜÉåI=~ÄëçäìíÉå=kìääéìåâí=ÉåíëéêáÅÜíK=kÉÖ~íáîÉ=tÉêíÉ=ëáåÇ=Ç~ãáí=ìåã∏ÖJ äáÅÜK=pçãáí=ÉêÜ®äí=åÉÄÉå=ÇÉã=ÉáåÑ~ÅÜÉå=^Äëí~åÇ=EÇáÉ=aáÑÑÉêÉåòF=~ìÅÜ=ÇÉê=nìçíáÉåí=EÇ~ë= sÉêÜ®äíåáëF=ÉáåÉ=ëáååîçääÉ=_ÉÇÉìíìåÖK=== a~ë=sÉêÜ®äíåáë=ä®ëëí=ëáÅÜ=Ç~ÄÉá=~ìÅÜ=áåíÉêéêÉíáÉêÉåW== jáí=TO=g~ÜêÉå=áëí=Éáå=jÉåëÅÜ=ëÉÅÜëã~ä=ëç=~äí=ïáÉ=ãáí=NO=g~ÜêÉåK=báå=báåâçããÉå=îçå=PSMMM= bìêç=áëí=åìê=Éáå=cΩåÑíÉä=ÇÉë=NUMMMMJbìêçJbáåâçããÉåë=ìëïK== =

=

=

NKO==a~íÉååáîÉ~ìI=pâ~äáÉêìåÖ=ÇÉê=jÉêâã~äÉ= Merkmal

NV


báåâçããÉå=Eáå=qëÇK=bìêçF=

MI=ÁI=NOI=ÁI=PSI=ÁI=NOMI=Á=

dÉïáÅÜí=EâÖF=

MI=ÁI=QRI=ÁI=USI=ÁI=NOPI=Á=

^äíÉê=Eg~ÜêÉF=

MI=ÁI=NOI=ÁI=OQI=ÁI=TUI=Á=

q~ÄK=NKPW=_ÉáëéáÉäÉ=ÑΩê=ê~íáçå~ä=ëâ~äáÉêíÉ=a~íÉå=

1.2.2

Ordinalskala

^äë= pâ~äÉåïÉêíÉ= ïÉêÇÉå= åìê=hä~ëëÉåÄÉòÉáÅÜåìåÖÉå= ~ÄÖÉíê~ÖÉåK= _Éáã= sÉêÖäÉáÅÜ=òïÉáÉê= jÉêâã~äëíê®ÖÉê= â~åå= áã= c~ääÉ= ÇÉê= sÉêëÅÜáÉÇÉå~êíáÖâÉáí= åìê= áÜêÉ= o~åÖÑçäÖÉ= ÑÉëíÖÉëíÉääí= ïÉêÇÉåK=aáÑÑÉêÉåòÉå=ëáåÇ=åáÅÜí=áåíÉêéêÉíáÉêÄ~êK== lêÇáå~ä=ëâ~äáÉêíÉ=a~íÉå=ÄÉëáíòÉå=åìê=åçÅÜ=ãáííäÉêÉë=a~íÉååáîÉ~ìK== = Merkmal


pÅÜìäåçíÉ=

ëÉÜê=ÖìíI=ÖìíI=ÄÉÑêáÉÇáÖÉåÇI=~ìëêÉáÅÜÉåÇI=ã~åÖÉäÜ~Ñí=

qÉãéÉê~íìêÉãéÑáåÇÉå=

ÜÉá≈I=ï~êãI=ä~ìï~êãI=â~äíI=ëÉÜê=â~äí==

^äíÉêëÖêìééÉ=

háåÇI=gìÖÉåÇäáÅÜÉêI=bêï~ÅÜëÉåÉêI=dêÉáë=

q~ÄK=NKQW=_ÉáëéáÉäÉ=ÑΩê=çêÇáå~ä=ëâ~äáÉêíÉ=a~íÉå= _Éá=çêÇáå~ä=ëâ~äáÉêíÉå=a~íÉå=â∏ååÉå=áããÉêÜáå=ÇáÉ=e®ìÑáÖâÉáíÉå=~ÄÖÉò®Üäí=ïÉêÇÉåX=òìë®íòJ äáÅÜ= â∏ååÉå= îÉêÖäÉáÅÜÉåÇÉ= ^ìëë~ÖÉå= ïáÉ= ÄÉëëÉêLëÅÜäÉÅÜíÉêI= ãÉÜêLïÉåáÖÉê= ìK= ®K= ÖÉã~ÅÜí= ïÉêÇÉåK== _ÉêÉÅÜåìåÖÉå=îçå=jáííÉäïÉêíÉå=çÇÉê=ïÉáíÉêÉå=ëí~íáëíáëÅÜÉå=j~≈ò~ÜäÉå=çêÇáå~ä=ëâ~äáÉêíÉê= a~íÉå=ëáåÇ=áã=~ääÖÉãÉáåÉå=åáÅÜí=ëáååîçääK==

1.2.3

Nominalskala

^äë=pâ~äÉåïÉêíÉ=ïÉêÇÉå=k~ãÉå=~ÄÖÉíê~ÖÉåX=Éë=â~åå=åìê=ÇáÉ=däÉáÅÜÜÉáí=çÇÉê=råÖäÉáÅÜJ ÜÉáí=ÖÉéêΩÑí=ïÉêÇÉåK== kçãáå~ä=ëâ~äáÉêíÉ=a~íÉå=ÄÉëáíòÉå=Ç~ë=ìåíÉêëíÉ=a~íÉååáîÉ~ìK=aáÉ=q~ÄÉääÉ=NKR=ÉåíÜ®äí=ÉáåáÖÉ= _ÉáëéáÉäÉ=ÑΩê=åçãáå~ä=ëâ~äáÉêíÉ=a~íÉåK= = Merkmal


dÉëÅÜäÉÅÜí=

ã®ååäáÅÜI=ïÉáÄäáÅÜ=

c~ãáäáÉåëí~åÇ=

äÉÇáÖI=îÉêÜÉáê~íÉíI=ÖÉëÅÜáÉÇÉåI=îÉêïáíïÉí=

miwJ_ÉêÉáÅÜ=

MI=NI=OI=ÁI=V=

q~ÄK=NKRW=_ÉáëéáÉäÉ=ÑΩê=åçãáå~ä=ëâ~äáÉêíÉ=a~íÉå= aáÉ=^åÖ~ÄÉ=îçå=^Äëí®åÇÉå=ìåÇLçÇÉê=lêÇåìåÖëÄÉòáÉÜìåÖÉå=òïáëÅÜÉå=òïÉá=jÉêâã~äëíê®ÖÉêå= áëí= ~åÜ~åÇ= ÇÉê= hä~ëëÉåÄÉòÉáÅÜåìåÖÉå= åáÅÜí= ã∏ÖäáÅÜK= ^ìÅÜ= ïÉåå= ÇáÉëÉ= EòìÑ®ääáÖF= ëçÖ~ê= ~ìë= w~ÜäÉå=ÄÉëíÉÜÉå=ëçääíÉåW=aÉê=miwJ_ÉêÉáÅÜ=U=áëí=âÉáåÉëÑ~ääë=łÄÉëëÉê=~äë=ÇÉê=miwJ_ÉêÉáÅÜ=SK== råÇ=ï~ë=ëçääíÉ=~ìÅÜ=ÇáÉ=ëáååäçëÉ=aáÑÑÉêÉåò=łmiwJ_ÉêÉáÅÜ=T=ãáåìë=miwJ_ÉêÉáÅÜ=P=~ìëë~ÖÉå\==

=

=OM

=

N==dêìåÇä~ÖÉå=

kçÅÜ= âìêáçëÉê= ï®êÉ=ÉëI= ïÉåå= ã~å= ÇáÉ= mçëíäÉáíò~Üä= VVVVV= ~äë= łÇêÉáã~ä= ëç= Öêç≈LÖìíLKKK= ïáÉ= ÇáÉ=mçëíäÉáíò~Üä=PPPPP=ÄÉòÉáÅÜåÉå=ïΩêÇÉK=

1.3

Verarbeitungsmöglichkeiten von Daten

a~ë= jÉëëåáîÉ~ì= ÇÉê= a~íÉå= ÄÉëíáããí= ïÉáíÖÉÜÉåÇ= ÇáÉ= j∏ÖäáÅÜâÉáíÉå= ìåÇ= dêÉåòÉå= ÇÉê= a~íÉå~å~äóëÉW= gÉ= åáÉÇêáÖÉê= Ç~ë=a~íÉååáîÉ~ì= áëíI= ÇÉëíç= ÖÉêáåÖÉê=áëí= Ç~ë= ^å~äóëÉéçíÉåòá~ä= ÇÉê=sÉêÑ~ÜêÉå=ìåÇ=ÇÉëíç=ÖÉêáåÖÉê=áëí=ÇÉê=fåÑçêã~íáçåëÖÉÜ~äí=ÇÉê=jÉêâã~äëïÉêíÉK== = Skalentyp Empirische Operationen

Nominalskala Bestimmung von Gleichheit und Ungleichheit

Ordinalskala Zusätzlich: Bestimmung einer Rangfolge z. B. x=

Abzählen von Postleitzahlen usw. mçëíäÉáíò~ÜäÉåI= ÉÄÉåëç= mÉêëçå~äåìããÉêåI= ^êíáâÉäåìããÉêåI= hÉååò~ÜäÉå=ìëïK= ÜÉá≈Éå= òï~ê= łw~ÜäÉåI=ÇΩêÑÉå=~ÄÉê=áå=bñÅÉäJq~ÄÉääÉå=åáÅÜí=ïáÉ=w~ÜäÉå=ÉáåÖÉÖÉÄÉå=ïÉêÇÉåK== mçëíäÉáíò~ÜäÉå= ãΩëëÉå= ïáÉ= åáÅÜíåìãÉêáëÅÜÉ= ^åÖ~ÄÉå= ÄÉÜ~åÇÉäí= ïÉêÇÉå= Ó= ëÅÜäáÉ≈äáÅÜ= ëçää=ãáí=áÜåÉå=à~=åáÅÜí=ÖÉêÉÅÜåÉí=ïÉêÇÉåI=îáÉäãÉÜê=ÖÉÜí=Éë=ìã=Ç~ë=^Äò®ÜäÉå=ÄÉëíáããíÉê= miw=çÇÉê=~ìÅÜ=åìê=îçå=miwJ_ÉêÉáÅÜÉå=EòK=_K=miwJ_ÉêÉáÅÜ=PFK==

cΩê=bñÅÉä=OMMTJ^åïÉåÇÉê=ÖáÄí=Éë=_ÉÇáÉåìåÖëÜáåïÉáëÉ=òì=ÇáÉëÉã=^ÄëÅÜåáíí=~Ä=pÉáíÉ=NUS=

PKN==báåÑ~ÅÜÉë=^Äò®ÜäÉå=ãáí=ZÄHLENWENN=

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= q~ÄK=PKRW=êáÅÜíáÖÉ=ìåÇ=Ñ~äëÅÜÉ=^ìÑå~ÜãÉ=ÉáåÉê=miw=áå=ÇáÉ=q~ÄÉääÉ= bë= ÖáÄí= äÉÇáÖäáÅÜ= ÇÉå= qêáÅâI= îçê= ÇáÉ= kìää= Ç~ë= eçÅÜâçãã~= ’= òì= ëÉíòÉåI= ÇKÜK= ~åëíÉääÉ= îçå= 09126= ÖáÄí= ã~å= ’09126= ÉáåK= a~ÇìêÅÜ= ïáêÇ= bñÅÉä= ÖÉòïìåÖÉåI= ÇáÉ= báåÖ~ÄÉ= ~äë= åáÅÜíåìãÉJ êáëÅÜ=òì=ëéÉáÅÜÉêåK=== aáÉ= q~ÄÉääÉå= PKS~LÄ= ÄÉëÅÜêÉáÄÉå= ÇÉå= ò®ÜäÉåÇÉå= rãÖ~åÖ= ãáí= mçëíäÉáíò~ÜäÉåW= j~å= â~åå= ò®ÜäÉå= ä~ëëÉåI= ïáÉ= çÑí= ÉáåÉ= ÄÉëíáããíÉ= miw= áã= a~íÉåÄÉëí~åÇ= ~ìÑíêáííI= ÇìêÅÜ= báåÖ~ÄÉ= îçå= qÉñíãìëíÉêå=ä~ëëÉå=ëáÅÜ=~ÄÉê=~ìÅÜ=Ö~åò=ÄÉëíáããíÉ=miwJ_ÉêÉáÅÜÉ=~Äò®ÜäÉåK== få=ÇÉê=q~ÄÉääÉ=PKS~=ÄÉ~ÅÜíÉ=ã~åI=Ç~ëë=ÇáÉ=fåÜ~äíÉ=ÇÉê=ÄÉáÇÉå=wÉääÉå= F1=ìåÇ= F2=îçå=bñÅÉä= ìåÄÉÇáåÖí=äáåâëÄΩåÇáÖ=ÉáåÖÉíê~ÖÉå=ïÉêÇÉå=ãΩëëÉåK== a~ë=ÉêêÉáÅÜí=ã~åI=ïáÉ=ëÅÜçå=Éêï®ÜåíI=ÇìêÅÜ=cçêã~íáÉêìåÖ=~äë=qÉñíëé~äíÉ=çÇÉê=sçêëíÉääÉå= ÇÉë=eçÅÜâçãã~ëK===


P==^ÄëçäìíÉ=e®ìÑáÖâÉáíÉå=

QQ =

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3.2

Klassenbildung

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3.2.1

Klassenzuordnung mit der Funktion WENN

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4.2.2

Nicht zusammenhängende Daten

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4.3

Zeitreihen

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4.4

Skalierung

4.4.1

Bedeutung

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4.4.2

Logarithmische Skalierung

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4.5

Grafische Darstellung von Pivot-Tabellen

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4.6

Darstellung von absoluten Summenhäufigkeiten

4.6.1

Bereits berechnete Summenhäufigkeiten

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4.6.2

100-Prozent-Diagramme

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4.6.3

100-Prozent-Diagramme im Zeitablauf

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5

Relative Häufigkeiten, empirische Verteilung

5.1

Berechnung relativer Häufigkeiten

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5.2

Excel rechnet falsch !?

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6

Statistische Maßzahlen

6.1

Mittelwerte

6.1.1

Median und arithmetisches Mittel (Durchschnitt)

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1000

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NMS

pÅÜäìëëÑçäÖÉêìåÖW= aÉê= h~í~äçÖ= ÇÉê= sÉêÖäÉáÅÜëïÉêíÉ= ãìëë= ~ìÑëíÉáÖÉåÇ= äÉñáâçÖê~ÑáëÅÜ= ÖÉJ çêÇåÉí=ÉáåÖÉíê~ÖÉå=ëÉáåK=== jáí=ÇÉê=cìåâíáçå= MITTELWERT(...)=â∏ååíÉ=ã~å=åìå=òìë®íòäáÅÜ=ìåëÅÜïÉê=ÜÉê~ìëÑáåÇÉåI=Ç~ëë= ÇÉê= jáííÉäïÉêí= ÇÉê= âçÇáÉêíÉå= tÉêíÉ= 2,333= ÄÉíê®ÖíK= t~ë= ~ÄÉêI= ëç= Ñê~ÖÉå= ïáê= ÇÉå= ÖÉåÉáÖíÉå= iÉëÉêI=Ü®ííÉ=ìåë=ÇáÉëÉê=ÉáÖÉå~êíáÖÉ=łc~ãáäáÉåëí~åÇëJjáííÉäïÉêí=2,333=ÜáÉê=ïçÜä=òì=ë~ÖÉå\\= pçïÉáí= òìã= ÖêìåÇë®íòäáÅÜÉå= ^åäáÉÖÉå= îçå= jÉÇá~å= ìåÇ= jáííÉäïÉêíK= _ÉëÅÜ®ÑíáÖÉå= ïáê= ìåë= åìå=ãáí=ïÉáíÉêÉå=báåòÉäÜÉáíÉå=áÜêÉê=_ÉêÉÅÜåìåÖK== e~í=ã~å=ÇÉå=îçääÉå=a~íÉåÄÉëí~åÇ=EÇK=ÜK=ÉáåÉ=rêäáëíÉF=òìê=sÉêÑΩÖìåÖI=áëí=ÇáÉ=_ÉêÉÅÜåìåÖ= îçå= jÉÇá~å= ìåÇ= ~êáíÜãÉíáëÅÜÉã= jáííÉä= ãáí= ÇÉå= bñÅÉäJcìåâíáçåÉå= MEDIAN(...)= ÄÉòáÉJ ÜìåÖëïÉáëÉ=MITTELWERT(...)=åìê=ÉáåÉ=cê~ÖÉ=ÇÉë=báåíê~ÖÉåëX=ëÅÜäáããëíÉåÑ~ääë=ãìëë=îçêÜÉê= ÉáåÉ=hçÇáÉêìåÖ=ÉêÑçäÖÉåK== táÉ=ëçää=ã~å=~ÄÉê=îçêÖÉÜÉåI=ïÉåå=åáÅÜí=ãÉÜê=ÇÉê=ìêëéêΩåÖäáÅÜÉI=îçääÉ=a~íÉåÄÉëí~åÇI=ëçåJ ÇÉêå=åìê=åçÅÜ=ÉáåÉ=e®ìÑáÖâÉáíëí~ÄÉääÉ=EëK=^ÄëÅÜåáíí=PKOKQ=~ìÑ=pÉáíÉ=RMF=îçêÜ~åÇÉå=áëí\== a~åå=ÄäÉáÄí=åìê=ÇÉê=^ìëïÉÖI=ÇáÉ=hä~ëëÉåãáííÉå=~ìë=ÇÉå=hä~ëëÉåÖêÉåòÉå=òì=ÄÉêÉÅÜåÉåK= aáÉëÉ=hä~ëëÉåãáííÉå=ïÉêÇÉå=Ç~åå=òìê=dêìåÇä~ÖÉ=ïÉáíÉêÉê=^ìëïÉêíìåÖÉå=ÖÉã~ÅÜíK== aáÉ=q~ÄÉääÉå=SKQ~LÄ=ÄÉëÅÜêÉáÄÉå=Ç~ë=sçêÖÉÜÉåK==

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6.1.2

NMT

Weitere Mittelwerte

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6.2

Streuungsmaße

6.2.1

Spannweite

aáÉ= pé~ååïÉáíÉ= áëí= ÇáÉ= aáÑÑÉêÉåò= ~ìë= ÇÉã= Öê∏≈íÉå= ìåÇ= ÇÉã= âäÉáåëíÉå= ÄÉçÄ~ÅÜíÉíÉå= jÉêâã~äëïÉêíK== páÉ=â~åå=áå=ÉáåÉê=bñÅÉäJq~ÄÉääÉ=ãáí=eáäÑÉ=ÇÉê=ÄÉáÇÉå=cìåâíáçåÉå= MIN(...)=ìåÇ= MAX(...)=ÄÉJ êÉÅÜåÉí=ïÉêÇÉå=EëK=q~ÄÉääÉ=SKRF=

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6.2.2

Mittlere absolute Abweichung

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6.2.3

Empirische Standardabweichung und Varianz

aáÉëÉ=ÄÉáÇÉå=píêÉììåÖëã~≈É=ïÉêÇÉå=~ã=Ü®ìÑáÖëíÉå=ÄÉåìíòí=Ó=Ç~ë=Ü®åÖí=ãáí=áÜêÉê=_ÉÇÉìJ íìåÖ=áå=ÇÉê=ÄÉìêíÉáäÉåÇÉå=pí~íáëíáâ=òìë~ããÉåI=~ìÑ=ÇáÉ=áã=o~ÜãÉå=ÇáÉëÉë=_ìÅÜÉë=~ÄÉê=äÉáÇÉê= åáÅÜí=ÉáåÖÉÖ~åÖÉå=ïÉêÇÉå=â~ååK= aáÉ= ÉãéáêáëÅÜÉ= s~êá~åò= áëí= ÇáÉ= pìããÉ= ÇÉê= èì~ÇêáÉêíÉå= ^ÄïÉáÅÜìåÖÉå= ÇÉê= jÉêâã~äëJ ïÉêíÉ=îçã=~êáíÜãÉíáëÅÜÉå=jáííÉäI=ÇáîáÇáÉêí=ÇìêÅÜ=ÇáÉ=^åò~Üä=ÇÉê=jÉêâã~äëïÉêíÉ=ãáåìë=N= EçÇÉê=ÇáîáÇáÉêí=ÇìêÅÜ=ÇáÉ=^åò~Üä=ÇÉê=jÉêâã~äëïÉêíÉFK== páÉ=â~åå=ãáí=bñÅÉä=ëçïçÜä=ÉäÉãÉåí~ê=~äë=~ìÅÜ=ãáí=eáäÑÉ=ÇÉê=cìåâíáçå=VARIANZ(...)=ÉêãáííÉäí= ïÉêÇÉåK=aáÉëÉ=cìåâíáçå=ÄÉåìíòí=ÇáÉ=îÉêêáåÖÉêíÉ=^åò~Üä=òìê=aáîáëáçåK= aáÉ=ÉãéáêáëÅÜÉ=pí~åÇ~êÇ~ÄïÉáÅÜìåÖ=áëí=ÇáÉ=nì~Çê~íïìêòÉä=~ìë=ÇÉê=ÉãéáêáëÅÜÉå=s~êá~åòK== cΩê=ëáÉ=ÖáÄí=Éë=ÇáÉ=bñÅÉäJcìåâíáçå=STABW(...)K==

