Regression: Unterschied zwischen den Versionen

[+/-]

Widgets

Widgets

Gewünschte Seiten
  • Keine Informationen verfügbar
Wer ist online?
  • Es ist niemand angemeldet.
Aus Matura Wiki
Wechseln zu: Navigation, Suche
Zeile 11: Zeile 11:
  
 
[[Grün: Arbeitsblätter | <span style="background-color:#00CD00"> $Aha!$ </span>]]  Dieses [http://tube.geogebra.org/m/1525527 Arbeitsblatt] zeigt dir die Grundlegende Idee am Beispiel einer linearen Regression (siehe weiter unten).  
 
[[Grün: Arbeitsblätter | <span style="background-color:#00CD00"> $Aha!$ </span>]]  Dieses [http://tube.geogebra.org/m/1525527 Arbeitsblatt] zeigt dir die Grundlegende Idee am Beispiel einer linearen Regression (siehe weiter unten).  
−
 
 
<ggb_applet width="950" height="600" version="5.0" ggbBase64="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" enableRightClick="false" showAlgebraInput="false" enableShiftDragZoom="true" showMenuBar="false" showToolBar="false" showToolBarHelp="true" enableLabelDrags="false" showResetIcon="true" />
 
<ggb_applet width="950" height="600" version="5.0" ggbBase64="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" enableRightClick="false" showAlgebraInput="false" enableShiftDragZoom="true" showMenuBar="false" showToolBar="false" showToolBarHelp="true" enableLabelDrags="false" showResetIcon="true" />
  

Version vom 27. August 2015, 09:23 Uhr

Einleitung

Sind zwei metrische Merkmale gegeben (z.B. Alter und Verdienst), so kann mithilfe der Regression der Zusammenhang dieser Merkmale überprüft und beschrieben werden.


Hierbei kann man die Merkmale in einer Punktwolke darstellen. Die Regression versucht nun, eine Funktion "möglichst gut" durch diese Punkte zu legen. "Möglichst gut" bedeutet dabei, dass die Summe der Quadrate der y-Abstände zwischen Funktion und Punkten so gering wie möglich sein soll.


$Aha!$ Dieses Arbeitsblatt zeigt dir die Grundlegende Idee am Beispiel einer linearen Regression (siehe weiter unten).

Da wir im Unterricht die Regressionsgleichung immer mithilfe des Technologieeinsatzes lösen, überspringen wir die Herleitung der Regressionsgleichungen.

Regressionsgleichung mithilfe von Technologie berechnen und darstellen

GeoGebra Ti-8x
!! Wichtig beim ersten Mal!! Damit bei der Regression auch der Korrelationskoeffizient angezeigt wird, muss "Diagnostic" auf "ON" sein. Dies machst du, indem du auf Folgendes klickst:

$[2nd]+[0]$ dann gehe hinunter zu $DiagnosticOn$ und drücke 2 Mal $[Enter]$

Das Video zeigt dir, wie die Regression mit einer linearen Funktion funktioniert.


Achtung Mit dem TI-82 musst du, um die lineare Funktion automatisch zu zeichnen (anders als im Video (siehe Minute 1:26 )), den Befehl $$LinReg(ax+b)\ L1,\ L2,\ Y1$$ eintippen. ($L1$ und $L2$ findest du bei $[2nd]+[1]$ bzw. $[2nd]+[2]$ und $Y1$ findest du unter $[VARS]+[\rightarrow ]+[Function]$)

Lineare Regression

Bei der linearen Regression werdne die Daten mithilfe einer linearen Funktion ("Gerade") verbunden. 

Beispiel

Korrelationskoeffizient $r$

Durch Berechnung der Regressionsgeraden kann noch keine Aussage über die Stärke des Zusammenhangs zweier Merkmale (X und Y) ausgesagt werden. Dazu benötigt man den


Definition
Grün rufezeichen.png
 Korrelationskoeffizient $r$

Der Korrelationskoeffizient $r$ gibt an, wie stark zwei Merkmale $X$ und $Y$ zusammenhängen. Je stärker die Korrelation, desto näher ist $r$ bei $+1$ (bei einem positiven Zusammenhang) oder bei $-1$ (bei einem negativen Zusammenhang. Ist $r$ nahe bei 0, so herrscht keine Korrelation. 

skizze mit r


Beispiele


Korrelation und Kausalität

Merke
Rotes rufezeichen.png
 Eine starke Korrelation (d.h. $\vert r\vert$ nahe bei 1) bedeutet noch lange nicht, dass es auch einen ursächlichen Zusammenhang zwischen zwei Merkmalen gibt. Oft spielen z.B. noch viel mehr mehr Einflüsse eine Rolle.


Beispiele für Korrelation aber (wahrscheinlich) keinen direkte ursächlichen Zusammenhang:

  • Die größe der Bevölkerung (X) hat Auswirkungen auf die Geschwindigkeit der Plattentektonik (Y).
Je mehr Menschen auf einer Kontinentalplatte leben, desto schneller bewegt sich diese. Beispiele: Indien, Japan.
  • Ein Rückgang an Störchen führt zu einer Abnahme an Neugeburten (Quelle).
Tatsächlich spielt hier eine dritte Variable, nämlich die Verstädterung einer Region eine Rolle.

Beispiele

Maturaaufgaben

Regressionsmodell mithilfe von Technologie bestimmen


Matura-Aufgaben

siehe

  • Urlaubsreisen
  • Schotterwerk
  • Sektkellerei
Von „https://3.vobs.at/maturawiki/index.php?title=Regression&oldid=4127“