Skip to main content

Measures of Association: Correlation and Regression

  • Chapter
Book cover Applied Statistics

Part of the book series: Springer Series in Statistics ((SSS))

  • 1165 Accesses

Abstract

In many situations it is desirable to learn something about the association between two attributes of an individual, a material, a product, or a process. In some cases it can be ascertained by theoretical considerations that two attributes are related to each other. The problem then consists of determining the nature and degree of the relation. First the pairs of values (x i , y i ) are plotted in a coordinate system in a two dimensional space. The resulting scatter diagram gives us an idea about the dispersion, the form and the direction of the point “cloud”.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

[8:5] Chapter 5

  1. Abbas, S.: Serial correlation coefficient. Bull. Inst. Statist. Res. Tr. 1 (1967), 65–76

    MathSciNet  Google Scholar 

  2. Acton, F. S.: Analysis of Straight-Line Data. New York 1959

    MATH  Google Scholar 

  3. Anderson, R. L., and Houseman, E. E.: Tables of Orthogonal Polynomial Values Extended to N = 104. Res. Bull. 297, Agricultural Experiment Station, Ames, Iowa 1942 (Reprinted March 1963)

    Google Scholar 

  4. Anderson, T. W.: An Introduction to Multivariate Statistical Analysis. New York 1958

    MATH  Google Scholar 

  5. Anderson, T. W., Gupta, S. D., and Styan, G. P. H.: A Bibliography of Multivariate Statistical Analysis. (Oliver and Boyd; pp. 654) Edinburgh and London 1973

    Google Scholar 

  6. Subrahmaniam, K. and K.: Multivariate Analysis, A Selected and Abstracted Bibliography 1957–1972. (M. Dekker; pp. 265) New York 1973

    MATH  Google Scholar 

  7. Bancroft, T. A.: Topics in Intermediate Statistical Methods. (Iowa State Univ.) Ames, Iowa 1968

    Google Scholar 

  8. Bartlett, M.S.: Fitting a straight line when both variables are subject to error. Biometrics 5 (1949), 207–212

    Article  MathSciNet  Google Scholar 

  9. Barton, D. E., and Casley, D. J.: A quick estimate of the regression coefficient. Biometrika 45 (1958), 431–435

    MATH  Google Scholar 

  10. Blomqvist, N.: On a measure of dependence between two random variables. Ann. Math. Statist. 21 (1950), 593–601.

    Article  MathSciNet  MATH  Google Scholar 

  11. Blomqvist, N.: Some tests based on dichotomization. Ann. Math. Statist. 22 (1951), 362–371

    Article  MathSciNet  MATH  Google Scholar 

  12. Brown, R. G.: Smoothing, Forecasting and Prediction of Discrete Time Series. (Prentice-Hall, pp. 468) London 1962 [cf. E. McKenzie, The Statistician 25 (1976), 3–14]

    Google Scholar 

  13. Carlson, F. D., Sobel, E., and Watson, G. S.: Linear relationships between variables affected by errors. Biometrics 22 (1966), 252–267

    Article  Google Scholar 

  14. Chambers, J. M.: Fitting nonlinear models: numerical techniques. Biometrika 60 (1973), 1–13

    Article  MathSciNet  MATH  Google Scholar 

  15. See also Murray, W. (Ed.): Numerical Methods for Unconstrained Optimization. (Acad. Press) London 1972

    Google Scholar 

  16. Cohen, J.: A coefficient of agreement for nominal scales. Educational and Psychological Measurement 20 (1960), 37–46 [see Biometrics 36 (1980), 207–216]

    Article  Google Scholar 

  17. Cole, La M. C.: On simplified computations. The American Statistician 13 (February 1959), 20

    Google Scholar 

  18. Cooley, W. W., and Lohnes, P. R.: Multivariate Data Analysis. (Wiley, pp. 400) London 1971

    MATH  Google Scholar 

  19. Cornfield, J.: Discriminant functions. Rev. Internat. Statist. Inst. 35 (1967), 142–153 [see also J. Amer. Statist. Assoc. 63 (1968), 1399–1412, Biometrics 35 (1979), 69–85 and 38 (1982), 191–200 and Biometrical Journal 22 (1980), 639–649]

    Article  MathSciNet  Google Scholar 

  20. Cowden, D. J., and Rucker, N. L.: Tables for Fitting an Exponential Trend by the Method of Least Squares. Techn. Paper 6, University of North Carolina, Chapel Hill 1965

