Summary
Zusammenfassung Deskriptive Statistik
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Deskriptive Statistik
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Statistik 15:Überblick:
• Lineare Regression
• Bestimmheitsmaß
LINEARE REGRESSION
Regression
• Funktionaler Zusammenhang zwischen metrischen Merkmalen
• Y: abhängige Variable, Regressand, zu erklärende Variable
• X: unabhängige Variable, Regressor, erklärende Variable
Regressionsfunktion • Einfachregression: Y = f(X)
Beziehung zwischen zwei Variablen (ein Regressand, ein Regressor)
• Mehrfachregression: Y = f(X1, X2, …, Xk)
Beziehung zwischen Regressand und mehreren Regressoren
Interpretation:
• Mathematische Beziehung
• Vorsicht: keine zwingende Kausalität (mögliche „spurious regression“)!
Die Gerade mit der besten Anpassung an die Daten wird berechnet.
LINEARE EINFACHREGRESSION
Regressionsfunktion:
• Y ist die abhängige Variable (Regressand, erklärte Variable, endogene Variable)
• X ist die unabhängige Variable X (Regressor, erklärende Variable, exogene Variable).
• a -> Achsenabschnitt
• b -> Steigung
Residuum:
REGRESSION: RESIDUEN
Definition der Residuen (e for errorterm):
Man bestimmt jene Gerade für die gilt, dass die Quadratsumme der Residuen am kleinsten ist.
d.h.
ist zu minimieren.
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