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6.2.4

Einschub: Normalverteilung

tÉååÖäÉáÅÜ= ÉãéáêáëÅÜÉ= s~êá~åò= ìåÇ= ÉãéáêáëÅÜÉ= pí~åÇ~êÇ~ÄïÉáÅÜìåÖ= ÜáåëáÅÜíäáÅÜ= ÇÉê= ~åëÅÜ~ìäáÅÜÉå= aÉìíìåÖ= ïÉåáÖÉê= ~ìëë~ÖÉâê®ÑíáÖ= ~äë= ÇáÉ= ãáííäÉêÉ= ~ÄëçäìíÉ= ^ÄïÉáÅÜìåÖ= ëáåÇI=ÄÉëáíòí=áåëÄÉëçåÇÉêÉ=ÇáÉ=ÉãéáêáëÅÜÉ=pí~åÇ~êÇ~ÄïÉáÅÜìåÖ=áå=sÉêÄáåÇìåÖ=ãáí=ÇÉã= ~êáíÜãÉíáëÅÜÉå=jáííÉä=~ì≈ÉêçêÇÉåíäáÅÜÉ=_ÉÇÉìíìåÖI=ïÉåå=Éë=ìã=ÇÉå=_ÉÖêáÑÑ=ÇÉê=kçêã~äJ îÉêíÉáäìåÖ=ÖÉÜíK== pçääíÉå= ÇáÉ=tÉêíÉ=ÇÉë=a~íÉåÄÉëí~åÇÉë= å®ãäáÅÜ= ~ìë=ÉáåÉê=píáÅÜéêçÄÉ= Éåíëí~ããÉåI= Ç~åå= áëí= ÑΩê=ÇáÉ=ïÉëÉåíäáÅÜÉå=_Éä~åÖÉ=ÇÉê=ÄÉìêíÉáäÉåÇÉå=pí~íáëíáâ=ÖêìåÇë®íòäáÅÜ=îçå=_ÉÇÉìíìåÖI=çÄ= ã~å=îçå=ÉáåÉê=åçêã~äîÉêíÉáäíÉå=dêìåÇÖÉë~ãíÜÉáí=~ìëÖÉÜÉå=â~åå=EîÖäK=òK=_K=xNz=I=xNNzI=xOMzFK== cΩê=ÇáÉëÉå=c~ää=ëíÉÜÉå=Ç~åå=îáÉäÉ=qÉëíãÉíÜçÇÉå=ëçÑçêí=òìê=sÉêÑΩÖìåÖK== fã=páååÉ=ÇÉê=ÄÉìêíÉáäÉåÇÉå=pí~íáëíáâ=ï®êÉ=Éë=ÑçäÖäáÅÜ=âçêêÉâíI=ïÉåå=Éáå=òì=ìåíÉêëìÅÜÉåJ ÇÉê=a~íÉåÄÉëí~åÇ=ëíÉíë=~äë=ÉêëíÉë=~ìÑ=kçêã~äîÉêíÉáäìåÖ=ÖÉíÉëíÉí=ïΩêÇÉK== aáÉëÉê=ëç=ÖÉå~ååíÉ=`ÜáJnì~Çê~íJ^åé~ëëìåÖëíÉëí=áëí=êÉÅÜí=~ìÑï®åÇáÖ=EëáÉÜÉ=xNNzF=K= bñÅÉä=äáÉÑÉêí=~ÄÉê=ÉáåÉ=j∏ÖäáÅÜâÉáíI=îáëìÉää=ÉáåÉ=ëÅÜåÉääÉ=sçê~ÄJfåÑçêã~íáçå=òì=ÉêÜ~äíÉåI=ÇáÉ= ÇÉã=mê~âíáâÉê=ÄáëïÉáäÉå=ëÅÜçå=~ìëêÉáÅÜíK== j~å=â~åå=å®ãäáÅÜ=îçå=ÉáåÉã=a~íÉåÄÉëí~åÇ=Ó=ÖêçÄ=ÖÉëéêçÅÜÉå=Ó=~ååÉÜãÉåI=Ç~ëë=Éê=~ìë= ÉáåÉê=åçêã~äîÉêíÉáäíÉå=dêìåÇÖÉë~ãíÜÉáí=ëí~ããÉå=â∏ååíÉI=ïÉåå=ÇáÉ=ÑçäÖÉåÇÉå=ÇêÉá=báÖÉåJ ëÅÜ~ÑíÉå=ÉêÑΩääí=ëáåÇW==



NNM

NK=^ääÉ=tÉêíÉ=âçåòÉåíêáÉêÉå=ëáÅÜ=ëí~êâ=ìã=Ç~ë=~êáíÜãÉíáëÅÜÉ=jáííÉäK= OK=aáÉ=tÉêíÉ=ÄÉÑáåÇÉå=ëáÅÜ=ìåÖÉÑ®Üê=òì=ÖäÉáÅÜÉå=qÉáäÉå=äáåâë=ìåÇ=êÉÅÜíë=îçã=~êáíÜãÉJ= ====íáëÅÜÉå=jáííÉäK= PK=^ì≈ÉêÜ~äÄ=ÇÉê=ëç=ÖÉå~ååíÉå=aêÉáJpáÖã~JdêÉåòÉå=ÖáÄí=Éë=ëç=Öìí=ïáÉ=âÉáåÉ=tÉêíÉ=ãÉÜêK== aáÉ=pí~íáëíáâ=~êÄÉáíÉí=éêáåòáéáÉää=åáÅÜí=ãáí=ÇÉê=sçâ~ÄÉä=łà~K=^äëç=òáÉÜí=ã~å=~ìë=ÇÉã=bêÑΩääíJ ëÉáå=~ääÉê=ÇêÉá=hêáíÉêáÉå=åáÉã~äë=ÇÉå=pÅÜäìëëI=Ç~ëë=kçêã~äîÉêíÉáäìåÖ=îçêäáÉÖÉK=pçåÇÉêå=ã~å= ÑçêãìäáÉêí=ëíÉíë=łåÉáå=çÇÉê=łåáÅÜí=åÉáåW==

=

páåÇ= ÇáÉ= ÇêÉá= oÉÖÉäå= ÉêÑΩääíI= Ç~åå= ëéêáÅÜí=Éêëí=Éáåã~ä=åáÅÜíë=ÖÉÖÉå=ÇáÉ=^åå~ÜãÉI= Ç~ëë= kçêã~äîÉêíÉáäìåÖ=îçêäáÉÖÉå=â~ååK== píÉääí= ã~å= ÑΩê= ÉáåÉå= a~íÉåÄÉëí~åÇ= àÉÇçÅÜ= ÇÉå= sÉêëíç≈= ÖÉÖÉå= ÉáåÉ= ÇáÉëÉê= ÇêÉá= oÉÖÉäå= ÑÉëíI=Ç~åå=áëí=ÇáÉ=^åå~ÜãÉI=Éê=Éåíëí~ããÉ=ÉáåÉê=åçêã~äîÉêíÉáäíÉå=dêìåÇÖÉë~ãíÜÉáíI=åáÅÜí= ÖÉêÉÅÜíÑÉêíáÖíK==

tçÄÉá= ÇáÉëÉ= pÅÜäìëëÑçäÖÉêìåÖÉå= ÉáåÉå= ëí~íáëíáëÅÜÉå= qÉëí= ÖÉã®≈= ÇÉå= ëíêÉåÖÉå= oÉÖÉäå= ÇÉê= ÄÉìêíÉáäÉåÇÉå=pí~íáëíáâ=íêçíòÇÉã=åáÅÜí=ÉêëÉíòÉå=â∏ååÉå=Ó=~ÄÉê=ÜáÉê=ëçää=à~=åìê=Éáå=ëÅÜåÉääÉê= ìåÇ=ÉáåÑ~ÅÜÉê=tÉÖ=òì=ÉáåÉê=îáëìÉääÉå=sÉêãìíìåÖ=ÖÉòÉáÖí=ïÉêÇÉåK==

= q~ÄK=SKU~W=cçêãÉäå=

= q~ÄK=SKUÄW=tÉêíÉ= aáÉ= q~ÄÉääÉå= SKU~LÄ= òÉáÖÉå= ÉáåÉå= a~íÉåÄÉëí~åÇI= ÇÉê= òïÉÅâë= k~ÅÜîçääòáÉÜÄ~êâÉáí= ÇáÉëã~ä= åáÅÜí=áå=ÉáåÉ=wÉáäÉ=çÇÉê=pé~äíÉI=ëçåÇÉêå=áå=ÇÉå=oÉÅÜíÉÅâÄÉêÉáÅÜ=A3:E12=ÉáåÖÉíê~ÖÉå=ïìêÇÉK===== pÉÜÉå=ïáê=ìåë=Ç~òì=Éáå=_ÉáëéáÉä=òìê=fääìëíê~íáçå=ÇÉë=sçêÖÉÜÉåë=~åK== cΩê= ÉáåÉ= pÅÜ®íòìåÖ=ÇÉê=aêÉáJpáÖã~JdêÉåòÉå= îÉêïÉåÇÉí= ã~å= Ç~ÄÉá= Ç~ë= äÉáÅÜí= îÉêÑΩÖÄ~êÉ= fåíÉêî~ää== [arithm.Mittel – 3*emp.Standardabweichung , arithm.Mittel + 3*emp.Standardabweichung]

j~å=äáÉëí=áå=ÇÉê=q~ÄÉääÉ=SKUÄ=~ÄW=a~ë=~êáíÜãÉíáëÅÜÉ=jáííÉä=áëí=ÖäÉáÅÜ=29,8=ìåÇ=ÇáÉ=ÉãéáêáëÅÜÉ= pí~åÇ~êÇ~ÄïÉáÅÜìåÖ=áëí=ÖäÉáÅÜ=4,7K==



NNN

a~ãáí=ÉêÜ®äí=ã~å=ëçÑçêí=pÅÜ®íòìåÖÉå=ÑΩê=ÇáÉ=ÄÉáÇÉå=aêÉáJpáÖã~JdêÉåòÉåW== pÅÜ®íòìåÖ=ÇÉê=äáåâÉå=PJpáÖã~JdêÉåòÉ=W==

29,8 - 3*4,7 = 15,7==

pÅÜ®íòìåÖ=ÇÉê=êÉÅÜíÉå=PJpáÖã~JdêÉåòÉW=

29,8 + 3*4,7 = 43,9=

a~ë=ÜÉá≈í=~äëçW=tÉåå=ëáÅÜ=åáÅÜí=å~ÜÉòì=~ääÉ=a~íÉå=áã=_ÉêÉáÅÜ=îçå= 15,7=Äáë= 43,9=ÄÉÑáåÇÉåI= ïáêÇ=ã~å=ÄÉêÉáíë=ÇÉê=sÉêãìíìåÖ=~ìÑ=kçêã~äîÉêíÉáäìåÖ=ïáÇÉêëéêÉÅÜÉå=ãΩëëÉåK=eáåòì=âçãJ ãÉå=Ç~åå=~ÄÉê=åçÅÜ=ÇáÉ=_ÉÇáåÖìåÖÉå=N=ìåÇ=OK== ^ääÉ=ÇêÉá=_ÉÇáåÖìåÖÉå=òìë~ããÉå=â~åå=ã~å=îáëìÉää=ãáí=eáäÑÉ=ÇÉë=tÉêâòÉìÖë= HISTOGRAMM= ΩÄÉêéêΩÑÉåK== a~òì=íÉáäí=ã~å=òìÉêëí=ÇÉå=ìåíÉê=sÉêïÉåÇìåÖ=îçå=jáííÉäïÉêí=ìåÇ=ÉãéáêáëÅÜÉê=pí~åÇ~êÇ~ÄJ ïÉáÅÜìåÖ= ÖÉëÅÜ®íòíÉå= aêÉáJpáÖã~J_ÉêÉáÅÜ= áå= ãáåÇÉëíÉåë=OM=ÖäÉáÅÜÉ=qÉáäÉ= ÉáåX= áå= ìåëÉêÉã= _ÉáëéáÉä=ÉêïÉáëí=Éë=ëáÅÜ=~äë=ÖΩåëíáÖI=~äë=ÉêëíÉ=hä~ëëÉåÖêÉåòÉ= 15=òì=ï®ÜäÉåI=Ç~åå= 16,5I=Ç~åå= 18,0=ìëïK=Äáë=45K==

=

=

q~ÄK=SKV~LÄW=bêòÉìÖÉå=ÇÉê=hä~ëëÉåÖêÉåòÉåW=cçêãÉä=ìåÇ=tÉêíÉ= kìå= ïáêÇ= ΩÄÉê= buqo^p^kîvpbJcrkhqflkbkefpqldo^jj= EëáÉÜÉ= pÉáíÉ= RMF= Ç~ë= é~ëëÉåÇÉ= tÉêâòÉìÖ= ~åÖÉÑçêÇÉêíI= ÇÉê= _ÉêÉáÅÜ= ÇÉë= a~íÉåÄÉëí~åÇÉë= ëçïáÉ= ÇÉê= _ÉêÉáÅÜ= ÇÉê= hä~ëëÉåJ ÖêÉåòÉå=ïáêÇ=ÉáåÖÉíê~ÖÉå=EëK=_áäÇ=SKNFK=== ^ìÑ= ÉáåÉã= ÖÉëçåÇÉêíÉå= q~ÄÉääÉåÄä~íí= ÉåíëíÉÜí= Ç~åå= ÇáÉ= e®ìÑáÖâÉáíëí~ÄÉääÉX= ãáí= aêìÅâ= ~ìÑ= ÇáÉ=q~ëíÉ= F11 =ÑΩÜêí=ëáÉ=ìåë=òìã=eáëíçÖê~ãã=E_áäÇ=SKOFK= aÉã=eáëíçÖê~ãã=áëí=òì=ÉåíåÉÜãÉåI=Ç~ëë=ÇáÉ=cçêÇÉêìåÖ=kìããÉê=ÇêÉá=çÑÑÉåëáÅÜíäáÅÜ=ÉêÑΩääí= áëíX= ~ìÅÜ= ÇáÉ= hçåòÉåíê~íáçå= ÇÉê= tÉêíÉ= áå= ÇÉê= k®ÜÉ= ÇÉë= ~êáíÜãÉíáëÅÜÉå= jáííÉäë= ëçïáÉ= ÇáÉ= póããÉíêáÉ=â~åå=ã~å=åáÅÜí=ÖêìåÇë®íòäáÅÜ=îçå=ÇÉê=e~åÇ=ïÉáëÉåK== sçêëáÅÜíI=Ö~åò= Öêç≈É= sçêëáÅÜí= ~ÄÉê=åìå=ãáí= ÇÉê= îçêëÅÜåÉääÉå= ^ìëë~ÖÉI= Ç~ëë=kçêã~äîÉêíÉáJ äìåÖ=îçêäáÉÖÉ=çÇÉê=îçêäáÉÖÉå=â∏ååÉK== bë= ëéêáÅÜí= ~ìÑ= ÇÉå= ÉêëíÉå= _äáÅâ= äÉÇáÖäáÅÜ= ïÉåáÖ= Ç~ÑΩêI= Ç~ëë= ã~å= ÇáÉ= kçêã~äîÉêíÉáäìåÖ= ÖêìåÇë®íòäáÅÜ=~ÄäÉÜåÉå=ãΩëëÉK=pç=áëí=ÇáÉ=péê~ÅÜÉ=ÇÉê=pí~íáëíáâK== =



NNO =

=

=

_áäÇ=SKNW=eáëíçÖê~ããW=báåÖ~ÄÉã~ëâÉ=ÇÉë=tÉêâòÉìÖë=

=

=

_áäÇ=SKOW=eáëíçÖê~ãã= tÉê= ëáÅÜ= ~å= ÇÉå= îÉêÑäçëëÉåÉå= wÉÜåJajJpÅÜÉáå= åçÅÜ= ÉêáååÉêå= â~ååI= ïáêÇ= îáÉääÉáÅÜí= ~ìÅÜ= åçÅÜ= ïáëëÉåI= Ç~ëë= Ççêí= ÇáÉ= ëç= ÖÉå~ååíÉ= d~ì≈ÛëÅÜÉ= däçÅâÉåâìêîÉ= ~ÄÖÉÄáäÇÉí= ï~ê= EëáÉÜÉ= _áäÇ=SKPFK== páÉ=äáÉÑÉêí=ÇáÉ=fÇÉ~äÑçêã=Ó=ëç=ãΩëëíÉå=eáëíçÖê~ããÉ=~ìëëÉÜÉåI=Ç~ãáí=ã~å=òïÉáÑÉäëÑêÉá=îçå= ÉáåÉê=åçêã~äîÉêíÉáäíÉå=dêìåÇÖÉë~ãíÜÉáí=ëéêÉÅÜÉå=ÇΩêÑíÉK==


SKP==pÅÜáÉÑÉ=ìåÇ=t∏äÄìåÖ=

=

NNP

=

= _áäÇ=SKPW=d~ì≈ÛëÅÜÉ=däçÅâÉåâìêîÉ= táÉ=äÉáÅÜí=òì=ëÉÜÉå=áëíI=áëí=ìåëÉê=_ÉáëéáÉä=Ç~îçå=ÇçÅÜ=ÉåíÑÉêåíK===

6.3

Schiefe und Wölbung

cΩê=ÄÉëíáããíÉ=c~ÅÜÖÉÄáÉíÉ=ëéáÉäí=Éë=ÉáåÉ=oçääÉI=çÄ=Ç~ë=eáëíçÖê~ãã=ÉáåÉë=a~íÉåÄÉëí~åJ ÇÉë=ëóããÉíêáëÅÜI=äáåâëJ=çÇÉê=êÉÅÜíëëÅÜáÉÑ=áëíK== a~òì=â~åå=ã~å=å~íΩêäáÅÜ=Ç~ë=eáëíçÖê~ãã=ëÉäÄëí=ÄÉåìíòÉåX=ã~å=ÉêãáííÉäí=ÇáÉ=pé~ååïÉáíÉI= äÉÖí=hä~ëëÉåÖêÉåòÉå=ÑÉëíI=åìíòí=Ç~ë=tÉêâòÉìÖ=HISTOGRAMMK== báåÑ~ÅÜÉê=áëí=Éë=Ç~åå=ÇçÅÜI=ÇáÉ=bñÅÉäJcìåâíáçå=SCHIEFE(...)=òì=îÉêïÉåÇÉåK=iáÉÑÉêí=ëáÉ=å®ãJ äáÅÜ=ÉáåÉå=tÉêí=å~ÜÉ=kìääI=Ç~åå=â~åå=ã~å=E~ìÅÜ=çÜåÉ=dê~ÑáâF=Ç~îçå=~ìëÖÉÜÉåI=Ç~ëë=Éáå= ëóããÉíêáëÅÜÉë= eáëíçÖê~ãã= ÉåíëíÉÜÉå= ïΩêÇÉK= mçëáíáîÉ= tÉêíÉ= ÇÉìíÉå= ~ìÑ= Éáå= êÉÅÜíëëÅÜáÉÑÉë= eáëíçÖê~ãã=Üáå=EëK=_áäÇ=SKQFI=åÉÖ~íáîÉ=tÉêíÉ=ä~ëëÉå=Éáå=äáåâëëÅÜáÉÑÉë=eáëíçÖê~ãã=Éêï~êíÉå= EëK=_áäÇ=SKRFK===

= _áäÇ=SKQW=oÉÅÜíëëÅÜáÉÑÉë=eáëíçÖê~ãã=

= _áäÇ=SKRW=iáåâëëÅÜáÉÑÉë=eáëíçÖê~ãã=



NNQ

däÉáÅÜÉêã~≈Éå=îçå=_ÉÇÉìíìåÖ=áëí=ÄáëïÉáäÉå=ÇáÉ=hÉååò~Üä=ÑΩê=ÇáÉ=t∏äÄìåÖ=Ó=ÇáÉ=hìêíçëáë= EbñòÉ≈I=píÉáäÜÉáíF=ÄÉëÅÜêÉáÄí=ãáí=ÉáåÉê=w~ÜäI=çÄ=Éáå=eáëíçÖê~ãã=Ñä~ÅÜ=çÇÉê=ëíÉáä=îÉêä®ìÑíK== aáÉ=Ç~ÑΩê=îÉêïÉåÇÄ~êÉ=bñÅÉäJcìåâíáçå=ÜÉá≈í=KURT(...)K= eáÉê=ÇáÉåí=ïáÉÇÉê=ÇáÉ=d~ì≈ÛëÅÜÉ=däçÅâÉåâìêîÉ=~äë=fÇÉ~äK=cΩê=ëáÉ=ÖáÄí=ÇáÉ=Éêï®ÜåíÉ=bñÅÉäJ cìåâíáçå=ÇÉå=w~ÜäÉåïÉêí=-1,37026103=~ìëK== gÉ= ®ÜåäáÅÜÉê= ÇáÉ= eáëíçÖê~ããÉ= ÇÉê= däçÅâÉåâìêîÉ= ïÉêÇÉåI= ÇÉëíç= ãÉÜê= å®ÜÉêí= ëáÅÜ= ÇÉê= hìêíçëáëJtÉêí=ÇÉã=ÇÉê=däçÅâÉåâìêîÉ=~åK=gÉ=Ñä~ÅÜÉê=Éáå=eáëíçÖê~ãã=îÉêä®ìÑíI=ÇÉëíç=Öê∏J ≈Éê=ïáêÇ=ÇÉê=îçå=ÇÉê=cìåâíáçå=KURT(...)==~ìëÖÉÖÉÄÉåÉ=w~ÜäÉåïÉêíK=== hçåëíêìáÉêí=ã~å=ÑΩê=ÇÉå=bñíêÉãÑ~ää=Éáå=eáëíçÖê~ãã=çÜåÉ=àÉÖäáÅÜÉ=t∏äÄìåÖI=ÇK=ÜK=ãáí=ÖäÉáJ ÅÜÉå=jÉêâã~äëïÉêíÉåI= Ç~åå= ãÉäÇÉí= ÇáÉ= cìåâíáçå= KURT(...)= ÉáåÉ= aáîáëáçå= ÇìêÅÜ= kìääX= ®åJ ÇÉêí=ã~å=Ç~îçå=åìê=ÉáåÉå=tÉêí=~ÄI=Ç~åå=ÄÉâçããí=ã~å=ÖÉå~ì=ÇáÉ=^åò~Üä=ÇÉê=îÉêÄäÉáÄÉåJ ÇÉå=áÇÉåíáëÅÜÉå=jÉêâã~äëïÉêíÉK===

6.4

Die Verführung: Populationskenngrößen

píÉääÉå= ïáê= ~ÄëÅÜäáÉ≈ÉåÇ= åçÅÜ= Éáåã~ä= ~ääÉ= bñÅÉäJcìåâíáçåÉå= ÉåíëéêÉÅÜÉåÇ= ÇÉê= cêÉèìÉåò= áÜêÉê= kìíòìåÖ= òìë~ããÉåI= ãáí= ÇÉåÉå= ïáê= ÇáÉ= ÄáëÜÉê= Éêï®ÜåíÉå= ëí~íáëíáëÅÜÉå= j~≈ò~ÜäÉå= äÉáÅÜí=ÉêãáííÉäå=â∏ååÉåI=ëçÑÉêå=ÇÉê=a~íÉåÄÉëí~åÇ=ëáÅÜ=áå=ÉáåÉê=bñÅÉäJq~ÄÉääÉ=ÄÉÑáåÇÉíW= = MIN(...)