    Google Scholar 

  21. Cox, D. R., and Snell, E. J.: A general definition of residuals. J. Roy. Statist. Soc. B 30 (1968), 248–275 [see also J. Qual. Technol. 1 (1969), 171–188, 294; Biometrika 58 (1971), 589–594; Biometrics 31 (1975), 387–410; Technometrics 14 (1972), 101–111, 781–790; 15 (1973), 677–695, 697–715; 17 (1975), 1–14]

    MathSciNet  Google Scholar 

  22. Cureton, E. E.: Quick fits for the lines y = bx and y = a + bx when errors of observation are present in both variables. The American Statistician 20 (June 1966), 49

    Google Scholar 

  23. Daniel, C., and Wood, F. S. (with J. W. Gorman): Fitting Equations to Data. Computer Analysis of Multifactor Data for Scientists and Engineers. (Wiley-Inter-science, pp. 342) New York 1971 [2nd edition, pp. 458, 1980] [see also Applied Statistics 23 (1974), 51–59 and Technometrics 16 (1974), 523–531]

    Google Scholar 

  24. Dempster, A. P.: Elements of Continuous Multivariate Analysis. (Addison-Wesley, pp. 400) Reading, Mass. 1968

    Google Scholar 

  25. Draper, N. R., and Smith, H.: Applied Regression Analysis. 2nd ed. (Wiley; pp. 709) New York 1981

    MATH  Google Scholar 

  26. Duncan, D. B.: Multiple comparison methods for comparing regression coefficients. Biometrics 26 (1970), 141–143 (see also B. W. Brown, 143–144)

    Article  Google Scholar 

  27. Dunn, O. J.: A note on confidence bands for a regression line over a finite range. J. Amer. Statist. Assoc. 63 (1968), 1028–1033

    Article  Google Scholar 

  28. Ehrenberg, A. S. C.: Bivariate regression is useless. Applied Statistics 12 (1963), 161–179

    Article  MATH  Google Scholar 

  29. Elandt, Regina, C.: Exact and approximate power function of the non-parametric test of tendency. Ann. Math. Statist. 33 (1962), 471–481

    Article  MathSciNet  MATH  Google Scholar 

  30. Emerson, Ph. L.: Numerical construction of orthogonal polynomials for a general recurrence formula. Biometrics 24 (1968), 695–701

    Article  Google Scholar 

  31. Enderlein, G.: Die Schätzung des Produktmoment-Korrelationsparameters mittels Rangkorrelation. Biometrische Zeitschr. 3 (1961), 199–212

    Article  MATH  Google Scholar 

  32. Ferguson, G. A.: Nonparametric Trend Analysis. Montreal 1965

    MATH  Google Scholar 

  33. Fisher, R. A.: Statistical Methods for Research Workers, 12th ed. Edinburgh 1954, pp. 197–204

    Google Scholar 

  34. Friedrich, H.: Nomographische Bestimmung und Beurteilung von Regressions- und Korrelationskoeffizienten. Biometrische Zeitschr. 12 (1970), 163–187

    Article  MATH  Google Scholar 

  35. Gallant, A. R.: Nonlinear regression. The American Statistician 29 (1975), 73–81, 175 [see also 30 (1976), 44–45]

    MathSciNet  MATH  Google Scholar 

  36. Gebelein, H., and Ruhenstroth-Bauer, G.: Über den statistischen Vergleich einer Normalkurve und einer Prüfkurve. Die Naturwissenschaften 39 (1952), 457–461

    Article  Google Scholar 

  37. Gibson, Wendy, M., and Jowett, G. H.: “Three-group” regression analysis. Part I. Simple regression analysis. Part II. Multiple regression analysis. Applied Statistics 6 (1957), 114–122 and 189–197

    Article  Google Scholar 

  38. Glasser, G. J., and Winter, R. F.: Critical values of the coefficient of rank correlation for testing the hypothesis of independence. Biometrika 48 (1961), 444–448

    MATH  Google Scholar 

  39. Gregg, I. V., Hossel, C. H., and Richardson, J. T.: Mathematical Trend Curves - An Aid to Forecasting. (I.C.I. Monograph No. 1), Edinburgh 1964

    Google Scholar 

  40. Griffin, H. D.: Graphic calculation of Kendall’s tau coefficient. Educ. Psychol. Msmt. 17 (1957), 281–285

    Article  Google Scholar 

  41. Hahn, G. J.: Simultaneous prediction intervals for a regression model. Technometrics 14 (1972), 203–214

    MATH  Google Scholar 

  42. Hahn, G. J., and Hendrickson, R. W.: A table of percentage points of the distribution of the largest absolute value of k student t variates and its applications. Biometrika 58 (1971), 323–332

    MathSciNet  MATH  Google Scholar 

  43. Hocking, R. R., and Pendleton, O. J.: The regression dilemma. Commun. Statist.- Theor. Meth. 12 (1983), 497–527

    Article  MATH  Google Scholar 

  44. Hotelling, H.: The selection of variates for use in prediction with some comments on the general problem of nuisance parameters. Ann. Math. Statist. 11 (1940), 271–283

    Article  MathSciNet  MATH  Google Scholar 

  45. Cf. O. J. Dunn et al., J. Amer. Statist. Assoc. 66 (1971), 904–908, Biometrics 31 (1975), 531–543 and Biometrika 63 (1976), 214–215.

