Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Erschienen in:
Introduction Kapitel lesen Erstes Kapitel lesen

2013 | OriginalPaper | Buchkapitel

13. Simple Linear Regression and the Correlation Coefficient

verfasst von : Cheng-Few Lee, John C. Lee, Alice C. Lee

Erschienen in: Statistics for Business and Financial Economics

Verlag: Springer New York

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

In Sect. 6.9, we used correlation to provide a measure of the strength of any linear relationship between a pair of random variables X and Y. The random variables are treated perfectly symmetrically; that is, “the correlation between X and Y” is equivalent to “the correlation between Y and X.” In this chapter, we first discuss the linear relationship between a pair of variables without perfect symmetry. In other words, we assume that Y is a dependent variable and X an independent variable: Y depends on X. Then we discuss the bivariate normal relationship and concepts related to the correlation coefficient.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren
Vorheriges Kapitel Analysis of Variance and Chi-Square Tests
Nächstes Kapitel Simple Linear Regression and Correlation: Analyses and Applications
Anhänge
Nur mit Berechtigung zugänglich
Fußnoten
1
For instance, the equation y = x + 3 is a linear model with x as the independent variable and y as the dependent variable. The variable x is considered independent because it is predetermined. For any given value of x, we can find a corresponding value of y, so the value of y is dependent on the value of x. When x is equal to 4, y is equal to 7. Strictly speaking, the word independent implies that the values of this variable are preassigned and that the values of the dependent variable follow, at least in part, from this preassignment.
 
2
From ΔABD, the slope of ABC can be defined as β = BD/AD = (97−93)/(57−55) = 2.
 
3
For an illustration of the meaning of the model, let x be the amount of advertising and Y be the amount of sales. Equation 13.3 tells us that, given a certain amount of advertising, the expected amount of sales is μ yx  = α + βx.
 
4
The second equality of Eq. 13.16 holds because
$$ \begin{array}{llll} \sum\limits_{i=1}^n {\left( {{x_i}-\bar{x}} \right)\left( {{y_i}-\bar{y}} \right)} =\sum\limits_{i=1}^n {\left( {{x_i}-\bar{x}} \right){y_i}-\bar{y}\sum\limits_{i=1}^n {\left( {{x_i}-\bar{x}} \right)} } \cr \quad\quad\quad\quad\quad=\sum\limits_{i=1}^n {\left( {{x_i}-\bar{x}} \right)} {y_i} \end{array} $$
 
5
In general, a sample of 6 would not be sufficient. We use a small sample here for computational ease only.
 
6
For instance, if in economic or business research, current instead of permanent income is used as the independent variable in estimating consumption function, then there are proxy errors associated with income measurements, as discussed in Appendix 14A. If the regression equation is part of interdependent equations, then x i and є i also are not independent of each other. However, we will take Assumption A as given.
 
7
Because
$$ \sum\limits_{i=1}^n {{{{({{\hat{y}}_i}-\bar{y})}}^2}=} \sum\limits_{i=1}^n {{{{[a+b{x_i}-(a+b\bar{x})]}}^2}={b^2}} \sum\limits_{i=1}^n {{{{({x_i}-\bar{x})}}^2}} $$
 
8
Strictly speaking, regression implies causality only under some prediction cases.
 
9
The bivariate normal density function will be discussed in Appendix 3.
 
10
C. C. Wallin and J. J. Gilman (1986). “Determining the Optimum Level for R&D Spending,” Research Management, Vol. 14, No. 5, Sept./Oct., 19–24.
 
11
The weights obtained here do not consider the information of the expected rates of return for both stock A and stock B. The formula of estimating the optimal weights in terms of both variances and expected rates of return can be found in Chap.​ 8 of Cheng F. Lee et al. (1990), Security Analysis and Portfolio Management (Glenview, Ill.: Scott Foresman/Little, Brown).
 
12
This equation is based upon Whaley, Robert E. (1981), “On the Valuation of American Call Options on Stocks With Known Dividends,” Journal of Financial Economics 9, 207–211.
 
13
This portion is based upon Appendix 13.1 of Hans R. Stoll and Robert E. Whaley (1993), Futures and Options (South Western Publishing, Cincinnati).
 
14
Results of column B are a different set of data. It is good exercise for students to try them.
 
Metadaten
Titel
Simple Linear Regression and the Correlation Coefficient
verfasst von
Cheng-Few Lee
John C. Lee
Alice C. Lee
Copyright-Jahr
2013
Verlag
Springer New York
Buch
Statistics for Business and Financial Economics

Print ISBN: 978-1-4614-5896-8

Electronic ISBN: 978-1-4614-5897-5

Copyright-Jahr: 2013

DOI
https://doi.org/10.1007/978-1-4614-5897-5_13