äáÉÑÉêí=ÇÉå=âäÉáåëíÉå=jÉêâã~äëïÉêí=

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äáÉÑÉêí=ÇÉå=Öê∏≈íÉå=jÉêâã~äëïÉêí=

MEDIAN(...)

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MITTELWERT(...)

äáÉÑÉêí=ÇÉå=aìêÅÜëÅÜåáíí=

VARIANZ(...)

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GEOMITTEL(...)

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7

Korrelation und Regression

7.1

Der Korrelationskoeffizient von Bravais-Pearson

7.1.1

Begriff, Bedeutung, Berechnung

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7.1.2

Herstellung der Punktwolke

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7.2

Regression

7.2.1

Berechnung der Regressionskonstanten

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aÉëÜ~äÄ=åÉååí=ã~å=ÇáÉ=_ÉêÉÅÜåìåÖëãÉíÜçÇÉI=å~ÅÜ=ÇÉê=ÇáÉ=ÄÉáÇÉå=bñÅÉäJcìåâíáçåÉå=STEIGUNG(...;...)=ìåÇ=ACHSENABSCHNITT(...;...)=~êÄÉáíÉåI=ÇáÉ=jÉíÜçÇÉ=ÇÉê=âäÉáåëíÉå=nì~Çê~íÉK== tÉê=ãÉÜê=Ç~êΩÄÉê=ïáëëÉå=ïáääI=ÇÉã=ëÉá=áåëÄÉëçåÇÉêÉ=ÇÉê=^ÄëÅÜåáíí=TKOKO=áå=xPz=ÉãéÑçÜäÉåK==== _Éíê~ÅÜíÉå= ïáê= åìå= åçÅÜ= òìê= fääìëíê~íáçå= ÇáÉ= ÉåíÖÉÖÉåÖÉëÉíòíÉ= ^åå~ÜãÉI= Ç~ëë= ÇáÉ= ìåíÉêÉ= a~íÉåêÉáÜÉ= RY= EÑΩê= óF= ÇáÉ= báåÑäìëëÖê∏≈É= ìåÇ= ÇáÉ= çÄÉêÉ= a~íÉåêÉáÜÉ= RX= EÑΩê= ñF= ÇáÉ= wáÉäÖê∏≈É= ÉåíÜ~äíÉW== aáÉ=a~íÉå=ÇÉê=wÉáäÉ=4=ãáí=ÇÉê=_ÉòÉáÅÜåìåÖ=RY=ïÉêÇÉå=~äë=báåÑäìëëÖê∏≈Éå=~åÖÉëÉÜÉåK== aáÉ=a~íÉå=ÇÉê=wÉáäÉ=3=ãáí=ÇÉê=_ÉòÉáÅÜåìåÖ=RX=ïÉêÇÉå=~äë=wáÉäÖê∏≈Éå=~åÖÉëÉÜÉåK== gÉíòí=ëíêÉÄÉå=ïáê=~äëç=ÇáÉ=ÑçäÖÉåÇÉ=cçêãÉä=~åW= ETKMRF=

=x

= a y→ x y + by→ x

aáÉ= ÄÉáÇÉå= bñÅÉäJcìåâíáçåÉå= STEIGUNG(...;...)= ìåÇ= ACHSENABSCHNITT(...;...)= ãΩëëÉå= åìå= ÉåíëéêÉÅÜÉåÇ=q~ÄÉääÉ=TKR~=~åÇÉêë=ÉáåÖÉíê~ÖÉå=ïÉêÇÉåW==

= q~ÄK=TKR~W=cçêãÉäåI=Ñ~ääë=RY=ÇáÉ=báåÑäìëëÖê∏≈É=êÉéê®ëÉåíáÉêí=

= q~ÄK=TKRÄW=tÉêíÉI=Ñ~ääë=RY=ÇáÉ=báåÑäìëëÖê∏≈É=êÉéê®ëÉåíáÉêí=

= _áäÇ=TKVW=mìåâíïçäâÉ=ãáí=oÉÖêÉëëáçåëÖÉê~ÇÉI=Ñ~ääë=RY=ÇáÉ=báåÑäìëëÖê∏≈É=êÉéê®ëÉåíáÉêí= jáí=ÇÉå=àÉíòí=~ÄÖÉäÉëÉåÉå=w~ÜäÉåïÉêíÉå=ÑΩê=ÇáÉ=píÉáÖìåÖ=ay→x=ìåÇ=ÇÉå=^ÅÜëÉå~ÄëÅÜåáíí=by→x== ÑáåÇÉí=ã~å=åìå=ÇáÉ=ÉãéáêáëÅÜÉ=oÉÖêÉëëáçåëÑçêãÉä== ETKMSF=

=x

= 0,965 ⋅ y + 12,491



NOS

wìê= a~êëíÉääìåÖ= ÇÉê= mìåâíïçäâÉ= ÄÉá= ÇáÉëÉê= òïÉáíÉå= rêë~ÅÜÉJtáêâìåÖëJhçåëíÉää~íáçå= ëçääíÉ= ã~å=~ã=ÄÉëíÉå=îçê=ÇÉã=aêìÅâ=~ìÑ=ÇáÉ=q~ëíÉ= F11 =ÇáÉ=ÄÉáÇÉå=wÉáäÉå=áã=a~íÉåÄÉëí~åÇ=îÉêJ í~ìëÅÜÉåK== aÉåå=bñÅÉä=íê®Öí=ëíÉíë=ÇáÉ=ÉêëíÖÉå~ååíÉ=a~íÉåêÉáÜÉ=EÉêëíÉ=wÉáäÉ=îçå=çÄÉå=çÇÉê=ÉêëíÉ=pé~äJ íÉ=îçå=äáåâëF=~ìÑ=ÇÉê=ï~~ÖÉêÉÅÜíÉå=oìÄêáâÉå~ÅÜëÉ=(X)=~ÄI=åáããí=ëáÉ=ÑçäÖäáÅÜ=ëíÉíë=~äë=rêJ ë~ÅÜÉ=EbáåÑäìëëÖê∏≈ÉF=~åK== aáÉ=~åÇÉêÉ=a~íÉåêÉáÜÉ=ïáêÇ=Ç~ÖÉÖÉå=~ìÑ=ÇÉê=ëÉåâêÉÅÜíÉå=dê∏≈Éå~ÅÜëÉ=(Y)=~ÄÖÉíê~ÖÉåK== _áäÇ=TKV=òÉáÖí=ÇáÉ=mìåâíïçäâÉ=ìåÇ=ÇáÉ=ÉáåÖÉòÉáÅÜåÉíÉ=oÉÖêÉëëáçåëÖÉê~ÇÉK=

7.2.2

Rechnung mit dem Werkzeug REGRESSION

råíÉê=buqo^p^kîvpbJcrkhqflkbk=ÑáåÇÉí=ã~å=ÄÉâ~ååíäáÅÜ=EëáÉÜÉ=^ÄëÅÜåáíí=PKOKQ=~ìÑ=pÉáíÉ= RMF=Éáå=ìãÑ~åÖêÉáÅÜÉë=^åÖÉÄçí=~å=bñÅÉäJtÉêâòÉìÖÉå=òìê=pí~íáëíáâI=ãáí=ÇÉåÉå=ÇÉã=kìíòÉê= ëÉäÄëí=Ç~ë=báåíê~ÖÉå=ÇÉê=bñÅÉäJcìåâíáçåÉå=Éêëé~êí=ïÉêÇÉå=ëçääK=bë=ïìêÇÉ=áã=sÉêä~ìÑ=ÇáÉëÉë= _ìÅÜÉë=ãÉÜêÑ~ÅÜ=~ìÑ=ëçäÅÜÉ=tÉêâòÉìÖÉ=ÜáåÖÉïáÉëÉåI=ìåÇ=åáÅÜí=ëÉäíÉå=Éêëé~êÉå=ëáÉ=í~íë®ÅÜJ äáÅÜ=ÇÉã=kìíòÉê=~ìÑï®åÇáÖÉë=báåíáééÉå=îçå=cìåâíáçåÉå=ìåÇ=cçêãÉäåK== sçê=ÇÉã=tÉêâòÉìÖ=REGRESSION=Ç~ÖÉÖÉå=ëçääíÉ=ÇÉê=^åÑ®åÖÉê=ÖÉï~êåí=ïÉêÇÉåK=t~êìã\==

= q~ÄK=TKSW=a~íÉåÄÉëí~åÇ=

= _áäÇ=TKNMW=tÉêâòÉìÖ=REGRESSION=



=

NOT

pÉÜÉå=ïáê=ìåë=áå=q~ÄÉääÉ=TKS=Éáå=äÉíòíÉë=j~ä=ìåëÉêÉå=a~íÉåÄÉëí~åÇ=~åK=aÉê=tÉêí=ÇÉë=hçêJ êÉä~íáçåëâçÉÑÑáòáÉåíÉå=îçå=0,994=ä®ëëí=~ìÑ=äáåÉ~êÉå=wìë~ããÉåÜ~åÖ=ëÅÜäáÉ≈ÉåK== kÉÜãÉå= ïáê= ïÉáíÉê= ÇÉå= ÉêëíÉå= c~ää= ~åI= Ç~ëë= ÇáÉ= çÄÉêÉ= a~íÉåêÉáÜÉ= R1= ÇáÉ= rêë~ÅÜÉåïÉêíÉ= ìåÇ=ÇáÉ=ìåíÉêÉ=a~íÉåêÉáÜÉ=ÇáÉ=táêâìåÖëïÉêíÉ=R2=ÉåíÜ~äíÉå=ëçääÉåK=== kìå=ïáêÇ=ΩÄÉê=buqo^p^kîvpbJcrkhqflkbkobdobppflk= Ç~ë=tÉêâòÉìÖ= REGRESSION=~åÖÉJ ÑçêÇÉêíK= _áäÇ= TKNM= òÉáÖí= Ç~ë= aá~äçÖÑÉåëíÉêI= áå= Ç~ë= ~ìÅÜ= ÖäÉáÅÜ= ÇáÉ= åçíïÉåÇáÖÉå= ^åÖ~ÄÉå= ÉáåÖÉíê~ÖÉå=ïìêÇÉåK=pç=ïÉáíI=ëç=ÖìíK== açÅÜ=ëÅÜçå=ÇáÉ=bêâä®êìåÖ=ÇÉê=_ÉÇÉìíìåÖ=~ääÉê=h®ëíÅÜÉå=ìåÇ=~ääÉê=_ÉëÅÜêáÑíìåÖÉå=îçå=_áäÇ= TKNM=ïΩêÇÉ=ÇÉå=o~ÜãÉå=ìåÇ=ÇáÉ=j∏ÖäáÅÜâÉáíÉå=ÇáÉëÉë=_ìÅÜÉë=ïÉáí=ΩÄÉêëíÉáÖÉåK=aÉê=Ç~ê~å= áåíÉêÉëëáÉêíÉ=iÉëÉê=ãìëë=äÉáÇÉê=~ìÑ=ÇáÉ=~ìëÑΩÜêäáÅÜÉ=açâìãÉåí~íáçå=áã=eáäÑÉJqÉñí=îÉêïáÉëÉå= ïÉêÇÉåK=táê=â∏ååÉå=ìåë=ÜáÉê=åìê=~ìÑ=dêìåÇë®íòäáÅÜÉë=áã=rãÖ~åÖ=ãáí=ÇÉã=tÉêâòÉìÖ=âçåJ òÉåíêáÉêÉå=Ó=ìåÇ=Ç~ÄÉá=ëÉáåÉ=dêÉåòÉå=ÑΩê=ÇÉå=^åÑ®åÖÉê=~ìÑòÉáÖÉåK===== bë= ÄÉÖáååí= ëÅÜçå= Ç~ãáíI= Ç~ëë= Ç~ë= tÉêâòÉìÖ= åáÅÜí= ãáí= ÉáåÉã= a~íÉåÄÉëí~åÇ= ~êÄÉáíÉå= ïáääI= ÇÉê= Ó= ïáÉ= ÄÉá= ìåë= Ó= ~ìë= êÉáå= Ç~êëíÉääÉêáëÅÜÉå= dêΩåÇÉå= áå= wÉáäÉå= ~åÖÉçêÇåÉí= áëíI= ïáÉ= ÇáÉ= cÉÜäÉêãÉäÇìåÖ=áå=_áäÇ=TKNN=ÉêâÉååÉå=ä®ëëíK=

== _áäÇ=TKNNW=aáÉ=a~íÉåêÉáÜÉå=ãΩëëÉå=áå=pé~äíÉå=ëíÉÜÉå>= kìå= ÖìíI= Ç~ê~å= ëçääÛë= åáÅÜí= ëÅÜÉáíÉêåW= aÉê= a~íÉåÄÉëí~åÇ= ïáêÇ= ã~êâáÉêíI= Ç~åå= âçéáÉêíI= ~åJ ëÅÜäáÉ≈ÉåÇ=ïáêÇ=ÇÉê=q~ÄÉääÉåâìêëçê=áå=ÇáÉ=wÉääÉ=A5=ÖÉëÉíòíK== bë=ÑçäÖí=_bô_bfqbkfkeîqb=bfkc§dbktboqbqo^kpmlkfbobkI=Ç~åå=ïÉêÇÉå=ÇáÉ=wÉáäÉå= 3= ìåÇ=4=ÖÉä∏ëÅÜíI=ìåÇ=ëÅÜçå=ëíÉÜÉå=ÇáÉ=§ÄÉêëÅÜêáÑíÉå=áå=ÇÉå=wÉääÉå=A3=ìåÇ=B3K== aÉê=a~íÉåÄÉëí~åÇ=ëíÉÜí=ÇÉã=tÉêâòÉìÖ=åìåI=ïáÉ=ÖÉïΩåëÅÜíI=áã=pé~äíÉåJ_ÉêÉáÅÜ=îçå=A4=Äáë= B21=òìê=sÉêÑΩÖìåÖK=båíëéêÉÅÜÉåÇ=ïÉêÇÉå=åìå=áã=aá~äçÖÑÉåëíÉê=ÇÉë=tÉêâòÉìÖë=ÇáÉ=pé~äíÉå= ãáí=~ÄÜ®åÖáÖÉê=ìåÇ=ìå~ÄÜ®åÖáÖÉê=s~êá~ÄäÉ=ÉáåÖÉíê~ÖÉåI=_áäÇ=TKNO=òÉáÖí=ÇÉå=sçêÖ~åÖK===

== _áäÇ=TKNOW=báåÖ~ÄÉã~ëâÉ=ÇÉë=tÉêâòÉìÖë=REGRESSION== kìå=ÉêëÅÜÉáåí=ÉåÇäáÅÜ=Ç~ë=cÉåëíÉê=ãáí=ÇÉå=bêÖÉÄåáëëÉåK== páÉ=â∏ååÉå=~åÇÉìíìåÖëïÉáëÉ=áå=_áäÇ=TKNP=ÄÉëí~ìåí=ïÉêÇÉåI=ÇáÉ=iÉëÉêáååÉå=ìåÇ=iÉëÉê=ã∏J ÖÉå= ìåë= îÉêòÉáÜÉåI= Ç~ëë= ïáê= Ö~ê= åáÅÜí= Éêëí= îÉêëìÅÜÉåI= ÇáÉ= PN= ~ìëÖÉÖÉÄÉåÉå= w~ÜäÉåïÉêíÉ= äÉëÄ~ê=òì=éê®ëÉåíáÉêÉåK===



NOU

bêáååÉêå=ïáê=ìåë=Ó=ïáê=ëìÅÜíÉå=åìê=òïÉá=w~ÜäÉåI=å®ãäáÅÜ=ÇáÉ=píÉáÖìåÖ=ìåÇ=ÇÉå=^ÅÜëÉå~ÄJ ëÅÜåáííK=kìå=ÖìíI=Ç~ëë=ÉáåÉ=ÇêáííÉ=w~ÜäI=å®ãäáÅÜ=ÇÉê=hçêêÉä~íáçåëâçÉÑÑáòáÉåí=Eáå=wÉääÉ= B4F=ìåJ ~ìÑÖÉÑçêÇÉêí=ãáíÖÉäáÉÑÉêí=ïáêÇI=Ç~ë=áëí=åçÅÜ=~åòìÉêâÉååÉåK== aáÉ= ~åÖÉÇÉìíÉíÉ= iìéÉ= òÉáÖíI= ïç= ïáê= ìåëÉêÉ= bêÖÉÄåáëëÉ= òì= ëìÅÜÉå= Ü~ÄÉå= Ó= áå= ÇÉå= wÉääÉå= B17=ìåÇ=B18K==

sÉêÖê∏≈Éêå=ïáê=ÇáÉëÉå=_ÉêÉáÅÜI=ëç=ÉêâÉååÉå=ïáê=áå=q~ÄÉääÉ=TKT=Ççêí=áå=ÇÉê=q~í=ÇáÉ=ÖÉëìÅÜJ íÉå= ÄÉáÇÉå= tÉêíÉ= Ó= ÇÉå= ^ÅÜëÉå~ÄëÅÜåáíí= EÜáÉê= ~äë= Schnittpunkt= ÄÉòÉáÅÜåÉíF= ìåÇ= ÇáÉ= píÉáJ ÖìåÖ=EÜáÉê=ÄÉòÉáÅÜåÉí=~äë=X Variable 1FK==