    Google Scholar 

  46. Hotelling, H.: New light on the correlation coefficient and its transforms. J. Roy. Statist. Soc. B 15 (1953), 193–232

    MathSciNet  Google Scholar 

  47. Hiorns, R. W.: The Fitting of Growth and Allied Curves of the Asymptotic Regression Type by Stevens Method. Tracts for Computers No. 28. Cambridge Univ. Press 1965

    MATH  Google Scholar 

  48. Hoerl, A. E., Jr.: Fitting Curves to Data. In J. H. Perry (Ed.): Chemical Business Handbook. (McGraw-Hill) London 1954, 20–55/20–77 (see also 20–16)

    Google Scholar 

  49. Kendall, M. G.: A new measure of rank correlation. Biometrika 30 (1938), 81–93.

    MathSciNet  MATH  Google Scholar 

  50. Kendall, M. G.: Multivariate Analysis. (Griffin; pp. 210) London 1975.

    MATH  Google Scholar 

  51. Kendall, M. G.: Rank Correlation Methods, 3rd ed. London 1962, pp. 38–41 (4th ed. 1970).

    Google Scholar 

  52. Kendall, M. G.: Ronald Aylmer Fisher, 1890–1962. Biometrika 50 (1963), 1–15.

    Article  MathSciNet  MATH  Google Scholar 

  53. Kendall, M. G.: Time Series. (Griffin; pp. 197) London 1973

    Google Scholar 

  54. Kerrich, J. E.: Fitting the line y = ax when errors of observation are present in both variables. The American Statistician 20 (February 1966), 24

    Google Scholar 

  55. Koller, S.: Statistische Auswertung der Versuchsergebnisse. In Hoppe-Seyler/Thier-felder’s Handb. d. physiologisch- und pathologisch-chemischen Analyse, 10th edition, vol. II, pp. 931–1036, Berlin-Göttingen-Heidelberg 1955, pp. 1002–1004.

    Google Scholar 

  56. Koller, S.: Typisierung korrelativer Zusammenhänge. Metrika 6 (1963), 65–75 [see also 17 (1971), 30–42].

    Article  Google Scholar 

  57. Koller, S.: Systematik der statistischen Schlußfehler. Method. Inform. Med. 3 (1964), 113–117.

    Google Scholar 

  58. Koller, S.: Graphische Tafeln zur Beurteilung statistischer Zahlen. 3rd edition. Darmstadt 1953 (4th edition 1969)

    MATH  Google Scholar 

  59. Konijn, H. S.: On the power of certain tests for independence in bivariate populations. Ann. Math. Statist. 27 (1956), 300–323

    Article  MathSciNet  MATH  Google Scholar 

  60. Kramer, C. Y.: A First Course in Methods of Multivariate Analysis. (Virginia Polytech. Inst.; pp. 353) Blacksburg, Virginia 1972

    Google Scholar 

  61. Kramer, C. Y., and Jensen, D. R. : Fundamentals of multivariate analysis. Part I-IV. Journal of Quality Technology 1 (1969), 120–133, 189–204, 264–276, 2 (1970), 32–40 and 4 (1972), 177–180

    Google Scholar 

  62. Kres, H.: Statistische Tafeln zur Multivariaten Analysis. (Springer; pp. 431) New York 1975

    MATH  Google Scholar 

  63. Krishnaiah, P. R. (Ed.): Multivariate Analysis and Multivariate Analysis II, III. (Academic Press; pp. 592 and 696, 450), New York and London 1966 and 1969, 1973

    Google Scholar 

  64. Kymn, K. O.: The distribution of the sample correlation coefficient under the null hypothesis. Econometrica 36 (1968), 187–189

    Article  Google Scholar 

  65. Lees, Ruth, W., and Lord, F. M.: Nomograph for computing partial correlation coefficients. J. Amer. Statist. Assoc. 56 (1961), 995–997.