== _áäÇ=TKNPW=bêÖÉÄåáëëÉ=ÇÉë=tÉêâòÉìÖë=REGRESSION=

= q~ÄK=TKTW=dÉëìÅÜíÉ=tÉêíÉ=áã=bêÖÉÄåáëÄä~íí=ÇÉë=tÉêâòÉìÖë=REGRESSION== råÇ= ÇáÉ= êÉëíäáÅÜÉå= OU= ^åÖ~ÄÉå\= eáÉê= Ü~í= ã~å= ÇÉë= dìíÉå= ïçÜä= òìîáÉä= ÖÉí~åX= áã= píêÉÄÉå= å~ÅÜ=ìãÑ~ëëÉåÇÉê=^ìëâìåÑí=ÑΩê=~ääÉ=ÇÉåâÄ~êÉå=mêçÑáë=ïìêÇÉ=ëçîáÉä=~å=iÉáëíìåÖëÑ®ÜáÖâÉáí=áå= Ç~ë=tÉêâòÉìÖ=REGRESSION=ÜáåÉáåÖÉé~ÅâíI=Ç~ëë=ÇÉê=^åÑ®åÖÉê=ÄÉá=ëÉáåÉê=pìÅÜÉ=å~ÅÜ=ÇÉå=ÄÉáJ ÇÉå=w~ÜäÉåïÉêíÉå= ÑΩê= píÉáÖìåÖ= ìåÇ= ^ÅÜëÉå~ÄëÅÜåáíí= îçê= ÇÉê= §ÄÉêÑΩääÉ= ~å= fåÑçêã~íáçåÉå= â~éáíìäáÉêÉå=ãìëëK== aÉã=^åÑ®åÖÉê=ëÅÜÉáåí=~äëç=ãÉÜê=Ç~ãáí=ÖÉÇáÉåí=òì=ëÉáåI=ïÉåå=Éê=~åëíÉääÉ=ÇÉë=tÉêâòÉìJ ÖÉë= REGRESSION= ÇáÉ= ÄÉáÇÉå= äÉáÅÜí= òì= åìíòÉåÇÉå= cìåâíáçåÉå= STEIGUNG(...;...)= ìåÇ= ACHSENABSCHNITT(...;...) ~åïÉåÇÉíK== a~åå=áëí=Éë=ΩÄêáÖÉåë=~ìÅÜ=î∏ääáÖ=ÖäÉáÅÜÖΩäíáÖI=çÄ=ÇÉê=a~íÉåÄÉëí~åÇ=áå=pé~äíÉå=çÇÉê=wÉáäÉå= çêÖ~åáëáÉêí=áëíK== råÇ=ÄÉá=àÉÇÉê=ûåÇÉêìåÖ=áã=a~íÉåÄÉëí~åÇ=é~ëëÉå=ëáÅÜ=ÇáÉ=ãáí=eáäÑÉ=ÇÉê=ÄÉáÇÉå=cìåâíáçJ åÉå= ÉêãáííÉäíÉå= oÉÖêÉëëáçåëâçÉÑÑáòáÉåíÉå= ëíÉíë= òìë®íòäáÅÜ= ~ìíçã~íáëÅÜ= ëçÑçêí= ~å= Ó= ï®ÜJ êÉåÇ= Ç~ë= ëí~íáëÅÜÉ= tÉêâòÉìÖ= REGRESSION= Ç~ÖÉÖÉå= å~ÅÜ= àÉÇÉê= ûåÇÉêìåÖ= âçãéäÉíí= åÉì= ~ìÑÖÉêìÑÉå=ïÉêÇÉå=ãΩëëíÉK==


TKP==jìäíáéäÉ=äáåÉ~êÉ=oÉÖêÉëëáçå=

7.3

NOV

Multiple lineare Regression

få=ÇÉê=q~ÄÉääÉ=TKU=ÄÉÑáåÇÉå=ëáÅÜ=áå=ÇÉå=pé~äíÉå=AI=B=ìåÇ=C=ÇêÉá=ÖäÉáÅÜä~åÖÉ=a~íÉåêÉáÜÉåK== fÜêÉ= pé~äíÉåΩÄÉêëÅÜêáÑíÉå= ÄêáåÖÉå= Éë= ÄÉêÉáíë= òìã= ^ìëÇêìÅâW= aáÉ= tÉêíÉ= ÇÉê= ÄÉáÇÉå= ÉêëíÉå= pé~äíÉå=ëçääÉå=åìå=~åÖÉëÉÜÉå=ïÉêÇÉå=~äë=òïÉá=báåÑäìëëÖê∏≈ÉåI=ï®ÜêÉåÇ=ÇáÉ=tÉêíÉ=áå=ÇÉê= pé~äíÉ=C=ÇáÉ=wáÉäÖê∏≈É=ÄÉëÅÜêÉáÄÉå=ëçääÉåK==

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= q~ÄÉääÉ=TKVÄW=cìåâíáçåëÑçêãÉä=ÉêëÅÜÉáåí=áã=ã~êâáÉêíÉå=_ÉêÉáÅÜ=äáåâë=çÄÉå= aáÉëÉ= cçêãÉä= íÉáäí= òìÉêëí= ÇÉå= _ÉêÉáÅÜ=ÇÉê=~ÄÜ®åÖáÖÉå=s~êá~ÄäÉå= C2:C9 ãáíI= Ç~òì= ÇÉå= ÖÉJ ë~ãíÉå=_ÉêÉáÅÜ=ÇÉê=ÄÉáÇÉå=ìå~ÄÜ®åÖáÖÉå=s~êá~ÄäÉå= A2:B9=ãáíI=ìåÇ=ëáÉ=îÉêä~åÖí=ïÉáíÉê=ÄÉJ ëíáããíÉ=ëí~íáëíáëÅÜÉ=hÉååÖê∏≈ÉåI=~ìÑ=ÇáÉ=ÜáÉê=åáÅÜí=ïÉáíÉê=ÉáåÖÉÖ~åÖÉå=ïÉêÇÉå=â~ååK== ^ÅÜíìåÖW=a~ãáí=ÇáÉ=cìåâíáçå=RGP=áÜêÉ=ÑΩåÑòÉÜå=tÉêíÉ=~ìÑ=~ääÉ=ã~êâáÉêíÉå=wÉääÉå=îÉêíÉáäÉå= â~ååI=ãìëë=ÇáÉ=báåÖ~ÄÉ=ÇÉê=cìåâíáçåëÑçêãÉä=~ÄÖÉëÅÜäçëëÉå=ïÉêÇÉå=ÇìêÅÜ=ÖäÉáÅÜòÉáíáÖÉë= aêΩÅâÉå=îçå==E==Strg==H ⇑ =F=ìåÇ= i↵ ↵i ==K== aÉê=ÉáåÑ~ÅÜÉ=aêìÅâ=~ìÑ=ÇáÉ=bkqboJq~ëíÉ= i↵ ↵i =äáÉÑÉêí=åìê=ÉáåÉå=ÉáåòáÖÉå=tÉêí=å~ÅÜ=A11K= táêÇ=ÇáÉëÉê=eáåïÉáë=ÄÉêΩÅâëáÅÜíáÖíI=Ç~åå=ÉêëÅÜÉáåÉå=í~íë®ÅÜäáÅÜ=áã=ã~êâáÉêíÉå=_ÉêÉáÅÜ=ÇáÉ= ÑΩåÑòÉÜå=bêÖÉÄåáëïÉêíÉ=ÇÉê=j~íêáñÑìåâíáçå=RGP=EëáÉÜÉ=q~ÄÉääÉ=TKVÅFK==


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wì=ÄÉ~ÅÜíÉå=áëí=ÜáÉêÄÉáI=Ç~ëë=ÇÉê=oÉÖêÉëëáçåëâçÉÑÑáòáÉåí=a1=åáÅÜí=ìåíÉê=x1=ìåÇ=ÇÉê=oÉÖêÉëJ ëáçåëâçÉÑÑáòáÉåí=a2=åáÅÜí=ìåíÉê=x2=ëíÉÜíK== aáÉ= wìçêÇåìåÖ= òì= ÇÉå= ÄÉáÇÉå= ìå~ÄÜ®åÖáÖÉå= s~êá~ÄäÉå= äáÉÑÉêí= Ç~åå= ÇáÉ= ÖÉëìÅÜíÉ= oÉÖêÉëëáJ çåëÑìåâíáçåW=== ETKMUF=

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7.4

Nichtlineare Zusammenhänge

7.4.1

Grundlagen

bë=áëí=ÇÉã=jÉåëÅÜÉå=òï~ê=ÖÉÖÉÄÉåI=ÉáåÉ=dê~Ñáâ=~äë=hêÉáë=òì=áÇÉåíáÑáòáÉêÉå=ìåÇ=ÇáÉëÉå=~ìÅÜ= ãΩÜÉäçë= áå= ëÉÅÜòáÖ= ÖäÉáÅÜÉ= qÉáäÉ= òì= ìåíÉêíÉáäÉå= Eëçåëí= â∏ååíÉ= åáÉã~åÇ= ÇáÉ= rÜê= ~ÄäÉëÉåFI= ~ÄÉê=~ì≈Éê=ÇáÉëÉê=c®ÜáÖâÉáí=ÖÉäáåÖí=Éë=åìê=åçÅÜI=ÉáåÉ=dÉê~ÇÉ=ÑÉëíòìëíÉääÉåK==



NPO

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Y = ln y

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= eb ⋅ x a

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y = e 0, 774 ⋅ x 5,72 = 2,7180 , 77 ⋅ x 5, 72 = 2,17 ⋅ x 5, 72

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NPR

t®ÜêÉåÇ=_áäÇ=TKNR=ÇáÉ=mìåâíïçäâÉ=ÇÉê=ÇçééÉäí=äçÖ~êáíÜãáëÅÜ=íê~åëÑçêãáÉêíÉå=a~íÉåêÉáÜÉå= X=ìåÇ=Y=áå=áÜêÉã=ÇÉìíäáÅÜ=ÉêâÉååÄ~êÉ=äáåÉ~êÉå=wìë~ããÉåÜ~åÖ=òÉáÖíI=áëí=áå=_áäÇ=TKNS=áå=ÇáÉ= ÄÉêÉáíë= ~ìë= _áäÇ= TKNQ=ÄÉâ~ååíÉ= mìåâíïçäâÉ= ÇáÉ= hìêîÉ= ÇÉê= ÉñéçåÉåíáÉääÉå= x-y-wìë~ããÉåJ Ü~åÖëÑìåâíáçå=ETKMQF=ÉáåÖÉòÉáÅÜåÉí=ïçêÇÉåK==

= RITO

_áäÇ=TKNSW=mìåâíïçäâÉ=îçå=ñ=ìåÇ=ó=ëçïáÉ=ÇáÉ=^ìëÖäÉáÅÜëâìêîÉ=óZOINT=G=ñ

=

j~å= â~åå= ÇÉìíäáÅÜ= ÉêâÉååÉåI= Ç~ëë= ÇÉê= ÖÉÑìåÇÉåÉ= åáÅÜíäáåÉ~êÉ= x-y-wìë~ããÉåÜ~åÖ= áå= ÇÉê=q~í=ÖÉÉáÖåÉí=áëíI=ÇáÉ=páíì~íáçå=áã=a~íÉåÄÉëí~åÇ=íêÉÑÑÉåÇ=ÑçêãÉäã®≈áÖ=òì=ÄÉëÅÜêÉáÄÉåK==

7.4.2

Transformationen

kìå= áëí= Éë= ~å= ÇÉê= wÉáíI= ÇáÉ= ~åÇÉêÉå= bêâÉååíåáëëÉ=ÇÉê= j~íÜÉã~íáâ=îçêòìëíÉääÉåI=ãáí= ÇÉåÉå= ÑΩê=ïÉáíÉêÉ=åáÅÜíäáåÉ~êÉ=rêë~ÅÜÉJtáêâìåÖëJwìë~ããÉåÜ®åÖÉ=ÉãéáêáëÅÜÉ=cçêãÉäå=ÖÉÑìåÇÉå= ïÉêÇÉå=â∏ååÉåW== p~íò= TKOW= dÉÖÉÄÉå= ëÉáÉå= òïÉá= ÖäÉáÅÜä~åÖÉ= a~íÉåêÉáÜÉå= ãáí= ÇÉå= _ÉòÉáÅÜåìåÖÉå= x= ìåÇ= yI= ïçÄÉá= ~ìë= ë~ÅÜäáÅÜÉå= dêΩåÇÉå= ÄÉâ~ååí= ëÉáI= Ç~ëë= ÇáÉ= oÉáÜÉ= y= ~äë= oÉáÜÉ= ÇÉê= ~ÄÜ®åÖáÖÉå=tÉêíÉ= EwáÉäÖê∏≈ÉF= ìåÇ= ÇáÉ= oÉáÜÉ= x= ~äë= oÉáÜÉ= ÇÉê= ìå~ÄÜ®åÖáÖÉå=tÉêíÉ= EbáåÑäìëëÖê∏≈ÉF=~åÖÉëÉÜÉå=ïÉêÇÉå=â~ååK= bêÖáÄí=ëáÅÜ=å~ÅÜ=ÇÉê=ÉáåÑ~ÅÜ=äçÖ~êáíÜãáëÅÜÉå=qê~åëÑçêã~íáçå=îçå=y ÖÉã®≈= ETKNQF==

=X

=x

Y = ln y

ÑΩê=ÇáÉ=íê~åëÑçêãáÉêíÉ=XJYJa~íÉåêÉáÜÉ=ÉáåÉ=ÉãéáêáëÅÜÉ=äáåÉ~êÉ=wìë~ããÉåÜ~åÖëÑçêãÉä= ETKNRF==

=Y = aX += b

ëç=ÄÉëíÉÜí=òïáëÅÜÉå=x=ìåÇ=y=ÇÉê=ÉãéáêáëÅÜÉ=åáÅÜíäáåÉ~êÉ=wìë~ããÉåÜ~åÖ= ETKNSF==

=y

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=



NPS

p~íò= TKPW= dÉÖÉÄÉå= ëÉáÉå= òïÉá= ÖäÉáÅÜä~åÖÉ= a~íÉåêÉáÜÉå= ãáí= ÇÉå= _ÉòÉáÅÜåìåÖÉå= x= ìåÇ= yI= ïçÄÉá= ~ìë= ë~ÅÜäáÅÜÉå= dêΩåÇÉå= ÄÉâ~ååí= ëÉáI= Ç~ëë= ÇáÉ= oÉáÜÉ= y= ~äë= oÉáÜÉ= ÇÉê= ~ÄÜ®åÖáÖÉå=tÉêíÉ= EwáÉäÖê∏≈ÉF= ìåÇ= ÇáÉ= oÉáÜÉ= x= ~äë= oÉáÜÉ= ÇÉê= ìå~ÄÜ®åÖáÖÉå=tÉêíÉ= EbáåÑäìëëÖê∏≈ÉF=~åÖÉëÉÜÉå=ïÉêÇÉå=â~ååK= bêÖáÄí=ëáÅÜ=å~ÅÜ=ÇÉê=ÉáåÑ~ÅÜ=äçÖ~êáíÜãáëÅÜÉå=qê~åëÑçêã~íáçå=îçå=x=ÖÉã®≈= ETKNTF==

=X

= ln x = Y = y=

ÑΩê=ÇáÉ=íê~åëÑçêãáÉêíÉ=XJYJa~íÉåêÉáÜÉ=ÉáåÉ=ÉãéáêáëÅÜÉ=äáåÉ~êÉ=wìë~ããÉåÜ~åÖëÑçêãÉä= ETKNUF==

=Y = aX += b

ëç=ÄÉëíÉÜí=òïáëÅÜÉå=x=ìåÇ=y=ÇÉê=ÉãéáêáëÅÜÉ=åáÅÜíäáåÉ~êÉ=wìë~ããÉåÜ~åÖ= ETKNVF==

=y

= b + a=⋅ ln x

a~ê~ìë=ÉêÖáÄí=ëáÅÜ=ÑçäÖÉåÇÉ=^åäÉáíìåÖ=òìã=e~åÇÉäåW== iáÉÖí=Éáå=a~íÉåÄÉëí~åÇ=îçêI=ÇÉê=~ìë=òïÉá=ÖäÉáÅÜä~åÖÉå=a~íÉåêÉáÜÉå=ÄÉëíÉÜíI=ìåÇ=ÄÉá=ÇÉJ åÉå=ÉáåÉ=a~íÉåêÉáÜÉ= ~ìë= ë~ÅÜäáÅÜÉå=dêΩåÇÉå= ~äë=báåÑäìëëÖê∏≈É= ExF= ìåÇ=ÇáÉ= ~åÇÉêÉ= a~J íÉåêÉáÜÉ=~äë=wáÉäÖê∏≈É=EyF=~åÖÉëÉÜÉå=ïÉêÇÉå=â~ååI=Ç~åå=ëçääíÉå=ÖêìåÇë®íòäáÅÜ=åÉÄÉå=ÇÉå= ^ìëÖ~åÖëÇ~íÉå=ïÉáíÉêÉ=ÇêÉá=wìë~ããÉåëíÉääìåÖÉå=îçå=íê~åëÑçêãáÉêíÉå=tÉêíÉé~~êÉåI=ïáÉ= áå=ÇÉê=q~ÄÉääÉ=TKNP=Ç~êÖÉëíÉääíI=áå=Ç~ë=bñÅÉäJ_ä~íí=ÉáåÖÉíê~ÖÉå=ïÉêÇÉåK==

= q~ÄK=TKNP~W=cçêãÉäå=

= q~ÄK=TKNPÄW=tÉêíÉ= aáÉ=îáÉê=hçêêÉä~íáçåëâçÉÑÑáòáÉåíÉå=áå=ÇÉê=ÉêëíÉå=wÉáäÉ=ÖÉÄÉå=Ç~åå=Ç~êΩÄÉê=^ìëâìåÑíI=ïÉäJ ÅÜÉë= pé~äíÉåé~~ê= ÑΩê= ÇáÉ= äáåÉ~êÉ=oÉÖêÉëëáçåëêÉÅÜåìåÖ= áåÑê~ÖÉ= âçããíW= fëí= ÇÉê= hçêêÉä~íáJ çåëâçÉÑÑáòáÉåí=áå=ÇÉê=wÉääÉ= A1=å~ÜÉ=N=çÇÉê=JNI=Ç~åå=áëí=ÉáåÑ~ÅÜÉ=äáåÉ~êÉ=oÉÖêÉëëáçå=ëáååJ îçääK= fëí= ÇÉê= tÉêí= áå= ÇÉê= wÉääÉ= D1= å~ÜÉ= N= çÇÉê= JNI= Ç~åå= â~åå= p~íò=TKP= òìê= ^åïÉåÇìåÖ= âçããÉåK=dáäí=Ç~ë=ÑΩê=ÇÉå=tÉêí=áå=ÇÉê=wÉääÉ= G1I=Ç~åå=âçããí=p~íò=TKO=òìê=^åïÉåÇìåÖK= cáåÇÉí=ëáÅÜ=áå=ÇÉê=wÉääÉ=J1=Éáå=ëçäÅÜÉê=tÉêíI=Ç~åå=â~åå=p~íò=TKN=~åÖÉï~åÇí=ïÉêÇÉåK==


=

8

Zeitreihen

8.1

Begriff und Erfassung

báåÉ=wÉáíêÉáÜÉ=áëí=ÉáåÉ=òÉáíäáÅÜ=ÖÉçêÇåÉíÉ=cçäÖÉ=îçå=jÉêâã~äëïÉêíÉåK== lÇÉê=~åÇÉêë=ÖÉëéêçÅÜÉå=Ó=ìåÇ=ìã=ÇáÉ=sÉêÄáåÇìåÖ=òìã=îçêáÖÉå=^ÄëÅÜåáíí=ÜÉêòìëíÉääÉå=Ó= ÇáÉ= ÄÉíê~ÅÜíÉíÉå= báåÑäìëëÖê∏≈Éå= ëáåÇ= ÜáÉê= ëéÉòáÉää= a~íìãëJ= çÇÉê= wÉáí~åÖ~ÄÉåI= òì= ÇÉåÉå= Ç~åå=~äë=wáÉäÖê∏≈Éå=àÉïÉáäë=ÄÉëíáããíÉ=~åÇÉêÉ=tÉêíÉ=ÖÉÜ∏êÉåK= bñÅÉä=ëíÉääí=òìê=^êÄÉáí=ãáí=wÉáíêÉáÜÉå=ÉáåÉ=ÄÉ~ÅÜíäáÅÜÉ=jÉåÖÉ=îçå=eáäÑëãáííÉäå=ÄÉêÉáíK== sçê~ìëëÉíòìåÖ= ÑΩê= ÇáÉ=kìíòÄ~êâÉáí= ÇáÉëÉê=eáäÑëãáííÉä= áëí= ~ääÉêÇáåÖë= áå= àÉÇÉã= c~ääÉI= Ç~ëë= ÇáÉ= a~íìãëJ=çÇÉê=wÉáí~åÖ~ÄÉå=~äë=åìãÉêáëÅÜÉ=tÉêíÉ=îçå=bñÅÉä=Éêâ~ååí=ïÉêÇÉå=â∏ååÉåK=== pçää= òìã= _ÉáëéáÉä= ÉáåÉ= ãçå~íäáÅÜÉ=båíïáÅâäìåÖ= Ç~êÖÉëíÉääí= ïÉêÇÉåI= Ç~åå= áëí= ÇáÉ= åáÅÜíåìJ ãÉêáëÅÜÉ=báåÖ~ÄÉ=ÇÉê=a~íìãë~åÖ~ÄÉå=EÜáÉê=ëáåÇ=Éë=ÇáÉ=jçå~íë~ÄâΩêòìåÖÉåF=ïáÉ=áå=q~ÄÉäJ äÉ=UKN~=çÑí=ìåÄê~ìÅÜÄ~ê=ÑΩê=ÇáÉ=ïÉáíÉêÉ=sÉê~êÄÉáíìåÖK==

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8.2

Experimentell-visuelle Trendermittlung

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aÉê=bÑÑÉâí=áëí=Ó=òìãáåÇÉëí=çéíáëÅÜ=Ó=ΩÄÉêòÉìÖÉåÇW== jáí=~ääÉå=ÇêÉá=qêÉåÇäáåáÉå=ÉêÜ®äí=ã~å=ÑΩê=kçîÉãÄÉê=ìåÇ=aÉòÉãÄÉê=å~ÜÉòì=ÇáÉ=ÖäÉáÅÜÉå= qêÉåÇïÉêíÉK== j~å=ëçääíÉ=ÇáÉëÉë=Ó=êÉáå=îáëìÉääÉ=bêÖÉÄåáë=Ó=~ääÉêÇáåÖë=åáÅÜí=ΩÄÉêÄÉïÉêíÉåI=ÉáåÉ=ëí~íáëíáëÅÜÉ= iÉÖáíáã~íáçå=ÑΩê=ÇáÉëÉë=sçêÖÉÜÉå=ëíÉÜí=åçÅÜ=~ìëK= _Éíê~ÅÜíÉå=ïáê=åçÅÜ=Éáå=òïÉáíÉë=_ÉáëéáÉäW=q~ÄÉääÉ=UKQ=ÉåíÜ®äí=jÉëëÉêÖÉÄåáëëÉI=ÇáÉ=òì=àÉÇÉê= Ü~äÄÉå=píìåÇÉ=~ÄÖÉäÉëÉå=ïìêÇÉåK=tÉäÅÜÉ=mêçÖåçëÉ=â∏ååíÉ=ã~å=Ç~ê~ìë=ÑΩê=NPWPM=rÜê=~ÄJ äÉáíÉå\==

= q~ÄK=UKQW=jÉëëÉêÖÉÄåáëëÉ= wìÉêëí=ëçääíÉ=ã~å=ëáÅÜ=ΩÄÉêòÉìÖÉåI=çÄ=ÇáÉ=rÜêòÉáíÉå=ÇÉë=a~íÉåÄÉëí~åÇÉë=í~íë®ÅÜäáÅÜ=åìãÉJ êáëÅÜ=ÉêÑ~ëëí=ïçêÇÉå=ëáåÇK== wìê= hçåíêçääÉ= ëÉíòí= ã~å= ÇÉå= q~ÄÉääÉåâìêëçê= áå= ÇáÉ= wÉääÉ= A1= ìåÇ= Ñçêã~íáÉêí= ãáííÉäë= cloJ j^qwbiibkwêibkwêi= ëÅÜåÉää= Éáåã~ä= ìãK= páÉÜí= ã~å= Ç~ååI= ïÉåå= ã~å=ÜáåêÉáÅÜÉåÇ=

îáÉäÉ= aÉòáã~äëíÉääÉå= ÉáåëíÉääíI= ÇáÉ= w~Üä= 0,354166666666667= Ó= Ç~åå= Ü~í= bñÅÉä= í~íë®ÅÜäáÅÜ= ~åJ ëíÉääÉ= ÇÉê= ~åÖÉòÉáÖíÉå=wÉáí=áÜêÉå= rÜêòÉáíïÉêí= Eëç= ÄÉòÉáÅÜåÉí= áå= ^åäÉÜåìåÖ= ~å= ÇÉå= ÑêΩÜÉê= ëÅÜçå=Éêï®ÜåíÉå=a~íìãëïÉêíF=ÖÉëéÉáÅÜÉêíK== ^äëç= áëí= ÇáÉ= sçê~ìëëÉíòìåÖ= ÉêÑΩääíI= ÇÉê= ÖÉë~ãíÉ=a~íÉåÄÉëí~åÇ=áëí=åìãÉêáëÅÜ=ÖÉëéÉáÅÜÉêíI= ÇáÉ=bñÅÉäJiÉáëíìåÖÉå=òìê=mêçÖåçëÉ=ãáí=eáäÑÉ=ÇÉê=qêÉåÇäáåáÉå=â∏ååÉå=áå=^åëéêìÅÜ=ÖÉåçãJ ãÉå=ïÉêÇÉåK== aáÉ= ^åòÉáÖÉ= ÇÉê= ÉêëíÉå= rÜêòÉáí= ïáêÇ= ~äëç= òìêΩÅâÖÉëíÉääíI= ÇÉê= q~ÄÉääÉåâìêëçê= áå= ÇÉå= ëÉé~J êáÉêíÉå=a~íÉåÄÉêÉáÅÜ=A1:L2=ÖÉëÉíòí=ìåÇ=ãáí=ÇÉã=aá~Öê~ãã~ëëáëíÉåíÉå=çÇÉê=ÇÉê= F11 =J=jÉJ íÜçÇÉ= ïáêÇ= òìã= a~íÉåÄÉëí~åÇ= Ç~ë= iáåáÉåÇá~Öê~ãã= EïáÉÇÉê= ~ã= ÄÉëíÉå= çÜåÉ= ÇáÉ= sÉêÄáåJ ÇìåÖëäáåáÉåI=åìê=ãáí=ÇÉå=j~êâáÉêìåÖëéìåâíÉåF=ÜÉêÖÉëíÉääíK=== _áäÇ= UKT= ~ìÑ= pÉáíÉ= NQO= ÉåíÜ®äí= ÇáÉ= wÉáíêÉáÜÉ= ãáí= ÇÉå= ÑêÉáÉå= mçëáíáçåÉå= ÑΩê= NPWPM= rÜê= ìåÇ= NQWMM=rÜêK=få=_áäÇ=UKU=áëí=ÇáÉ=äáåÉ~êÉ=qêÉåÇäáåáÉ=ÉáåÖÉíê~ÖÉåK=_áäÇ=UKV=ÉåíÜ®äí=ÇáÉ=wÉáíêÉáÜÉ= ãáí=ÉñéçåÉåíáÉääÉê=qêÉåÇäáåáÉK== eáÉê=~ääÉêÇáåÖë=ëÅÜÉáåí=çÑÑÉåëáÅÜíäáÅÜ=òì=ëÉáåI=Ç~ëë=ÇáÉ=ÉñéçåÉåíáÉääÉ=qêÉåÇäáåáÉ=ÇÉå=ÖÉãÉëJ ëÉåÉå=sÉêä~ìÑ=~ã=ÄÉëíÉå=ïáÉÇÉêÖáÄí=ìåÇ=ëáÉ=ëçãáí=~ìÅÜ=ÑΩê=ÇáÉ=mêçÖåçëÉ=ÖÉÉáÖåÉí=ëÅÜÉáåíK==

8.3

Lineare Zeitreihen und die TREND-Funktion

fëí= ÇÉê=a~íÉåÄÉëí~åÇ= áå=ÇÉå= a~íìãëJ= çÇÉê= wÉáí~åÖ~ÄÉå= åìãÉêáëÅÜ=ÉêÑ~ëëíI= Ç~åå=ëíÉÜí= å~J íΩêäáÅÜ=~ìÅÜ=ÇÉê=hçêêÉä~íáçåëâçÉÑÑáòáÉåí=EîÉêÖäK=^ÄëÅÜåáíí=TKNF=òìê=_ÉïÉêíìåÖ=ã∏ÖäáÅÜÉê=iáJ åÉ~êáí®í=ÇÉë=wìë~ããÉåÜ~åÖÉë=òìê=sÉêÑΩÖìåÖK== tÉåå=Éë=~ìëëÅÜäáÉ≈äáÅÜ=ìã=ÇáÉ=iáåÉ~êáí®í=ÖÉÜí=ìåÇ=ÇáÉ=oáÅÜíìåÖ=ÇÉë=^åëíáÉÖë=âÉáåÉ=oçääÉ= ëéáÉäíI=ÄÉåìíòí=ã~å=ÖÉêå=~ìÅÜ=Ç~ë=nì~Çê~í=ÇÉë=mÉ~êëçåÛëÅÜÉå=hçêêÉä~íáçåëâçÉÑÑáòáÉåíÉåI= Ç~ë=~äë=_ÉëíáããíÜÉáíëã~≈=ÄÉòÉáÅÜåÉí=ïáêÇK== pÉÜÉå=ïáê=ìåë=ÇáÉë=~ã=_ÉáëéáÉä=~ìë=ÇÉå=q~ÄÉääÉå=UKR~LÄ=~ìÑ=pÉáíÉ=NQP=~åK=a~=ÇáÉ=a~íìãëJ ïÉêíÉ=åìãÉêáëÅÜ=ÉêÑ~ëëí=ëáåÇI=â∏ååÉå=hçêêÉä~íáçåëâçÉÑÑáòáÉåí=ìåÇ=_ÉëíáããíÜÉáíëã~≈=ëçÑçêí= ãáí=eáäÑÉ=ÇÉê=ÉåíëéêÉÅÜÉåÇÉå=bñÅÉäJcìåâíáçåÉå=ÄÉêÉÅÜåÉí=ïÉêÇÉåK==



NQO =

= _áäÇ=UKTW=jÉëëïÉêíÉ=îçå=UWPM=Äáë=NPWMM=rÜê=

= _áäÇ=UKUW=jÉëëïÉêíÉ=îçå=UKPM=Äáë=NPWMM=rÜê=ìåÇ=äáåÉ~êÉ=qêÉåÇäáåáÉ=

= = =

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UKP==iáåÉ~êÉ=wÉáíêÉáÜÉå=ìåÇ=ÇáÉ=qobkaJcìåâíáçå=

NQP

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= q~ÄK=UKR~W=cçêãÉäå=

= q~ÄK=UKRÄW=tÉêíÉ= j~å=â~åå=ïçÜä=ÉáåÉå=äáåÉ~êÉå=wìë~ããÉåÜ~åÖ=~ååÉÜãÉå=Ó=Ç~ë=ï®êÉ=~ìÅÜ=ëçÑçêí=~ìë=ÉáJ åÉê=dê~Ñáâ=ãáí=ÇÉê=mìåâíïçäâÉ=ÉêâÉååÄ~êK== cçäÖäáÅÜ=áëí=Éë=åìå=ã∏ÖäáÅÜI=ÇáÉ=ÄÉáÇÉå=ÖÉëìÅÜíÉå=qêÉåÇïÉêíÉ=ÑΩê=kçîÉãÄÉê=ìåÇ=aÉòÉãJ ÄÉê= êÉÅÜåÉêáëÅÜ= ÖÉå~ì= òì=ÄÉëíáããÉåK= a~òì= ïÉêÇÉå= òìÉêëí= ÇáÉ=hçÉÑÑáòáÉåíÉå=ÇÉê=oÉÖêÉëëáJ çåëÖÉê~ÇÉ=ÉêãáííÉäíK== aáÉ=q~ÄÉääÉå=UKS~LÄ=òÉáÖÉå=cçêãÉäå=ìåÇ=bêÖÉÄåáëëÉK==

= q~ÄK=UKS~W=cçêãÉäå=

= q~ÄK=UKSÄW=tÉêíÉ= j~å=äáÉëí=ëçÑçêí=ÇáÉ=däÉáÅÜìåÖ=ÇÉê=oÉÖêÉëëáçåëÖÉê~ÇÉ=~ÄW== EUKMNF=

=Merkmalswert

= 0,001122709 ⋅ Datumswert - 29,43253314

rã=ÇáÉ=mêçÖåçëÉïÉêíÉ=ÑΩê=kçîÉãÄÉê=ìåÇ=aÉòÉãÄÉê=ÄÉêÉÅÜåÉå=òì=â∏ååÉåI=ÄÉå∏íáÖÉå=ïáê= ÑçäÖäáÅÜ=ÇáÉ=ÄÉáÇÉå=òìÖÉÜ∏êáÖÉå=a~íìãëïÉêíÉK=páÉ=â∏ååÉå=ïáê=ÉêÜ~äíÉåI=áåÇÉã=ïáê=ÇáÉ=^åJ òÉáÖÉ=ãáííÉäë=cloj^qwbiibkwêi=ìãëíÉääÉåE=ëK=q~ÄÉääÉ=UKTFK===

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NQQ = EUKMOF=

=Novemberwert

= 0,001123 ⋅ 39387 - 29,43253314 ≈ 14,79

EUKMPF=

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= 0,001122709 ⋅ 39417 - 29,43253314 ≈ 14,82

k~íΩêäáÅÜ= Ü®ííÉ= ã~å= ~ìÅÜ= ÖäÉáÅÜ= áå= ÇÉê= bñÅÉäJq~ÄÉääÉ= êÉÅÜåÉå= ä~ëëÉå= â∏ååÉåK= açÅÜ= ~ìÅÜ= Ç~ë= áëí=åáÅÜí=å∏íáÖ=Ó=ÇáÉ= ÄÉáÇÉå= ÖÉëìÅÜíÉå=qêÉåÇïÉêíÉ= ä~ëëÉå=ëáÅÜ=ãáí=bñÅÉä= îáÉä=ëÅÜåÉääÉê= ìåÇ=ÄÉèìÉãÉê=ÉêãáííÉäåK== táêÇ=ÇáÉ=bñÅÉäJcìåâíáçå= TREND(...;...;...)=îÉêïÉåÇÉíI=Ç~åå=â~åå=ã~å=ëáÅÜ=ÇáÉ=bêãáííJ äìåÖ=ÇÉê=oÉÖêÉëëáçåëÑçêãÉä=ëé~êÉåK= ^å=ÇáÉ=ÉêëíÉ=mçëáíáçå=ÇÉê= TRENDJcìåâíáçå=áëí=Ç~ÄÉá=ÇÉê=_ÉêÉáÅÜ=ãáí=ÇÉå=~ÄÜ®åÖáÖÉå=s~êá~ÄJ äÉå= EÄÉá= ìåëÉêÉå= wÉáíêÉáÜÉå= ~äëç= ÇÉê= _ÉêÉáÅÜ= ÇÉê= jÉêâã~äëïÉêíÉF= Éáåòìíê~ÖÉåK= aáÉ= òïÉáíÉ= mçëáíáçå= ãìëë= ÇÉå= _ÉêÉáÅÜ=ÇÉê=ìå~ÄÜ®åÖáÖÉå=s~êá~ÄäÉå= ÄÉâçããÉå= Erêë~ÅÜÉåïÉêíÉW= ÄÉá= ìåë= ÇáÉ= a~íìãë~åÖ~ÄÉåFK= ^å= ÇáÉ= ÇêáííÉ= píÉääÉ= ëÅÜäáÉ≈äáÅÜ= âçããí= ÇáÉ= wÉääÉ= ãáí= ÇÉã= a~J íìãëïÉêí=ÇÉë=ÖÉëìÅÜíÉå=jçå~íëK==

= q~ÄK=UKU~W=^åïÉåÇìåÖ=ÇÉê=TRENDJcìåâíáçå=

= q~ÄK=UKUÄW=TRENDJcìåâíáçåW=tÉêíÉ få=ÇÉå=ÄÉáÇÉå=q~ÄÉääÉå=UKU~=ìåÇ=UKUÄ=áëí=Ç~ë=sçêÖÉÜÉå=Ç~êÖÉëíÉääíK=bë=ÉêÖÉÄÉå=ëáÅÜ=Ó=å~J íΩêäáÅÜ=Ó=ÇáÉëÉäÄÉå=w~ÜäÉåïÉêíÉ=ïáÉ=ÄÉá=ÇÉê=çÄáÖÉå=^ìëïÉêíìåÖ=ÇÉê=oÉÖêÉëëáçåëÑçêãÉäK== a~ë=Ç~êÑ= ~ìÅÜ= åáÅÜí=îÉêïìåÇÉêäáÅÜ= ëÉáåI= ÇÉåå=ÇáÉ=cìåâíáçå= TREND(...;...;...)= ~êÄÉáíÉí= ÖÉå~ì=ëçI=ïáÉ=ïáê=Éë=ÉáåÖ~åÖë=ÇÉãçåëíêáÉêíÉåW== páÉ=ÄÉëíáããí=ÉÄÉåÑ~ääë=òìÉêëí=ÇáÉ=oÉÖêÉëëáçåëâçÉÑÑáòáÉåíÉå=ãáí=eáäÑÉ=ÇÉê=cìåâíáçåÉå=STEIGUNG(...;...)= ìåÇ= ACHSENABSCHNITT(...;...),= ìåÇ= Ç~åå= ëÉíòí= ëáÉ= ÇÉå= àÉïÉáäáÖÉå= a~J íìãëïÉêí=áå=ÇáÉ=däÉáÅÜìåÖ=ÇÉê=oÉÖêÉëëáçåëÖÉê~ÇÉå=ÉáåK=

8.4

Gleitender Durchschnitt

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NQS =

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= _áäÇ=UKNNW=däÉáíÉåÇÉê=aìêÅÜëÅÜåáíí=ãáí=ÑΩåÑ=ÉáåÄÉòçÖÉåÉå=tÉêíÉå= iáÉÖí=ÉáåÉ=ÖÉê~ÇÉ=^åò~Üä=îçå=òÉáíêÉáÜÉåïÉêíÉå=îçêI=Ç~åå=ÇΩêÑÉå=ÇÉê=ÉêëíÉ=ìåÇ=äÉíòíÉ=ÄÉJ êΩÅâëáÅÜíáÖíÉ= tÉêí= àÉïÉáäë= åìê= òìê=e®äÑíÉ= áå= ÇáÉ=aìêÅÜëÅÜåáííëÄáäÇìåÖ= ÉáåÖÉÜÉåI= ìåÇ=Éë= ãìëë=ÇìêÅÜ=ÇáÉ=ìã=báåë=îÉêêáåÖÉêíÉ=^åò~Üä=ÇáîáÇáÉêí=ïÉêÇÉåK== aáÉ=q~ÄÉääÉå=UKNN~=ìåÇ=UKNNÄ=ëÅÜáäÇÉêå=Ç~ë=sçêÖÉÜÉåI=Ñ~ääë=ëÉÅÜë=jçå~íëïÉêíÉ=áå=ÇÉå=ÖäÉáJ íÉåÇÉå=aìêÅÜëÅÜåáíí=ÉáåÄÉòçÖÉå=ïÉêÇÉå=ëçääÉåK==


UKR==dêìåÇä~ÖÉå=ÇÉê=wÉáíêÉáÜÉå~å~äóëÉ=

NQT

=

= q~ÄK=UKNN~W=cçêãÉäåW=aìêÅÜëÅÜåáííëòÉáíê~ìã=ãáí=ëÉÅÜë=tÉêíÉå=

= q~ÄK=UKNNÄW=bêÖÉÄåáëëÉW=aìêÅÜëÅÜåáííëòÉáíê~ìã=ãáí=ëÉÅÜë=tÉêíÉå= aáÉ= jÉíÜçÇÉ= ÇÉê= ÖäÉáíÉåÇÉå= aìêÅÜëÅÜåáííÉ= ïáêÇ= îÉêÉáåòÉäí= ~äë= ÉáåÉ= łêÉä~íáî= ~åëéêìÅÜëäçëÉ= jÉíÜçÇÉ=ÄÉòÉáÅÜåÉíI=ÇÉê=ÇÉëÜ~äÄ=ÖÉäÉÖÉåíäáÅÜ=ÖÉêáåÖÉ=^ìÑãÉêâë~ãâÉáí=ÖÉëÅÜÉåâí=ïáêÇK== jáí=ÇÉê=_ÉêÉÅÜåìåÖ=ÖäÉáíÉåÇÉê=aìêÅÜëÅÜåáííÉ=ÄÉÖáååí=~ÄÉê=áã=oÉÖÉäÑ~ää=ÇáÉ=ëç=ÖÉå~ååíÉ= wÉáíêÉáÜÉå~å~äóëÉI=Éáå=ëí~íáëíáëÅÜÉë=sÉêÑ~ÜêÉåI=ÄÉá=ÇÉã=ÉáåÉ=îçêäáÉÖÉåÇÉ=wÉáíêÉáÜÉ=òÉêäÉÖí= ïáêÇ=áå=qêÉåÇÉåíïáÅâäìåÖI=òóâäáëÅÜÉ=pÅÜï~åâìåÖÉåI=ë~áëçå~äÉ=ëçïáÉ=áêêÉÖìä®êÉ=pÅÜï~åJ âìåÖÉåK==

8.5

Grundlagen der Zeitreihenanalyse

aáÉ= jÉíÜçÇÉ= ÇÉê= ÖäÉáíÉåÇÉå= aìêÅÜëÅÜåáííÉ= áããÉê= Ç~åå= Öìí= ÉáåÖÉëÉíòí= ïÉêÇÉåI= ïç= Éë= ìã=Ç~ë=bêâÉååÉå=ÉáåÉë=qêÉåÇë=~ìë=wÉáíêÉáÜÉåïÉêíÉå=ÖÉÜíK== aáÉ=wÉáíêÉáÜÉå~å~äóëÉ=Ä~ëáÉêí=áã=ïÉëÉåíäáÅÜÉå=~ìÑ=ÇÉã=~ÇÇáíáîÉå=wÉáíêÉáÜÉåãçÇÉääI=Ç~ë=òìJ å®ÅÜëí= âìêò= îçêÖÉëíÉääí= ïÉêÇÉå= ëçääI= ÄÉîçê= ~ìÑ= ÇáÉ= jÉíÜçÇÉå= ÇÉê= wÉáíêÉáÜÉå~å~äóëÉ= å®ÜÉê= ÉáåÖÉÖ~åÖÉå=ïáêÇK==