    MathSciNet  MATH  Google Scholar 

  66. Lees, Ruth, W., and Lord, F. M.: Corrigenda 57 (1962), 917–918

    Google Scholar 

  67. Lieberson, S.: Non-graphic computation of Kendall’s tau. Amer. Statist. 17 (Oct. 1961), 20–21

    Google Scholar 

  68. Linder, A.: Statistische Methoden für Naturwissenschaftler, Mediziner und Ingenieure. 3rd edition. Basel 1960, page 172.

    MATH  Google Scholar 

  69. Linder, A.: Anschauliche Deutung und Begründung des Trennverfahrens. Method. Inform. Med. 2 (1963), 30–33.

    Google Scholar 

  70. Linder, A.: Trennverfahren bei qualitativen Merkmalen. Metrika 6 (1963), 76–83

    Article  MathSciNet  MATH  Google Scholar 

  71. Lord, F. M.: Nomograph for computing multiple correlation coefficients. J. Amer. Statist. Assoc. 50 (1955), 1073–1077 [see also Biometrika 59 (1972), 175–189]

    MathSciNet  MATH  Google Scholar 

  72. Ludwig, R.: Nomogramm zur Prüfung des Produkt-Moment-Korrelationskoeffizienten r. Biometrische Zeitschr. 7 (1965), 94–95

    Article  Google Scholar 

  73. Madansky, A.: The fitting of straight lines when both variables are subject to error. J. Amer. Statist. Assoc. 54 (1959), 173–205 [see also 66 (1971), 587–589 and 77 (1982), 71–79]

    MathSciNet  MATH  Google Scholar 

  74. Mandel, J.: Fitting a straight line to certain types of cumulative data. J. Amer. Statist. Assoc. 52 (1957), 552–566.

    MathSciNet  MATH  Google Scholar 

  75. Mandel, J.: Estimation of weighting factors in linear regression and analysis of variance. Technometrics 6 (1964), 1–25

    Google Scholar 

  76. Mandel, J., and Linning, F. J.: Study of accuracy in chemical analysis using linear calibration curves. Analyt. Chem. 29 (1957), 743–749

    Article  Google Scholar 

  77. Meyer-Bahlburg, H. F. L.: Spearmans rho als punktbiserialer Korrelationskoeffizient. Biometrische Zeitschr. 11 (1969), 60–66

    Article  Google Scholar 

  78. Miller, R. G.: Simultaneous Statistical Inference. (McGraw-Hill, pp. 272), New York 1966 (Chapter 5, pp. 189–210)

    MATH  Google Scholar 

  79. Morrison, D. F.: Multivariate Statistical Methods. 2nd ed. (McGraw-Hill, pp. 425), New York 1979

    Google Scholar 

  80. Natrella, M. G.: Experimental Statistics, National Bureau of Standards Handbook 91, U.S. Govt. Printing Office, Washington, D.C., 1963, pp. 5–31

    Google Scholar 

  81. Neter, J., and Wasserman, W.: Applied Linear Statistical Models. R. D. Irwin, Homewood, IL, 1974

    Google Scholar 

  82. Nowak, S.: in Blalock, H. M., et al.: Quantitative Sociology. Academic Press, New York, 1975, Chapter 3 (pp. 79–132)

    Google Scholar 

  83. Olkin, I., and Pratt, J. W.: Unbiased estimation of certain correlation coefficients. Ann. Math. Statist. 29 (1958), 201–211

    Article  MathSciNet  Google Scholar 

  84. Olmstead, P. S., and Tukey, J. W.: A corner test of association. Ann. Math. Statist. 18 (1947), 495–513

    Article  MathSciNet  MATH  Google Scholar 

  85. Ostle, B., and Mensing, R. W.: Statistics in Research. 3rd edition. (Iowa Univ. Press; pp. 596), Ames, Iowa 1975

    Google Scholar 

  86. Pfanzagl, J.: Über die Parallelität von Zeitreihen. Metrika 6 (1963), 100–113

    Article  MATH  Google Scholar 

  87. Plackett, R. L.: Principles of Regression Analysis. Oxford 1960

    MATH  Google Scholar 

  88. Potthoff, R. F.: Some Scheffé-type tests for some Behrens-Fisher type regression problems. J. Amer. Statist. Assoc. 60 (1965), 1163–1190

    MathSciNet  MATH  Google Scholar 

  89. Press, S. J.: Applied Multivariate Analysis. (Holt, Rinehart and Winston; pp. 521) New York 1972

    MATH  Google Scholar 

  90. Prince, B. M., and Tate, R. F.: The accuracy of maximum likelihood estimates of correlation for a biserial model. Psychometrika 31 (1966), 85–92