NQU

8.5.1

Aufbau des additiven Zeitreihenmodells

a~ë=~ÇÇáíáîÉ=wÉáíêÉáÜÉåãçÇÉää=Ä~ëáÉêí=~ìÑ=ÇÉê=sçêëíÉääìåÖI=Ç~ëë=ëáÅÜ=wÉáíêÉáÜÉåïÉêíÉ=áå=îÉêJ ëÅÜáÉÇÉåÉ=qÉáäâçãéçåÉåíÉå=òÉêäÉÖÉå=ä~ëëÉåK== aáÉ= _ÉòÉáÅÜåìåÖ= ~ÇÇáíáîÉë=wÉáíêÉáÜÉåãçÇÉää= êΩÜêí= Ç~ÜÉêI= Ç~ëë= ÇáÉ= pìããÉ=ÇÉê=qÉáäâçãJ éçåÉåíÉå=áã=båÇÉêÖÉÄåáë=ïáÉÇÉê=ÇáÉ=ìêëéêΩåÖäáÅÜÉ=wÉáíêÉáÜÉ=ÉêÖáÄíK== iÉÖí= ã~å= ÉáåÉ= wÉáíêÉáÜÉ= òìÖêìåÇÉI= ÇáÉ= ëáÅÜ= ΩÄÉê= ÉáåÉå= ä®åÖÉêÉå= wÉáíê~ìã= ÉêëíêÉÅâíI= òK= _K= ΩÄÉê=ãÉÜêÉêÉ=g~ÜêÉI=ìåÇ=ÑΩê=ÇáÉ=tÉêíÉ=ÑΩê=âäÉáåÉêÉ=fåíÉêî~ääÉI=òK=_K=jçå~íëïÉêíÉI=òìê=sÉêJ ÑΩÖìåÖ=ëíÉÜÉåI=Ç~åå=ä~ëëÉå=ëáÅÜ=Ç~ê~ìë=áã=fÇÉ~äÑ~ää=îáÉê=hçãéçåÉåíÉå=łÜÉê~ìëÑáäíÉêåK== aáÉëÉ=hçãéçåÉåíÉå=ëáåÇ=áã=ÉáåòÉäåÉåW= Trendkomponente T

aáÉ= qêÉåÇâçãéçåÉåíÉ= T= ÅÜ~ê~âíÉêáëáÉêí= ÇáÉ= ä~åÖÑêáëíáÖÉ= båíïáÅâäìåÖ= ÇÉê= wÉáíêÉáÜÉX= ëáÉ= áëí= ÉåíïÉÇÉê=ãçåçíçå=ëíÉáÖÉåÇ=çÇÉê=Ñ~ääÉåÇK== aáÉ=qêÉåÇâçãéçåÉåíÉ=ïáêÇ=áã=~ääÖÉãÉáåÉå=ÇìêÅÜ=ÉáåÉ=äáåÉ~êÉ=oÉÖêÉëëáçå=Eãáí=ÇÉê=wÉáí=~äë= báåÑäìëëÖê∏≈ÉF=ÄÉêÉÅÜåÉí=EëáÉÜÉ=^ÄëÅÜåáíí=TKO=~ìÑ=pÉáíÉ=NOPFK= Zyklische Komponente Z

aáÉ=òóâäáëÅÜÉ=hçãéçåÉåíÉ=Z=Ü~í=áã=fÇÉ~äÑ~ää=ÉáåÉå=ïÉääÉåÑ∏êãáÖÉå=sÉêä~ìÑ=ìåÇ=ÅÜ~ê~âíÉêáJ ëáÉêí=ÇáÉ=âçåàìåâíìêÉääÉå=pÅÜï~åâìåÖÉå=ÉáåÉê=wÉáíêÉáÜÉK== aáÉ= hÉååíåáë= ÇÉë= äáåÉ~êÉå=qêÉåÇë= T= ìåÇ= ÇÉê= âçåàìåâíìêÉääÉå= båíïáÅâäìåÖ= w= áëí= áåëÄÉëçåJ ÇÉêÉ=ÄÉá=îçäâëïáêíëÅÜ~ÑíäáÅÜÉå=^å~äóëÉå=ìåÇ=ÄÉá=ä~åÖÑêáëíáÖÉå=mêçÖåçëÉå=EÄáë=NM=g~ÜêÉ=îçêJ ~ìëF=îçå=fåíÉêÉëëÉK== aáÉ= òóâäáëÅÜÉ= hçãéçåÉåíÉ= ÉêêÉÅÜåÉí= ëáÅÜ= ÇìêÅÜ= pìÄíê~âíáçå= ÇÉë= qêÉåÇë= îçå= ÇÉê= Öä~ííÉå= hçãéçåÉåíÉ=GI=ÇáÉ=ÇìêÅÜ=ÇÉå=ÖäÉáíÉåÇÉå=NOJjçå~íëJaìêÅÜëÅÜåáíí=ÉêêÉÅÜåÉí=ïáêÇK= Saisonkomponente S

aÉê=sÉêä~ìÑ=ÇÉê=p~áëçåâçãéçåÉåíÉ=S=áëí=ÉÄÉåÑ~ääë=ïÉääÉåÑ∏êãáÖ=ìåÇ=ÉåíëéêáÅÜí=ÇÉê=sÉê®åÇÉJ êìåÖ=ÇÉê=wÉáíêÉáÜÉåïÉêíÉ=áååÉêÜ~äÄ=ÉáåÉê=p~áëçå=EòK=_K=ÉáåÉë=g~ÜêÉëI=jçå~íë=ìëïKFK== aáÉ=hÉååíåáë=ÇÉê=p~áëçåâçãéçåÉåíÉ=Éêã∏ÖäáÅÜí=ÉëI=âìêòÑêáëíáÖÉ=mêçÖåçëÉå=EòK=_K=ΩÄÉê=ÇáÉ= å®ÅÜëíÉå=jçå~íÉF=~åòìëíÉääÉå=ìåÇ=áëí=ÇÉëÜ~äÄ=ÄÉëçåÇÉêë=ÑΩê=ÄÉíêáÉÄëïáêíëÅÜ~ÑíäáÅÜÉ=cê~ÖÉJ ëíÉääìåÖÉå=ïáÅÜíáÖK== aáÉ=_ÉêÉÅÜåìåÖëïÉáëÉ=òìê=bêãáííäìåÖ=ÇÉê=p~áëçåâçãéçåÉåíÉ=ïáêÇ=ïÉáíÉê=ìåíÉå=îçêÖÉëíÉääíK= Irreguläre Komponente I

aáÉ=áêêÉÖìä®êÉ=hçãéçåÉåíÉ=I=ÉåíëéêáÅÜí=ÇÉå=ìåêÉÖÉäã®≈áÖÉå=pÅÜï~åâìåÖÉå=ÉáåÉê=wÉáíêÉáÜÉK== aáÉ= áêêÉÖìä®êÉ= hçãéçåÉåíÉ= áëí= ÇÉêàÉåáÖÉ= oÉëí= ~å= sÉê®åÇÉêìåÖÉå= ÇÉê= wÉáíêÉáÜÉI= ÇÉê= åáÅÜí= ÇìêÅÜ=qêÉåÇI=hçåàìåâíìê=çÇÉê=ë~áëçå~äÉ=báåÑäΩëëÉ=Éêâä®êí=ïÉêÇÉå=â~ååK== eáÉêÄÉá=Ü~åÇÉäí=Éë=ëáÅÜ=ìã=łÉáåã~äáÖÉ=báåÄêΩÅÜÉ=EòK=_K=h~í~ëíêçéÜÉåF=çÇÉê=ìã=łòìÑ®ääáÖÉ= pí∏êìåÖÉå=EòK=_K=píêçã~ìëÑ®ääÉFI=ÇáÉ=åáÅÜí=îçêÜÉêë~ÖÄ~ê=ëáåÇK== råíÉê=ÄÉëíáããíÉå=dÉëáÅÜíëéìåâíÉåI=òK=_K=ÇÉê=pìÅÜÉ=å~ÅÜ=bêâä®êìåÖÉå=ÑΩê=^ìëêÉá≈ÉêïÉêíÉI= â~åå=~ìÅÜ=ÇáÉ=^å~äóëÉ=ÇÉê=áêêÉÖìä®êÉå=hçãéçåÉåíÉ=îçå=fåíÉêÉëëÉ=ëÉáåK== aáÉ=áêêÉÖìä®êÉ=hçãéçåÉåíÉ= I=ÉêêÉÅÜåÉí=ëáÅÜ=ÇìêÅÜ=pìÄíê~âíáçå=ÇÉë=qêÉåÇëI=ÇÉê=hçåàìåâíìê= ìåÇ=ÇÉê=p~áëçåâçãéçåÉåíÉ=îçã=ìêëéêΩåÖäáÅÜÉå=wÉáíêÉáÜÉåïÉêíK== cΩê=bñÅÉä=OMMTJ^åïÉåÇÉê=ÖáÄí=Éë=_ÉÇáÉåìåÖëÜáåïÉáëÉ=òì=ÇáÉëÉã=^ÄëÅÜåáíí=~Ä=pÉáíÉ=NVV=


NQV

=

= _áäÇ=UKNOW=qêÉåÇÉåíïáÅâäìåÖ=

= _áäÇ=UKNPW=wóâäáëÅÜÉ=pÅÜï~åâìåÖÉå=

= _áäÇ=UKNQW=p~áëçå~äÉ=pÅÜï~åâìåÖÉå=

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NRM

8.5.2

Gleitende Durchschnitte und das additive Zeitreihenmodell

^äë=ïáÅÜíáÖÉë=báåë~íòÖÉÄáÉí=ÇÉê=jÉíÜçÇÉ=ÇÉê=ÖäÉáíÉåÇÉå=aìêÅÜëÅÜåáííÉ=áëí=ÇáÉ=^å~äóëÉ=îçå= wÉáíêÉáÜÉåÇ~íÉå=òì=åÉååÉåK== aáÉ=^å~äóëÉ=îçå=wÉáíêÉáÜÉå=îÉêÑçäÖí=ÇêÉá=wáÉäÉW= i~åÖÑêáëíáÖÉ=qêÉåÇë=ÉêâÉååÄ~ê=ã~ÅÜÉå= jçå~íëíóéáëÅÜÉ=^ÄïÉáÅÜìåÖÉå=ÄÉêÉÅÜåÉå= p~áëçåÄÉêÉáåáÖíÉ=wÉáíêÉáÜÉå=ÄÉêÉÅÜåÉå= táê=ïçääÉå=ÇáÉ=ëÅÜêáííïÉáëÉ=sÉêÑçäÖìåÖ=ÇáÉëÉê=ÇêÉá=wáÉäÉ=~å=ÉáåÉã=_ÉáëéáÉä=ÇÉãçåëíêáÉêÉåK== ^ìëÖ~åÖëéìåâí=ÑΩê=Ç~ë=_ÉáëéáÉä=ëçääÉå=jçå~íëïÉêíÉ=ΩÄÉê=ÇáÉ=rãë®íòÉ=ÉáåÉë=råíÉêåÉÜãÉåë= áå= ÇÉå= g~ÜêÉå= OMMN= Äáë= OMMQ= áå= ÉáåÉê=ÄÉëíáããíÉå=dÉäÇÉáåÜÉáí= EòK= _K= jáääáçåÉå= rpJAF= ëÉáåK= q~ÄÉääÉ=UKNO=ÉåíÜ®äí=ÇáÉ=tÉêíÉ=áå=ΩÄÉêëáÅÜíäáÅÜÉê=cçêã=Ó=ÑΩê=ÇáÉ=Öê~ÑáëÅÜÉ=a~êëíÉääìåÖ=ïáÉ=áå= _áäÇ=UKNT=ãΩëëÉå=ëáÉ=áå=òïÉá=pé~äíÉå=ÉáåÉê=bñÅÉäJq~ÄÉääÉ=~åÖÉçêÇåÉí=ïÉêÇÉåK===

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8.5.3

NRN

Langfristige Trends erkennbar machen

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få=ÇÉê=_áäÇ==UKNU=ëáåÇ=ÇáÉ=rêëéêìåÖëïÉêíÉ=ìåÇ=ÇáÉ=ÖäÉáíÉåÇÉå=NOJjçå~íëJaìêÅÜëÅÜåáííÉ=~ÄJ ÖÉíê~ÖÉåK== t®ÜêÉåÇ=ÇÉê=hìêîÉåîÉêä~ìÑ=ÇÉê=í~íë®ÅÜäáÅÜÉå=tÉêíÉ=ëí~êâÉ=pÅÜï~åâìåÖÉå=ìåÇ=råêÉÖÉäã®J ≈áÖâÉáíÉå=~ìÑïÉáëíI=áëí=ÇÉê=hìêîÉåîÉêä~ìÑ=ÇÉê=ÖäÉáíÉåÇÉå=NOJjçå~íëJaìêÅÜëÅÜåáííÉ=ÇÉìíäáÅÜ= Ñä~ÅÜÉê=ìåÇ=Ç~ãáí=äÉáÅÜíÉê=òì=ÇÉìíÉåW== bë=ä~ëëÉå=ëáÅÜ=áå=ÇÉã=hìêîÉåîÉêä~ìÑ=âçåàìåâíìêÉääÉ=wóâäÉå=ÉêâÉååÉåW=få=ÇÉã=g~Üê=OMMO=ÑáåJ ÇÉí= Éáå= âçåàìåâíìêÉääÉê=oΩÅâÖ~åÖ= ëí~ííX= áå= ÇÉå= g~ÜêÉå= OMMN= ìåÇ= OMMPLOMMQ= ëáåÇ= Ç~ÖÉÖÉå= âçåàìåâíìêÉääÉ=bêÜçäìåÖÉå=ÑÉëíòìëíÉääÉåK== fåëÖÉë~ãí= ëÅÜÉáåí= ëáÅÜ= ~ÄÉê= Éáå= äÉáÅÜí= ~ÄåÉÜãÉåÇÉê= qêÉåÇ= ~ÄòìòÉáÅÜåÉåK= táê= ïÉêÇÉå= Éë= ëÉÜÉåK=

8.5.4

Monatstypische Abweichungen berechnen

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8.5.5

Saisonbereinigte Zeitreihe berechnen

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8.5.6

Ausblick

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NRU


j~å= â~åå= ~ìÑÖêìåÇ= ÄÉêÉáíë=îçêäáÉÖÉåÇÉê=ë~áëçåÄÉêÉáåáÖíÉê=jçå~íëïÉêíÉ= Ç~ë= g~ÜêÉëÉêÖÉÄåáë= éêçÖåçëíáòáÉêÉåK== j~å=â~åå=~ìë=ÇÉê=ë~áëçåÄÉêÉáåáÖíÉå=wÉáíêÉáÜÉ=mêçÖåçëÉå=ÑΩê=ÇáÉ=å®ÅÜëíÉå=jçå~íÉ=ìåÇ=g~ÜJ êÉ= EÇìêÅÜëÅÜåáííäáÅÜÉ= g~ÜêÉëïÉêíÉF= ãáííÉäë= qêÉåÇ~å~äóëÉ= ìåÇ= ÉñéçåÉåíáÉääÉê= dä®ííìåÖ= ÄÉJ êÉÅÜåÉåK= j~å=â~åå=Éáå=îçê~ìëÖÉëÅÜ®íòíÉë=g~ÜêÉëÉêÖÉÄåáë=ãáí=eáäÑÉ=ÇÉê=ãçå~íëíóéáëÅÜÉå=^ÄïÉáÅÜìåJ ÖÉå=~ìÑ=ÇáÉ=ÉáåòÉäåÉå=jçå~íÉ=~ìÑíÉáäÉåK== ^ìÑ=ÇáÉëÉ=tÉáëÉ=ÉêÜ®äí=ã~å=ãçå~íäáÅÜÉ=mêçÖåçëÉïÉêíÉK= pÉäÄëíîÉêëí®åÇäáÅÜ=ÖáÄí=Éë=~ÄÉê=~ìÅÜ=dêÉåòÉå=ÇÉê=^åïÉåÇÄ~êâÉáí=ÇÉê=jÉíÜçÇÉ=ÇÉê=ÖäÉáíÉåJ ÇÉå=aìêÅÜëÅÜåáííÉW= ^åÜ~åÇ=ÇÉê=çÄáÖÉå=^ìëÑΩÜêìåÖÉå=ïìêÇÉå=ÄÉêÉáíë=ÉáåáÖÉ=pÅÜï®ÅÜÉå=ÇÉê=wÉáíêÉáÜÉå~å~äóëÉ= ãáí=eáäÑÉ=ÇÉê=jÉíÜçÇÉ=ÇÉê=ÖäÉáíÉåÇÉå=aìêÅÜëÅÜåáííÉ=ëáÅÜíÄ~êK=aáÉ=^åïÉåÇìåÖëëÅÜï®ÅÜÉå= ÇÉë=jçÇÉääë=ìåÇ=ÇÉê=_ÉêÉÅÜåìåÖëãÉíÜçÇÉ=òÉáÖÉå=ëáÅÜ=áå=ÑçäÖÉåÇÉå=mìåâíÉåW== qêÉåÇÄÉêÉÅÜåìåÖW=cΩê=ÇáÉ=ÄÉáÇÉå=båÇÉå=ÇÉê=wÉáíêÉáÜÉ=E^åÑ~åÖ=ìåÇ=pÅÜäìëëF=â∏ååÉå=âÉáåÉ= ÖäÉáíÉåÇÉå=aìêÅÜëÅÜåáííÉ=ÄÉêÉÅÜåÉí=ïÉêÇÉåK=aÉëÜ~äÄ=â~åå=ÇÉê=qêÉåÇ=~ìÅÜ=åáÅÜí=ïÉáí=ΩÄÉê= ÇÉå=~âíìÉääÉå=pí~åÇ=Üáå~ìë=áåíÉêéêÉíáÉêí=ïÉêÇÉåK=eáÉêÄÉá=òÉáÖí=ëáÅÜ=Éáå=ÇÉìíäáÅÜÉê=k~ÅÜíÉáä= ÖÉÖÉåΩÄÉê= ÇÉê= qêÉåÇÄÉêÉÅÜåìåÖ= ãáííÉäë= äáåÉ~êÉê=oÉÖêÉëëáçå= çÇÉê= ÇÉê= jÉíÜçÇÉ= ÇÉë= ÉñéçJ åÉåíáÉääÉå=dä®ííÉåë=EëáÉÜÉ=òK=_K=áå=xNzFI=ÇáÉ=~âíìÉääÉ=tÉêíÉ=ÄÉëëÉê=ÄÉêΩÅâëáÅÜíáÖÉåK== wìâìåÑíëéêçàÉâíáçåÉå=â∏ååÉå=åìê=ãáí=eáäÑÉ=ïÉáíÉêÉê=jÉíÜçÇÉå=EäáåÉ~êÉ=oÉÖêÉëëáçå=çÇÉê=ÉñJ éçåÉåíáÉääÉ=dä®ííìåÖF=ÉêêÉÅÜåÉí=ïÉêÇÉåK= jçå~íëíóéáëÅÜÉ=^ÄïÉáÅÜìåÖÉåW= ^ìÅÜ= ÇáÉ= p~áëçåÑáÖìê= ïáêÇ= åìê=~ìë=ÜáëíçêáëÅÜÉå=a~íÉå= ÉêJ êÉÅÜåÉíK= ^âíìÉääÉ= a~íÉå= ïÉêÇÉå= ÜáÉê= ÉÄÉåÑ~ääë= åìê= ìåòìêÉáÅÜÉåÇ= ÄÉêΩÅâëáÅÜíáÖí= ìåÇ= ãáí= ÜáëíçêáëÅÜÉå=a~íÉå=ÖäÉáÅÜÖÉïáÅÜíáÖ=îÉêêÉÅÜåÉíK== a~ë=jçÇÉää=áëí=ÇÉëíç=ÄÉëëÉêI=àÉ=âäÉáåÉê=ÇáÉ=áêêÉÖìä®êÉ=hçãéçåÉåíÉ=áëí=ìåÇ=àÉ=êÉÖÉäã®≈áÖÉê= ëáÅÜ=ÇáÉ=sÉê®åÇÉêìåÖÉå=ÇÉå=ä~åÖÑêáëíáÖÉåI=âçåàìåâíìêÉääÉå=ìåÇ=ãçå~íëíóéáëÅÜÉå=_ÉïÉJ ÖìåÖÉå=~åé~ëëÉåK= ^ÄëÅÜäáÉ≈ÉåÇ=ëáåÇ=åçÅÜ=òïÉá=ãÉíÜçÇáëÅÜÉ=^åãÉêâìåÖÉå=òì=ã~ÅÜÉåW= cΩê=âΩêòÉêÉ=p~áëçåÑáÖìêÉå=EòK_K=nì~êí~äëÇ~íÉåF=ãìëë=Ç~ë=fåíÉêî~ää=òìê=_ÉêÉÅÜåìåÖ=ÇÉê=ÖäÉáJ íÉåÇÉå=aìêÅÜëÅÜåáííÉ=ÉåíëéêÉÅÜÉåÇ=ÇÉê=îçêäáÉÖÉåÇÉå=p~áëçåÇ~ìÉê=~åÖÉé~ëëí=ïÉêÇÉåK=pç=áëí= ÄÉá=nì~êí~äëÇ~íÉå=ÇÉê=ÖäÉáíÉåÇÉ=aìêÅÜëÅÜåáíí=ÇÉê=lêÇåìåÖ=Q=òì=ï®ÜäÉåK=_Éá=p~áëçåÑáÖìêÉå= ãáí= ãÉÜê= fåíÉêî~ääÉå= EòK_K= ëíΩåÇäáÅÜÉê= píêçãîÉêÄê~ìÅÜ= éêç= q~ÖF= ï®Üäí= ã~å= ÉåíëéêÉÅÜÉåÇ= ÉáåÉå=ÖäÉáíÉåÇÉå=aìêÅÜëÅÜåáíí=Ü∏ÜÉêÉê=lêÇåìåÖ=EòK_K=lêÇåìåÖ=OQFK= a~ë= Ç~êÖÉëíÉääíÉ= jçÇÉää= òìê= p~áëçåÄÉêÉáåáÖìåÖ= Öáäí= åìê= ÑΩê= âçåëí~åíÉ=p~áëçåÑáÖìêÉåI= ÇK= ÜK= ÇáÉ=ë~áëçå~äÉå=pÅÜï~åâìåÖÉå=ëçääíÉå=áå=àÉÇÉê=p~áëçå=Éíï~=ÖäÉáÅÜ=Öêç≈=ëÉáåK=wÉáÖí=ëáÅÜI=Ç~ëë= ÇáÉ=^ìëëÅÜä®ÖÉ=E^ãéäáíìÇÉåF=ÇÉê=p~áëçåÑáÖìê=ãáí=ÇÉã=^åï~ÅÜëÉå=ÇÉê=Öä~ííÉå=hçãéçåÉåíÉ= ET= ìåÇ= wF= ÉÄÉåÑ~ääë= ~åï~ÅÜëÉåI= Ç~åå= ãìëë= Éáå= ^å~äóëÉãçÇÉää= ÑΩê= î~êá~ÄäÉ= p~áëçåÑáÖìêÉå= ÖÉï®Üäí=ïÉêÇÉå=EîÖäK=ÜáÉêòìW=xNzI=pK=TM=ÑÑKFK= c~òáíW= aáÉ= wÉáíêÉáÜÉå~å~äóëÉ= ãáííÉäë= ÖäÉáíÉåÇÉê= aìêÅÜëÅÜåáííÉ= ÉáÖåÉí= ëáÅÜ= áåëÄÉëçåÇÉêÉ= òìê=áåíÉåëáîÉå=^å~äóëÉ=ìåÇ=fåíÉêéêÉí~íáçå=ÜáëíçêáëÅÜÉê=båíïáÅâäìåÖÉåK=mêçÖåçëÉå=ÑΩê=ÇáÉ= wìâìåÑí=â∏ååÉå=åìê=ìåíÉê=wìÜáäÑÉå~ÜãÉ=~åÇÉêÉê=mêçÖåçëÉîÉêÑ~ÜêÉå=EäáåÉ~êÉ=oÉÖêÉëëáçåI= ÉñéçåÉåíáÉääÉ=dä®ííìåÖ=ìëïKF=ÖÉíêçÑÑÉå=ïÉêÇÉåK== =


=

9

Import von Daten aus Datenbanken

9.1

Grundsätzliches

få= ÇáÉëÉã= h~éáíÉä= ëçää= Ç~ê~ìÑ= ÉáåÖÉÖ~åÖÉå= ïÉêÇÉåI= ïáÉ= a~íÉå= òìê= ëí~íáëíáëÅÜÉå= ^ìÑÄÉJ êÉáíìåÖ=~ìë=ÉáåÉê=îçêÜ~åÇÉåÉå=a~íÉåÄ~åâ=áå=ÉáåÉ=bñÅÉäJq~ÄÉääÉ=Éñíê~ÜáÉêí=ïÉêÇÉå=â∏åJ åÉåK== få= îáÉäÉå= c®ääÉå= îÉêÑΩÖÉå= råíÉêåÉÜãÉå= ÄÉêÉáíë= ΩÄÉê= Öêç≈É= a~íÉåÄ~åâÉå= ÑΩê= cáå~åòÄìÅÜJ Ü~äíìåÖI=`çåíêçääáåÖI=`ìëíçãÉê=oÉä~íáçåëÜáé=j~å~ÖÉãÉåí=EòjF=ìåÇ=ëç=ïÉáíÉêK=aáÉëÉ=a~J íÉå=ëíÉÜÉå=áã=oÉÖÉäÑ~ääÉ=ÇÉå=jáí~êÄÉáíÉêå=ÑΩê=^ìëïÉêíìåÖÉå=éÉê=iÉëÉòìÖêáÑÑ=òìê=sÉêÑΩÖìåÖK= káÅÜí=ëÉäíÉå=ÉåíëíÉÜí=Ç~ÄÉá=ÇÉê=tìåëÅÜI=ëáÅÜ=ÉáåÉå=qÉáä=ÇÉê=a~íÉå=~ìë=ÇÉê=Öêç≈Éå=a~J íÉåÄ~åâ= áå= ÉáåÉ= éêáî~íÉ= bñÅÉäJq~ÄÉääÉ= ~ã= äçâ~äÉå= m`= òì= ÜçäÉåI= ìã= ëáÉ= Ç~åå= Ççêí= ãáí= ÇÉã=ÄÉäáÉÄíÉå=bñÅÉä=ÑΩê=áåÇáîáÇìÉääÉ=wïÉÅâÉ=~ìÑÄÉêÉáíÉåI=ëí~íáëíáëÅÜ=~ìëïÉêíÉåI=Öê~ÑáëÅÜ= Ç~êëíÉääÉå=òì=â∏ååÉåK==

9.2

Import aus MS-Access

báåÉ=^ÅÅÉëëJa~íÉåÄ~åâ=EsÉêëáçå=OMMPF=ÉåíÜ~äíÉ=mÉêëçå~äÇ~íÉå=áå=ÉáåÉê=ìãÑ~åÖêÉáÅÜÉå=q~J ÄÉääÉ=ãáí=ÇÉã=k~ãÉå=Personal=E_áäÇ=VKNFK==

== _áäÇ=VKNW=q~ÄÉääÉ=Personal=ÉáåÉê=^ÅÅÉëëJa~íÉåÄ~åâ== ^ìÑ= ÉáåÉ= ëçäÅÜÉ= a~íÉåÄÉëí~åÇëJq~ÄÉääÉ= ãáí= ÇÉå=îçääëí®åÇáÖÉå=^åÖ~ÄÉå= òì= ~ääÉå=mÉêëçåÉå= ïáêÇ= ïçÜä=åáÉã~äë=Éáå=jáí~êÄÉáíÉê= ÇáêÉâí= òìÖêÉáÑÉå= ÇΩêÑÉå=Ó= Ç~ë= áëí= Éáå=dêìåÇéêáåòáé=ÇÉê= a~íÉåÄ~åâ~êÄÉáíI= ÄÉá= ÇÉê= ÇáÉ= páÅÜÉêÜÉáí=ÇÉê=a~íÉåI= îçê= ~ääÉã= ~ìÅÜ= ÖÉÖÉå= ìåÄÉÑìÖíÉ= báåJ ëáÅÜíå~ÜãÉI=~äë=Éáå=ÄÉÇÉìíÉåÇÉë=hêáíÉêáìã=~åÖÉëÉÜÉå=ïáêÇK== sáÉäãÉÜê=ïáêÇ=ÇìêÅÜ=ÇÉå=^ÅÅÉëëJa~íÉåÄ~åâ~Çãáåáëíê~íçê=ÑΩê=àÉÇÉå=^êÄÉáíëéä~íòI=îçå=ÇÉã= ~ìë= ~ìÑ= ÇáÉ= a~íÉåÄ~åâ= òìÖÉÖêáÑÑÉå= ïÉêÇÉå= Ç~êÑI= äÉÇáÖäáÅÜ= ÉáåÉ= é~ëëÉåÇÉI= ÉáåëÅÜê®åâÉåÇÉ= ^ÄÑê~ÖÉ=îçêÄÉêÉáíÉíK== báåÉ=^ÄÑê~ÖÉ=áëí=Éáå=mêçÖê~ããI=Ç~ë=ëíÉíë=åìê=ÉáåÉå=qÉáä=ÇÉë=a~íÉåÄÉëí~åÇÉëI=áå=ÇÉê=oÉÖÉä= ïáÉÇÉê=áå=q~ÄÉääÉåÑçêãI=äáÉÑÉêíK=== pí~êíÉí=Éáå=jáí~êÄÉáíÉê=ÇáÉ=ÑΩê=áÜå=ìåÇ=ëÉáåÉå=^êÄÉáíëéä~íò=îçêÄÉêÉáíÉíÉ=^ÄÑê~ÖÉI=Ç~åå=ÉêÜ®äí= Éê=ÇÉåàÉåáÖÉå=qÉáä=ÇÉë=a~íÉåÄÉëí~åÇÉëI=ÇÉå=Éê=ÉáåëÉÜÉå=ìåÇ=~ìëïÉêíÉå=Ç~êÑK==


V==fãéçêí=îçå=a~íÉå=~ìë=a~íÉåÄ~åâÉå=

NSM

få=_áäÇ=VKO=áëí=òì=ëÉÜÉåI=Ç~ëë=ÇáÉ=^ÄÑê~ÖÉ= Fuer_MusterfrauI=ÇáÉ=ÇÉê=a~íÉåÄ~åâ~Çãáåáëíê~íçê= ÑΩê= ÇáÉëÉ= jáí~êÄÉáíÉêáå= îçêÄÉêÉáíÉí= Ü~íI= çÑÑÉåëáÅÜíäáÅÜ= åìê= ÉáåáÖÉ=^åÖ~ÄÉå= ~ìë= ÇÉã= mÉêëçJ å~äÇ~íÉåÄÉëí~åÇ= éêÉáëÖáÄí= Ó= ìåÇ= Ç~êΩÄÉê= Üáå~ìë= åìê= ÇáÉàÉåáÖÉå= mÉêëçåÉå= ~ìëäáëíÉíI= ÇáÉ= áå= lêíÉå=ãáí=ÇÉã=^åÑ~åÖëÄìÅÜëí~ÄÉå=B=ïçÜåÉåK==

== _áäÇ=VKOW=aáÉ=^ÄÑê~ÖÉ=Fuer_Musterfrau=äáÉÑÉêí=ÉáåÉå=qÉáä=ÇÉë=a~íÉåÄÉëí~åÇÉë== aáÉëÉåI=ÑΩê=ëáÉ=~äëç=ÑêÉáÖÉÖÉÄÉåÉå=qÉáä=ÇÉë=a~íÉåÄÉëí~åÇÉë=Ç~êÑ=ÇáÉ=_É~êÄÉáíÉêáå=åìå=åìíJ òÉåI=~ìëïÉêíÉåI=~å~äóëáÉêÉåK== páÉ= ã∏ÅÜíÉ= Ç~ÑΩê= áÜê= îÉêíê~ìíÉë= bñÅÉä= îÉêïÉåÇÉåK= ^äëç= ï®Üäí= ëáÉ= áå= ^ÅÅÉëë= òìÉêëí= a^J qbfbumloqfbobk=E_áäÇ=VKPFK==

= _áäÇ=VKPW=bñéçêí=îÉê~åä~ëëÉå=


VKP==báåêáÅÜíìåÖ=ÉáåÉë=la_`JqêÉáÄÉêë= =

NSN

^åëÅÜäáÉ≈ÉåÇ=Ó=ìåÇ=Ç~ë=áëí=ïáÅÜíáÖ=Ó=ãìëë=ëáÉ=áã=cÉåëíÉê= Dateityp=ÇáÉ=bñÅÉäJsÉêëáçå=ÉáåJ ëíÉääÉåI=ãáí=ÇÉê=ëáÉ=~êÄÉáíÉí=E_áäÇ=VKQFK=tÉåå=ëáÉ=âÉáåÉå=ÉáÖÉåÉå=a~íÉáå~ãÉå=Éáåíê®ÖíI=îÉêJ ïÉåÇÉí=^ÅÅÉëë=ÑΩê=ÇáÉ=òì=ÉêòÉìÖÉåÇÉ=bñÅÉäJa~íÉá=ÇÉå=k~ãÉå=ÇÉê=^ÄÑê~ÖÉK====

== _áäÇ=VKQW=qóé=ÇÉê=wáÉäÇ~íÉá=ÉáåëíÉääÉåI=k~ãÉ=îÉêÖÉÄÉå=== a~ë=áëí=ëÅÜçå=~ääÉëK=kìå=ëáåÇ=ÇáÉ=a~íÉå=~ìë=ÇÉê=^ÄÑê~ÖÉ=~ìÑ=ÇÉã=m`=îçå=cê~ì=jìëíÉêÑê~ì=áå= ÉáåÉê=bñÅÉäJq~ÄÉääÉ=îÉêÑΩÖÄ~êI=ìåÇ=ëáÉ=â~åå=å~ÅÜ=eÉêòÉåëäìëí=Ç~ãáí=~êÄÉáíÉåK== ^ääÉêÇáåÖëW= pçääíÉ= ëáÅÜ= å~ÅÜ= ÉáåáÖÉê= wÉáí= áã= òÉåíê~ä=îÉêï~äíÉíÉå=a~íÉåÄÉëí~åÇ= ÉáåÉ= ûåÇÉJ êìåÖ=ÉêÖÉÄÉåI=ÇáÉ=~ìÅÜ=ÇáÉ=häáÉåíÉä=îçå=cê~ì=jìëíÉêã~åå=ÄÉíêáÑÑí=Ó=Éë=ÖáÄí=å~íΩêäáÅÜ=Ç~åå= âÉáåÉ=~ìíçã~íáëÅÜÉ=^âíì~äáëáÉêìåÖ=áÜêÉê=bñÅÉäJq~ÄÉääÉI=ïáÉ=ëçääíÉ=Éë=~ìÅÜ\== aáÉ=jáí~êÄÉáíÉêáå=ãΩëëíÉ=ëáÅÜ=ÉêåÉìí=ÄÉá=^ÅÅÉëë=~åãÉäÇÉåI=áÜêÉ=^ÄÑê~ÖÉ=ïáÉÇÉê=ëí~êíÉåI=ÇáÉ= a~íÉå=ÉêåÉìí=ÉñéçêíáÉêÉå=ìåÇ=ëç=ïÉáíÉêK== tΩåëÅÜÉåëïÉêí=ï®êÉ=~äëç=ÜáÉê=ÉáåÉ=^ìÑêÉÅÜíÉêÜ~äíìåÖ=ÇÉê=sÉêÄáåÇìåÖ=òìê=a~íÉåÄ~åâI=ëç= Ç~ëë=ÖÉïáëëÉêã~≈Éå=~ìÑ=håçéÑÇêìÅâ=îçå=bñÅÉä=~ìë=EìåÇ=çÜåÉ=ÇáÉ=^ÅÅÉëëJ^ÄÑê~ÖÉ=ÉêåÉìí= ëí~êíÉå=òì=ãΩëëÉåF=ÇáÉ=a~íÉå=áå=ÇÉê=àÉïÉáäë=~âíìÉääÉå=cçêã=~åÖÉÑçêÇÉêí=ïÉêÇÉå=â∏ååÉåK== a~ãáí= ïΩêÇÉå= ~ìÅÜ= áå= bñÅÉä= ëíÉíë=~âíìÉääÉ=a~íÉå=îÉê~êÄÉáíÉíK= fã=^ÄëÅÜåáíí=VKRKO= ~ìÑ= pÉáíÉ= NSU=ïáêÇI=ÄÉáëéáÉäÜ~Ñí=ÄÉòçÖÉå=~ìÑ=ÉáåÉ=lê~ÅäÉJa~íÉåÄ~åâI=ÇÉê=jÉÅÜ~åáëãìë=ÄÉëÅÜêáÉÄÉåI= ãáí=ÇÉã=ÇáÉëÉê=tìåëÅÜ=ÉêÑΩääí=ïÉêÇÉå=â~ååK=

9.3

Einrichtung eines ODBC-Treibers

a~íÉåÄ~åâÉå=ÄÉÑáåÇÉå=ëáÅÜ=ΩÄäáÅÜÉêïÉáëÉ=~ìÑ=ÉáåÉã=òÉåíê~äÉå=pÉêîÉê=ÇÉë=råíÉêåÉÜãÉåëK== rã=~ìë=bñÅÉä=ÜÉê~ìë=Ç~ê~ìÑ=òìÖêÉáÑÉå=òì=â∏ååÉåI=ãΩëëÉå=ÉáåáÖÉ=sçê~ìëëÉíòìåÖÉå=ÉêÑΩääí= ëÉáåW= aÉê=^åïÉåÇÉê=ãìëë=áå=ÇÉê=ÉåíëéêÉÅÜÉåÇÉå=a~íÉåÄ~åâ=Éáå=_ÉåìíòÉêâçåíç=E^ÅÅçìåíF= ÄÉëáíòÉåK=



NSO

^ìÑ=ÇÉã=m`=ÇÉë=^åïÉåÇÉêë=ãìëë=Éáå=ÉåíëéêÉÅÜÉåÇÉê=la_`JqêÉáÄÉê=EléÉå=a~í~Ä~ëÉ= `çååÉÅíáîáíóF= áåëí~ääáÉêí= ëÉáåK= báåáÖÉ= ÇáÉëÉê= qêÉáÄÉê= ëáåÇ= áã= fåëí~ää~íáçåëìãÑ~åÖ= îçå= táåÇçïë=um=ÉåíÜ~äíÉåK= fååÉêÜ~äÄ=ÇÉë=jp=lÑÑáÅÉ=m~âÉíÉë=ãìëë=Ç~ë=qççä=MS Query=áåëí~ääáÉêí=ëÉáåK= få= ÇáÉëÉã= ^ÄëÅÜåáíí= ïáêÇ= òìÉêëí= pÅÜêáíí= ÑΩê= pÅÜêáíí= ÇáÉ= báåêáÅÜíìåÖ=ÇÉë=la_`JqêÉáÄÉêë= ÄÉJ ëÅÜêáÉÄÉåK=fã=ÑçäÖÉåÇÉå=^ÄëÅÜåáíí=~Ä=pÉáíÉ=NSP=ïáêÇ=Ç~åå=ÇáÉ=sçêÖÉÜÉåëïÉáëÉ=òìê=bñíê~âJ íáçå=ÇÉê=a~íÉå=ÄÉëÅÜêáÉÄÉåK== aáÉ= báåêáÅÜíìåÖ=ÉáåÉë=la_`JqêÉáÄÉêë= ïáêÇ= ~åÜ~åÇ= ÇÉë= _ÉíêáÉÄëëóëíÉãë= jp= táåÇçïë= um= mêçÑÉëëáçå~ä= îÉê~åëÅÜ~ìäáÅÜíK= aÉê= ëé®íÉê= ÄÉå∏íáÖíÉ= la_`JqêÉáÄÉê= ÑΩê= lê~ÅäÉ= ÖÉÜ∏êí= ÜáÉê= òìã=iáÉÑÉêìãÑ~åÖ=ÇÉë=_ÉíêáÉÄëëóëíÉãëK= aáÉ= ^Çãáåáëíê~íáçå= ÇáÉëÉê= qêÉáÄÉê= ÑáåÇÉí= ã~å= ΩÄÉê= pqôqbfkpqbiirkdbkpvpqbjpqbrbJ orkdsbotîqrkd=E_áäÇ=VKRFW=

= _áäÇ=VKRW=råíÉêÖêìééÉ=VERWALTUNG=áå=ÇÉê=póëíÉãëíÉìÉêìåÖ=îçå=táåÇçïë=um==

== _áäÇ=VKSW=pí~åÇ~êÇã®≈áÖ=îçêÜ~åÇÉåÉ=a~íÉåèìÉääÉå=


VKQ==wìÖêáÑÑ=~ìÑ=âçåâêÉíÉ=a~íÉåÄ~åâÉå=

NSP

aÉê= ^ìÑêìÑ= ÇÉë= póãÄçäë= Datenquellen (ODBC)= ∏ÑÑåÉí= Ç~ë= cÉåëíÉê= ÇÉë= la_`Ja~íÉåèìÉääÉåJ ^Çãáåáëíê~íçêëI=áå=ÇÉëëÉå=cÉåëíÉê= Benutzerdatenquellen ëáÅÜ=ÄÉêÉáíë=ÉáåáÖÉ=ÇÉê=ëí~åÇ~êÇã®J ≈áÖ=îçêÜ~åÇÉåÉå=a~íÉåèìÉääÉå=ÄÉÑáåÇÉå=E_áäÇ=VKSFK=