    Article  MathSciNet  Google Scholar 

  91. Puri, M. L., and Sen, P. K.: Nonparametric Methods in Multivariate Analysis. (Wiley, pp. 450) London 1971

    MATH  Google Scholar 

  92. Quenouille, M. H.: Rapid Statistical Calculations. Griffin, London 1959

    MATH  Google Scholar 

  93. Raatz, U.: Die Berechnung des SPEARMANschen Rangkorrelationskoeffizienten aus einer bivariaten Häufigkeitstabelle. Biom. Z. 13 (1971), 208–214

    Article  MathSciNet  MATH  Google Scholar 

  94. Radhakrishna, S.: Discrimination analysis in medicine. The Statistician 14 (1964), 147–167

    Article  Google Scholar 

  95. Rao, C. R.: Multivariate analysis: an indispensable aid in applied research (with an 81 reference bibliography). Sankhya 22 (1960), 317–338.

    MathSciNet  MATH  Google Scholar 

  96. Rao, C. R.: Linear Statistical Inference and Its Applications. New York 1965 (2nd ed. 1973).

    MATH  Google Scholar 

  97. Rao, C. R.: Recent trends of research work in multivariate analysis. Biometrics 28 (1972), 3–22

    Article  MathSciNet  Google Scholar 

  98. Robson, D. S.: A simple method for constructing orthogonal polynomials when the independent variable is unequally spaced. Biometrics 15 (1959), 187–191 [see Int. Statist. Rev. 47 (1979), 31–36]

    Article  MathSciNet  MATH  Google Scholar 

  99. Roos, C. F.: Survey of economic forecasting techniques. Econometrica 23 (1955), 363–395

    Article  MATH  Google Scholar 

  100. Roy, S. N.: Some Aspects of Multivariate Analysis. New York and Calcutta 1957

    Google Scholar 

  101. Sachs, L.: Statistische Methoden. 6th revised edition. (Springer, 133 pages) Berlin, Heidelberg, New York 1984, pages 92–94

    Google Scholar 

  102. Sahai, H.: A bibliography on variance components. Int. Statist. Rev. 47 (1979), 177–222.

    MathSciNet  MATH  Google Scholar 

  103. Salzer, H. E., Richards, Ch. H., and Arsham, Isabelle: Table for the Solution of Cubic Equations. New York 1958

    MATH  Google Scholar 

  104. Samiuddin, M.: On a test for an assigned value of correlation in a bivariate normal distribution. Biometrika 57 (1970), 461–464

    MathSciNet  Google Scholar 

  105. Cf., 65 (1978), 654–656 and K. Stange: Statist. Hefte 14 (1973), 206–236

    Article  MathSciNet  MATH  Google Scholar 

  106. Saxena, A. K.: Complex multivariate statistical analysis: an annotated bibliography. International Statistical Review 46 (1978), 209–214

    MathSciNet  Google Scholar 

  107. Saxena, H. C., and Surendran, P. U.: Statistical Inference. (Chand, pp. 396), Delhi, Bombay, Calcutta 1967 (Chapter 6, 258–342), (2nd ed. 1973)

    Google Scholar 

  108. Schaeffer, M. S., and Levitt, E. E.: Concerning Kendall’s tau, a nonparametric correlation coefficient. Psychol. Bull. 53 (1956), 338–346

    Article  Google Scholar 

  109. Scharf, J.-H.: Was ist Wachstum? Nova Acta Leopoldina NF (Nr. 214) 40 (1974), 9–75 [see also Biom. Z. 16 (1974), 383–399 23 (1981), 41–54

    Google Scholar 

  110. Kowalski, Ch. J. and K. E. Guire, Growth 38 (1974), 131–169

    Google Scholar 

  111. Peil, J., Gegenbaurs morph. Jb. 120 (1974), 832–853, 862–880; 121 (1975), 163–173, 389–420; 122 (1976), 344–390; 123 (1977), 236–259; 124 (1978), 525–545, 690–714; 125 (1979), 625–660 and Biometrics 35 (1979), 255–271, 835–848; 37 (1981), 383–390]

    Google Scholar 

  112. Seal, H.: Multivariate Statistical Analysis for Biologists. London 1964

    MATH  Google Scholar 

  113. Searle, S. R.: Linear Models. (Wiley, pp. 532) New York 1971

    MATH  Google Scholar 

  114. Spearman, C.: The proof and measurement of association between two things. Amer. J. Psychol. 15 (1904), 72–101.

    Article  Google Scholar 

  115. Spearman, C.: The method “of right and wrong cases” (“constant stimuli”) without Gauss’ formulae. Brit. J. Phychol. 2 (1908), 227–242