= _áäÇ=VKTW=sÉêÑΩÖÄ~êÉ=la_`JqêÉáÄÉê=ìåíÉê=jp=táåÇçïë=um=mêçÑÉëëáçå~ä= aáÉ=_ÉåìíòÉêJapk=ëáåÇ=ÇáÉ=ÉáåÖÉêáÅÜíÉíÉå=a~íÉåèìÉääÉåI=ÇáÉ=åìê=ÇÉã=~âíìÉää=~ã=m`=~åÖÉJ ãÉäÇÉíÉå=_ÉåìíòÉê=òìê=sÉêÑΩÖìåÖ=ëíÉÜÉåK== pçää=ÉáåÉ=ïÉáíÉêÉ=a~íÉåèìÉääÉ=ÜáåòìÖÉÑΩÖí=ïÉêÇÉåI=Ç~åå=áëí=ãáííÉäë= Hinzufügen =Ç~ë=cÉåëJ íÉê=Neue Datenquelle erstellen=E_áäÇ=VKTF=òì=∏ÑÑåÉåX=Ççêí=â~åå=Ç~åå=~ìëÖÉï®Üäí=ïÉêÇÉåK==

9.4

Zugriff auf konkrete Datenbanken

9.4.1

Microsoft SQL-Server

aÉê=pniJpÉêîÉêI=Éáå=jáÅêçëçÑíJmêçÇìâíI=áëí=Éáå=äÉáëíìåÖëÑ®ÜáÖÉë=a~íÉåÄ~åâJpóëíÉãI=Ç~ë=áå= îáÉäÉå=_ÉêÉáÅÜÉå=^åïÉåÇìåÖ=ÑáåÇÉíK== ^ìÅÜ= Ççêí= ïáêÇ= ãáí= eáäÑÉ= îçå= ^ÄÑê~ÖÉå= ÑΩê= àÉÇÉå= ^êÄÉáíëéä~íò= åìê= ÉáåÉ= ëçäÅÜÉ= qÉáäãÉåÖÉ= ÇÉë=a~íÉåÄÉëí~åÇÉë=ÄÉêÉáíÖÉëíÉääíI=ÇáÉ=ÇÉê=hçãéÉíÉåò=ìåÇ=ÇÉã=fåÑçêã~íáçåëÄÉÇΩêÑåáë=ÇÉë= àÉïÉáäáÖÉå=_É~êÄÉáíÉêë=ÉåíëéêáÅÜíK== aáÉ= sÉêëáçå= bñÅÉä= OMMP= ÄáÉíÉí= ÉáåÉ= iÉáëíìåÖ= Add-In für SQL Server Analysis Services= ~åI= ÇáÉ=áå== http://go.microsoft.com/?linkid= 1140024

ïáÉ=ÑçäÖí=ÄÉëÅÜêáÉÄÉå=áëíW== dêÉáÑÉå=páÉ=ëÅÜåÉää=ìåÇ=éêçÄäÉãäçë=~ìÑ=ãìäíáÇáãÉåëáçå~äÉ=a~íÉå=òìI=ÑΩÜêÉå=páÉ=ÇÉí~áääáÉêíÉ= a~íÉå~å~äóëÉå=ÇìêÅÜ=ìåÇ=ÉêëíÉääÉå=páÉ=ÑäÉñáÄäÉI=áåíÉê~âíáîÉ=_ÉêáÅÜíÉ=áå=jáÅêçëçÑí=bñÅÉäK==

9.4.2

Oracle

cΩê=ÇáÉ=hçåÑáÖìêáÉêìåÖ=ÇÉë=la_`JqêÉáÄÉêë=ÑΩê=lê~ÅäÉ=ãìëë=ÇÉê=sÉêÄáåÇìåÖëÄÉòÉáÅÜåÉê= ETNS-AliasF=ÑΩê=ÇáÉ=a~íÉåÄ~åâ=ÄÉâ~ååí=ëÉáåI=ÜáÉê=ëçääíÉ=ã~å=ëáÅÜ=~å=ÇÉå=^Çãáåáëíê~íçê= ïÉåÇÉåK==


NSQ


tÉáíÉêÜáå=ãìëë=ÇáÉ=lê~ÅäÉ=`äáÉåí=pçÑíï~êÉ=ÄÉêÉáíë=áåëí~ääáÉêí=ëÉáåK=aáÉë=áëí=áããÉê=Ç~åå=ÇÉê= c~ääI= ïÉåå= ÇÉê= _ÉåìíòÉê= ÄÉêÉáíë= ãáí= `äáÉåíJpÉêîÉêJ^åïÉåÇìåÖÉå= ~êÄÉáíÉíI= ÇáÉ= ~ìÑ= lê~ÅäÉJ a~íÉåÄ~åâÉå=Ä~ëáÉêÉåK= få= ÇÉå= ãÉáëíÉå= lê~ÅäÉJa~íÉåÄ~åâÉå= áëí= Éáå= pí~åÇ~êÇÄÉåìíòÉê= å~ãÉåë= scott= Em~ëëïçêí= tigerF=òì=pÅÜìäìåÖëòïÉÅâÉå=ãáí=ÉáåÖÉêáÅÜíÉíK== bë=ÖáÄí=~ÄÉê=àÉíòí=ãáí=ÉáåÉê=åÉì=îÉêÑΩÖÄ~êÉå=sÉêëáçå=lê~ÅäÉ=a~í~Ä~ëÉ=bñéêÉëë=bÇáíáçå=EOracle Database XEF=ÉáåÉ=òìê=Öêç≈Éå=a~íÉåÄ~åâ=âçãé~íáÄäÉ=sÉêëáçå=îçå=lê~ÅäÉ=NMÖK=páÉ=áëí=äÉJ ÇáÖäáÅÜ=äáãáíáÉêíI=Ç~ëë=ã~ñáã~ä=Éáå=mêçòÉëëçêI=N=d_=e~ìéíëéÉáÅÜÉê=ìåÇ=ã~ñáã~ä=Q=d_=a~J íÉå=îÉêïÉåÇÉí=ïÉêÇÉå=â∏ååÉåK=j~å=â~åå=ëáÉ=âçëíÉåäçë=ÜÉêìåíÉê=ä~ÇÉå=ìåÇ=ÄÉåìíòÉåI=~ìÅÜ= ÑΩê=âçããÉêòáÉääÉ=wïÉÅâÉK== få= ÇÉê= a~íÉåÄ~åâ= Oracle Database XE= E~ìÑ= ÇáÉ= áå= ÇáÉëÉã= ^ÄëÅÜåáíí= _ÉòìÖ= ÖÉåçããÉå= ïáêÇF=ãÉäÇÉí=ã~å=ëáÅÜ=~äë=_ÉåìíòÉê=hr=ãáí=ÇÉã=ÖäÉáÅÜä~ìíÉåÇÉå=m~ëëïçêí=hr ~åK====== aÉê= _ÉåìíòÉê= hr= áëí= ~ÄÉê= ~ìÅÜ= áå= àÉÇÉê= Öêç≈Éå= lê~ÅäÉ=NMÖJa~íÉåÄ~åâ= îçêÜ~åÇÉåI= ëçÑÉêå= ÄÉá=ÇÉê=fåëí~ää~íáçå=ÇáÉ=_ÉáëéáÉäJpÅÜÉã~ë=ãáí=áåëí~ääáÉêí=ïìêÇÉåK= lÄïçÜä=áå=ÇáÉëÉã=_ÉáëéáÉä=~ìÑ=ÉáåÉ=lê~ÅäÉJa~íÉåÄ~åâ=òìÖÉÖêáÑÑÉå=ïáêÇI=áëí=ÇáÉ=sçêÖÉJ ÜÉåëïÉáëÉ=ÑΩê=~åÇÉêÉ=a~íÉåÄ~åâÉåI=òK_K=jp=pni=pÉêîÉêI=f_j=a_LO=ìëïK=~å~äçÖK= k~ÅÜ=_Éí®íáÖÉå=ÇÉë=_ìííçåë= Hinzufügen =E_áäÇ=VKS=~ìÑ=pÉáíÉ=NSOF=ï®Üäí=ã~å=~äëç=~ìë=ÇÉê= iáëíÉ=ÇÉê=îÉêÑΩÖÄ~êÉå=qêÉáÄÉê=ÇÉå=lê~ÅäÉJqêÉáÄÉê=E_áäÇ=VKT=~ìÑ=pÉáíÉ=NSPF=~ìëK== pçääíÉ=ÇáÉ=lê~ÅäÉ=`äáÉåíJpçÑíï~êÉ=åáÅÜí=áåëí~ääáÉêí=ëÉáåI=ÉêÜ®äí=ã~å=ÉáåÉ=cÉÜäÉêãÉäÇìåÖ=E_áäÇ= VKUFK= få= ÇáÉëÉã= c~ää= ãìëë= ÇáÉ= fåëí~ää~íáçå= ÇÉê= lê~ÅäÉJhçãéçåÉåíÉå= ESQL*Net ClientF= Éêëí= å~ÅÜÖÉÜçäí=ïÉêÇÉåK==

= _áäÇ=VKUW=cÉÜäÉêãÉäÇìåÖ=ÄÉá=åáÅÜí=îçêÜ~åÇÉåÉê=lê~ÅäÉJ`äáÉåíJpçÑíï~êÉ= fã= c~ääÉI= Ç~ëë= ÇáÉ= lê~ÅäÉ= `äáÉåíJpçÑíï~êÉ= ÄÉêÉáíë= îçêÜ~åÇÉå= áëíI= ÉêëÅÜÉáåí= ÇÉê= aá~äçÖ= ~ìë= _áäÇ=VKVX=áã=_áäÇ=ëáåÇ=ÇêÉá=báåÖ~ÄÉå=ÄÉêÉáíë=ÇìêÅÜÖÉÑΩÜêí=ïçêÇÉåK==

= _áäÇ=VKVW=kçíïÉåÇáÖÉ=báåÖ~ÄÉå=ÑΩê=ÇÉå=lê~ÅäÉJla_`JqêÉáÄÉê= aÉê=a~íÉåèìÉääÉåå~ãÉ=áëí=Ç~ÄÉá=ÉáåÉ=ÑêÉá=ï®ÜäÄ~êÉ=_ÉòÉáÅÜåìåÖI=ìåíÉê=ïÉäÅÜÉê=ÇÉê=_ÉåìíJ òÉê=ëé®íÉê=áã= MS Query=ÇáÉ=a~íÉåÄ~åâ=~åÖáÄíI=~ìë=ÇÉê=ÇáÉ=a~íÉå=ëí~ããÉå=ëçääÉåK=aáÉ=_ÉJ ëÅÜêÉáÄìåÖ=áëí=çéíáçå~äI=â~åå=~äëç=ÑêÉá=ÖÉä~ëëÉå=ïÉêÇÉåK=aÉê=_ÉåìíòÉêå~ãÉ=áëí=ÇÉê=hçåíçJ å~ãÉ=áå=ÇÉê=a~íÉåÄ~åâI=áå=_áäÇ=VKV=ïìêÇÉ=Ç~ÑΩê=ÇÉê=lê~ÅäÉJubJrëÉê=hr=ÉáåÖÉíê~ÖÉåK=


VKR==bñÅÉäJwìÖêáÑÑ=~ìÑ=lê~ÅäÉ= =

NSR

eáåíÉê= ÇÉê= _ÉòÉáÅÜåìåÖ= pÉêîÉê= Eáå= _áäÇ= VKV= ÄÉäÉÖí= ãáí= xeF= îÉêÄáêÖí= ëáÅÜ= Éáå= ëç= ÖÉå~ååíÉê= TNS-AliasI= Ç~ë= áëí= Éáå= hΩêòÉä= ÑΩê= ÉáåÉ= lê~ÅäÉJa~íÉåÄ~åâJsÉêÄáåÇìåÖI= ÇáÉ= áå= ÇÉê= lê~ÅäÉJ `äáÉåíJpçÑíï~êÉ=ÄÉâ~ååí=ëÉáå=ãìëëK=a~ÑΩê=ãìëë=ã~å=ëáÅÜ=ÖÉÖÉÄÉåÉåÑ~ääë=~å=ëÉáåÉå=a~íÉåJ Ä~åâ~Çãáåáëíê~íçê=ïÉåÇÉåK== EpçÑÉêå=ÇáÉëÉ=^äá~ëJk~ãÉå=åáÅÜí=ìåíÉêåÉÜãÉåëïÉáí=òÉåíê~ä=îÉêï~äíÉí=ïÉêÇÉåI=ÜáäÑí=~ìÅÜ=Éáå= _äáÅâ=áå=ÇáÉ=a~íÉá=%ORACLE_HOME%\network\admin\tnsnames.oraI=ÇáÉë=~ÄÉê=åìê=ÑΩê=fåëáÇÉêFK= iÉáÇÉê= áëí= Éë= ~å= ÇáÉëÉê= píÉääÉ= ìåÇ= òì= ÇáÉëÉã= wÉáíéìåâí= åçÅÜ= åáÅÜí= ã∏ÖäáÅÜI= ÇáÉ= âçêêÉâíÉ= sÉêÄáåÇìåÖ=òìê=a~íÉåÄ~åâ=ÖäÉáÅÜ=òì=íÉëíÉåI=ÇáÉë=â~åå=Éêëí=ëé®íÉê=áã=^ÄÑê~ÖÉïÉêâòÉìÖ= MS Query=îÉêáÑáòáÉêí=ïÉêÇÉåK= aáÉ=hçåÑáÖìê~íáçå=ÇÉë=la_`JqêÉáÄÉêë=áëí=~ÄÉê=Ç~ãáí=~ÄÖÉëÅÜäçëëÉåK=

9.5

Excel-Zugriff auf Oracle

9.5.1

Daten importieren

k~ÅÜ= ÇÉã= pí~êíÉå= îçå= bñÅÉä= ï®Üäí= ã~å= a^qbkbuqbokb= a^qbk= fjmloqfbobkkbrb= ^_J co^db=bopqbiibk=~ìëK== pçääíÉ=Ç~ë=lÑÑáÅÉJtÉêâòÉìÖ=MS Query=åáÅÜí=áåëí~ääáÉêí=ëÉáåI=ïΩêÇÉ=åìå=ÉáåÉ=ÉåíëéêÉÅÜÉåÇÉ= cÉÜäÉêãÉäÇìåÖ=ÉêëÅÜÉáåÉå=ìåÇ=ÇáÉëÉ=fåëí~ää~íáçå=ãΩëëíÉ=Éêëí=ãáí=eáäÑÉ=ÇÉê=jp=lÑÑáÅÉJà= å~ÅÜÖÉÜçäí=ïÉêÇÉåK= ^åëçåëíÉå=ÉêëÅÜÉáåí=ÇÉê=aá~äçÖI=ÇÉê=ÇáÉ=îçêÜ~åÇÉåÉå=DSN=EÇ~í~=ëçìêÅÉ=å~ãÉF=~ìÑäáëíÉíK=eáÉê= ëçääíÉ=ÇáÉ=îçêÜáå=âçåÑáÖìêáÉêíÉ=a~íÉåÄ~åâîÉêÄáåÇìåÖ=îçêÖÉÑìåÇÉå=ïÉêÇÉå=E_áäÇ=VKNMFK=

== _áäÇ=VKNMW=iáëíÉ=ÇÉê=áã=póëíÉã=ÄÉâ~ååíÉå=a~íÉåèìÉääÉå=EDSNF= k~ÅÜ=ÇÉê=^ìëï~Üä=ÇÉê=é~ëëÉåÇÉå=a~íÉåèìÉääÉ=ÉêëÅÜÉáåí=ÇáÉ=m~ëëïçêíJ^ÄÑê~ÖÉ=E_áäÇ=VKNNFK==

= _áäÇ=VKNNW=m~ëëïçêíJ^ÄÑê~ÖÉ=



NSS

aÉê=_ÉåìíòÉêå~ãÉ=ìåÇ=ÇáÉ=a~íÉåÄ~åâ=ëáåÇ=Ççêí=òï~ê=ÄÉêÉáíë=ÉáåÖÉíê~ÖÉåI=â∏ååíÉå=ÜáÉê=~ÄÉê= åçÅÜ=~ÄÖÉ®åÇÉêí=ïÉêÇÉå=EaáÉ=ÉáÖÉåíäáÅÜÉ=la_`JhçåÑáÖìê~íáçå=®åÇÉêí=ëáÅÜ=Ç~ÇìêÅÜ=åáÅÜíFK== táÉ= ëÅÜçå= Éêï®ÜåíI= ïáêÇ= ÜáÉê= Ç~ë= îçå= lê~ÅäÉ= ãáí= ÇÉê= sÉêëáçå= ub= ÑΩê= iÉêåÉåÇÉ= ÄÉêÉáíÖÉJ ëíÉääíÉ=m~~ê=hrLhr=ÑΩê=_ÉåìíòÉêå~ãÉ=ìåÇ=hÉååïçêí=îÉêïÉåÇÉíK== pçÑÉêå=ÇáÉ=báåêáÅÜíìåÖ=ÇÉë=la_`JqêÉáÄÉêë=âçêêÉâí=ï~êI=ëí~êíÉí=àÉíòí=áã=eáåíÉêÖêìåÇ=Ç~ë= mêçÖê~ãã=MS QueryK== få= ÉáåÉã= aá~äçÖÑÉåëíÉê= ÉêëÅÜÉáåÉå= åìå= ~ääÉ= lÄàÉâíÉ= ÇÉê= lê~ÅäÉJa~íÉåÄ~åâ= Eq~ÄÉääÉåI= sáÉïëL^åëáÅÜíÉåI=póåçåóãÉFI=~ìÑ=ÇáÉ=ÇÉê=~åÖÉãÉäÇÉíÉ=_ÉåìíòÉê=EÜáÉêW=hrF=wìÖêáÑÑ=ÄÉëáíòíK= fã=_áäÇ=VK= NO=ïìêÇÉ=ÄÉêÉáíë=Äáë=òìê=q~ÄÉääÉ= EMPLOYEES=E^åÖÉëíÉääíÉåJq~ÄÉääÉF=ÖÉëÅêçääí=ìåÇ= ÇÉê=^åÑ~åÖ=ÇÉê=q~ÄÉääÉåëíêìâíìê=~åÖÉòÉáÖíK=

== _áäÇ=VKNOW=iáëíÉ=ÇÉê=lÄàÉâíÉ=ÇÉë=a~íÉåÄ~åâÄÉåìíòÉêë= eáÉê=â∏ååÉå=åìå=ÉåíïÉÇÉê=ÇáÉ=ÖÉë~ãíÉ=q~ÄÉääÉ=çÇÉê=ÉáåòÉäåÉ=pé~äíÉå=áå=ÇáÉ=^ÄÑê~ÖÉ=ΩÄÉêJ åçããÉå=ïÉêÇÉåK== fã=_ÉáëéáÉä=E_áäÇ=VKNPF=ïáêÇ=ÇáÉ=ÖÉë~ãíÉ=q~ÄÉääÉåëíêìâíìê=éÉê=häáÅâ=~ìÑ= > =ΩÄÉêåçããÉåK==

== _áäÇ=VKNPW=§ÄÉêåçããÉåÉ=pé~äíÉå= k~ÅÜ= Weiter > = ÉêëÅÜÉáåí= Éáå= aá~äçÖI= ãáí= ïÉäÅÜÉã= ÇáÉ= òì= ëÉäÉâíáÉêÉåÇÉå= a~íÉå= ÉáåÖÉJ ëÅÜê®åâí=ïÉêÇÉå=â∏ååÉåK==


VKR==bñÅÉäJwìÖêáÑÑ=~ìÑ=lê~ÅäÉ= =

NST

fã=_ÉáëéáÉä=E_áäÇ=VKNQF=ïÉêÇÉå=åìê=~ääÉ=ÇáÉàÉåáÖÉå=^åÖÉëíÉääíÉå=~ìëÖÉï®ÜäíI=ÇáÉ=áå=aÉé~êJ íÉãÉåíë=ãáí=ÉáåÉê=aÉé~êíãÉåíJkìããÉê=ìåíÉêÜ~äÄ=îçå=RM=~êÄÉáíÉå=Eáå=pni=ï®êÉ=ÇáÉë=ÉáåÉ= WHEREJ_ÉÇáåÖìåÖFK=a~=ÇÉê=^ëëáëíÉåí=ÇáÉ=^êÄÉáí=ã~ñáã~ä=ÉêäÉáÅÜíÉêå=ïáääI=ÖêÉáÑí=Éê=ÄÉêÉáíë=~ìÑ= ÇáÉ=a~íÉåÄ~åâ=òì=ìåÇ=ÉêãáííÉäí=~ääÉ=ã∏ÖäáÅÜÉå=tÉêíÉ=ÑΩê=ÇáÉ=êÉÅÜíÉ=tÉêíÉäáëíÉK== aáÉë=â~åå=ÄÉá=ëÉÜê=Öêç≈Éå=a~íÉåãÉåÖÉå=òì=t~êíÉòÉáíÉå=ÑΩÜêÉåK= =

= _áäÇ=VKNQW=báåëÅÜê®åâìåÖ=ÇÉê=a~íÉåãÉåÖÉ=

== _áäÇ=VKNRW=sçêÖ~ÄÉ=ÇÉê=pçêíáÉêêÉáÜÉåÑçäÖÉ=Ó=å~ÅÜ=dÉÜ~äí=~ÄëíÉáÖÉåÇ=

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