    Google Scholar 

  116. Stammberger, A.: Ein Nomogramm zur Beurteilung von Korrelationskoeffizienten. Biometrische Zeitschr. 10 (1968), 80–83

    Article  Google Scholar 

  117. Stilson, D. W., and Campbell, V. N.: A note on calculating tau and average tau on the sampling distribution of average tau with a criterion ranking. J. Amer. Statist. Assoc. 57 (1962), 567–571

    MathSciNet  MATH  Google Scholar 

  118. Stuart, A.: Calculation of Spearman’s rho for ordered two-way classifications. American Statistician 17 (Oct. 1963), 23–24

    Google Scholar 

  119. Student: Probable error of a correlation coefficient. Biometrika 6 (1908), 302–310

    Google Scholar 

  120. Swanson, P., Leverton, R., Gram, M. R., Roberts, H., and Pesek, I.: Blood values of women: cholesterol. Journal of Gerontology 10 (1955) 41–47

    Google Scholar 

  121. cited by Snedecor, G. W., Statistical Methods, 5th ed., Ames 1959, p. 430

    Google Scholar 

  122. Tate, R. F.: Correlation between a discrete and a continuous variable. Pointbiserial correlation. Ann. Math. Statist. 25 (1954), 603–607.

    Article  MathSciNet  MATH  Google Scholar 

  123. Tate, R. F.: The theory of correlation between two continuous variables when one is dichotomized. Biometrika 42 (1955), 205–216.

    MathSciNet  MATH  Google Scholar 

  124. Tate, R. F.: Applications of correlation models for biserial data. J. Amer. Statist. Assoc. 50 (1955), 1078–1095.

    MATH  Google Scholar 

  125. Tate, R. F.: Conditional-normal regression models. J. Amer. Statist. Assoc. 61 (1966), 477–489

    MathSciNet  MATH  Google Scholar 

  126. Thöni, H.: Die nomographische Bestimmung des logarithmischen Durchschnittes von Versuchsdaten und die graphische Ermittlung von Regressionswerten. Experientia 19 (1963), 1–4

    Article  Google Scholar 

  127. Tukey, J. W.: Components in regression. Biometrics 7 (1951), 33–70

    Article  Google Scholar 

  128. Waerden, B. L. van der: Mathematische Statistik. 2nd edition. (Springer, 360 pages), Berlin 1965, page 324

    MATH  Google Scholar 

  129. Wagner, G.: Zur Methodik des Vergleichs altersabhängiger Dermatosen. (Zugleich korrelationsstatistische Kritik am sogenannten „Status varicosus“). Zschr. menschl. Vererb.-Konstit.-Lehre 53 (1955), 57–84

    Google Scholar 

  130. Walter, E.: Rangkorrelation und Quadrantenkorrelation. Zúchter Sonderh. 6, Die Frühdiagnose in der Züchtung und Züchtungsforschung II (1963), 7–11

    Article  Google Scholar 

  131. Weber, Erna: Grundriß der biologischen Statistik. 7th revised edition. (Fischer, 706 pages), Stuttgart 1972, pages 550–578 [Discr. Anal.: see also Technometrics 17 (1975), 103–109] (8th revised edition 1980)

    Google Scholar 

  132. Williams, E. J.: Regression Analysis. New York 1959

    MATH  Google Scholar 

  133. Yule, G. U., and Kendall, M. G.: Introduction to the Theory of Statistics. London 1965, pp. 264–266

    Google Scholar 

[8:5a] Factor analysis

  • Adam, J., and Enke, H.: Zur Anwendung der Faktorenanalyse als Trennverfahren. Biometr. Zeitschr. 12 (1970), 395–411

    Article  Google Scholar 

  • Bartholomew, D. J.: Factor analysis for categorical data. J. Roy. Statist. Soc. B 42 (1980), 293–321

    MathSciNet  Google Scholar 

  • Browne, M. W.: A comparison of factor analytic techniques. Psychometrika 33 (1968), 267–334

    Article  MathSciNet  Google Scholar 

  • Corballis, M. C., and Traub. R. E.: Longitudinal factor analysis. Psychometrika 35 (1970), 79–98 [see also 36 (1971), 243–249 and Brit. J. Math. Statist. Psychol. 26 (1973), 90–97]

    Article  MATH  Google Scholar 

  • Derflinger, G.: Neue Iterationsmethoden in der Faktorenanalyse. Biometr. Z. 10 (1968), 58–75

    Article  MathSciNet  MATH  Google Scholar 

  • Gollob, H. F.: A statistical model which combines features of factor analytic and analysis of variance techniques. Psychometrika 33 (1968), 73–115

    Article  MathSciNet  MATH  Google Scholar 

  • Harman, H. H.: Modern Factor Analysis. 2nd rev. ed. (Univ. of Chicago, pp. 474), Chicago 1967

    MATH  Google Scholar 

  • Jöreskog, K. G.: A general approach to confirmatory maximum likelihood factor analysis. Psychometrika 34 (1969), 183–202 [see also 36 (1971), 109–133, 409–426 and 37 (1972), 243–260, 425–440 as well as Psychol. Bull. 75 (1971), 416–423]

    Article  Google Scholar 

  • Lawley, D. N., and Maxwell, A. E.: Factor Analysis as a Statistical Method. 2nd ed. (Butterworths; pp. 153) London 1971 [see also Biometrika 60 (1973), 331–338]

    MATH  Google Scholar 

  • McDonald, R. P.: Three common factor models for groups of variables. Psychometrika 35 (1970), 111–128 [see also 401–415 and 39 (1974), 429–444]

    Article  MATH  Google Scholar 

  • Rummel, R. J.: Applied Factor Analysis. (Northwestern Univ. Press, pp. 617) Evanston, Ill. 1970

    MATH  Google Scholar 

  • Sheth, J. N.: Using factor analysis to estimate parameters. J. Amer. Statist. Assoc. 64 (1969), 808–822

    MATH  Google Scholar 

  • Überla, K.: Faktorenanalyse. Eine systematische Einführung in Theorie und Praxis für Psychologen, Mediziner, Wirtschafts- und Sozialwissenschaftler. 2nd edition. (Springer, 399 pages), Berlin-Heidelberg-New York 1971 (see in particular pages 355–363)

    Google Scholar 

  • Weber, Erna: Einführung in die Faktorenanalyse. (Fischer, 224 pages), Stuttgart 1974

    MATH  Google Scholar 

[8:5b] Multiple regression analysis

  • Abt. K.: On the identification of the significant independent variables in linear models. Metrika 12 (1967), 1–15, 81–96

    Article  MathSciNet  MATH  Google Scholar 

  • Anscombe, F. J.: Topics in the investigation of linear relations fitted by the method of least squares. With discussion. J. Roy. Statist. Soc. B 29 (1967), 1–52 [see also A 131 (1968), 265–329]

    MathSciNet  Google Scholar 

  • Beale, E. M. L.: Note on procedures for variable selection in multiple regression. Technometrics 12 (1970), 909–914 [see also 16 (1974), 221–227, 317–320 and Biometrika 54 (1967), 357–366 (see J. Amer. Statist. Assoc. 71 (1976), 249)]

    Google Scholar 

  • Bliss, C. I.: Statistics in Biology. Vol. 2. (McGraw-Hill, pp. 639), New York 1970, Chapter 18

    MATH  Google Scholar 

  • Cochran, W. G.: Some effects of errors of measurement on multiple correlation. J. Amer. Statist. Assoc. 65 (1970), 22–34

    MATH  Google Scholar 

  • Cramer, E. M.: Significance tests and tests of models in multiple regression. The American Statistician 26 (Oct. 1972), 26–30 [see also 25 (Oct. 1971), 32–34, 25 (Dec. 1971), 37–39 and 26 (April 1972), 31–33 as well as 30 (1976), 85–87]

    Google Scholar 

  • Darlington, R. B.: Multiple regression in psychological research and practice. Psychological Bulletin 69 (1968), 161–182 [see also 75 (1971), 430–431]

    Article  Google Scholar 

  • Donner, A.: The relative effectiveness of procedures commonly used in multiple regression analysis for dealing with missing values. Amer. Statist. 36 (1982), 378–381

    Google Scholar 

  • Draper, N. R., and Smith, H.: Applied Regression Analysis. (Wiley, pp. 407), New York 1966 [2nd edition, pp. 709, 1981]

    Google Scholar 

  • Dubois, P. H.: Multivariate Correlational Analysis. (Harper and Brothers, pp. 202), New York 1957

    MATH  Google Scholar 

  • Enderlein, G.: Kriterien zur Wahl des Modellansatzes in der Regressionsanalyse mit dem Ziel der optimalen Vorhersage. Biometr. Zeitschr. 12 (1970), 285–308 [see also 13 (1971), 130–156]

    Article  MathSciNet  MATH  Google Scholar 

  • Enderlein, G., Reiher, W., and Trommer, R.: Mehrfache lineare Regression, polynomial Regression und Nichtlinearitätstests. In: Regressionsanalyse und ihre Anwendungen in der Agrarwissenschaft. Vorträge des 2. Biometr. Seminars d. Deutsch. Akad. d. Landwirtschaftswissensch. Berlin, März 1965. Tagungsber. Nr. 87, Berlin 1967, pages 49–78

    Google Scholar 

  • Folks, J. L., and Antle, C. E.: Straight line confidence regions for linear models. J. Amer. Statist. Assoc. 62 (1967), 1365–1374

    MathSciNet  Google Scholar 

  • Goldberger, A. S.: Topics in Regression Analysis. (Macmillan, pp. 144), New York 1968

    Google Scholar 

  • Graybill, F. A., and Bowden, D. C.: Linear segment confidence bands for simple linear models. J. Amer. Statist. Assoc. 62 (1967), 403–408

    MathSciNet  Google Scholar 

  • Hahn, G. J., and Shapiro. S. S.: The use and misuse of multiple regression. Industrial Quality Control 23 (1966), 184–189 [see also Applied Statistics 14 (1965), 196–200; 16 (1967), 51–64, 165–172; 23 (1974), 51–59]

    Google Scholar 

  • Herne, H.: How to cook relationships. The Statistician 17 (1967), 357–370

    Article  Google Scholar 

  • Hinchen, J. D.: Multiple regression with unbalanced data. J. Qual. Technol. 2 (1970), 1, 22–29

    Google Scholar 

  • Hocking, R. R.: The analysis and selection of variables in linear regression. Biometrics 32 (1976), 1–49

    Article  MathSciNet  MATH  Google Scholar 

  • Huang, D. S.: Regression and Econometric Methods. (Wiley, pp. 274), New York 1970

    MATH  Google Scholar 

  • La Motte, L. R., and Hocking, R. R.: Computational efficiency in the selection of regression variables. Technometrics 12 (1970), 83–93 [see also 13 (1971), 403–408 and 14 (1972), 317–325, 326–340]

    Google Scholar 

  • Madansky, A.: The fitting of straight lines when both variables are subject to error. J. Amer. Statist. Assoc. 54 (1959), 173–205

    MathSciNet  MATH  Google Scholar 

  • Robinson, E. A.: Applied Regression Analysis. (Holden-Day, pp. 250), San Francisco 1969

    Google Scholar 

  • Rutemiller, H. C., and Bowers, D. A.: Estimation in a heteroscedastic regression model. J. Amer. Statist. Assoc. 63 (1968), 552–557

    Article  MathSciNet  Google Scholar 

  • Schatzoff, M., Tsao, R., and Fienberg, S.: Efficient calculation of all possible regressions. Technometrics 10 (1968), 769–779 [see also Mandel, J. (1972), 317–325]

    Article  Google Scholar 

  • Seber, G. A. F.: The Linear Hypothesis. A General Theory. (No. 19 of Griffin’s Statistical Monographs and Courses. Ch. Griffin, pp. 120), London 1966

    MATH  Google Scholar 

  • Smillie, K. W.: An Introduction to Regression and Correlation. (Acad. Pr., pp. 168), N.Y.1966

    Google Scholar 

  • Thompson, M. L.: Selection of variables in multiple regression. Part I. A review and evaluation. Part II. Chosen procedures, computations and examples. International Statistical Review 46 (1978), 1–19 and 129–146

    Article  MathSciNet  MATH  Google Scholar 

  • Toro-Vizcarrondo, C., and Wallace, T. D.: A test of the mean square error criterion for restrictions in linear regression. J. Amer. Statist. Assoc. 63 (1968), 558–572

    Article  MathSciNet  MATH  Google Scholar 

  • Ulmo, J.: Problèmes et programmes de regression. Revue de Statistique Appliquée 19 (1971), No. 1, 27–39

    MathSciNet  Google Scholar 

  • Väliaho, H.: A synthetic approach to stepwise regression analysis. Commentationes Physico-Mathematicae 34 (1969), 91–131 [supplemented by 41 (1971), 9–18 and 63–72]

    Google Scholar 

  • Wiezorke, B.: Auswahlverfahren in der Regressionsanalyse. Metrika 12 (1967), 68–79

    Article  MathSciNet  MATH  Google Scholar 

  • Wiorkowski, J. J.: Estimation of the proportion of the variance explained by regression, when the number of parameters in the model may depend on the sample size. Technometrics 12 (1970), 915–919

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1984 Springer-Verlag New York Inc.

About this chapter

Cite this chapter

Sachs, L. (1984). Measures of Association: Correlation and Regression. In: Applied Statistics. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-5246-7_8

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-5246-7_8

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-9755-0

  • Online ISBN: 978-1-4612-5246-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics