Skip to main content
SpringerLink
Log in

Measures of Association: Correlation and Regression

  • Chapter
Applied Statistics

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

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

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

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

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

    MathSciNet  Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  • 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 [see also Subrahmaniam, K. and K.: Multivariate Analysis, A Selected and Abstracted Bibliography 1957–1972. M. Dekker; pp. 265 New York 1973]

    Google Scholar 

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

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  • Blomqvist, N.: (1) On a measure of dependence between two random variables. Ann. Math. Statist. 21(1950), 593–601. (2) Some tests based on dichotomization. Ann. Math. Statist. 22 (1951), 362–371

    Article  MATH  MathSciNet  Google Scholar 

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

    Google Scholar 

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

    Article  Google Scholar 

  • Chambers, J. M.: Fitting nonlinear models: numerical techniques. Biometrika 60(1973), 1–13[see also Murray, W. (Ed.): Numerical Methods for Unconstrained Optimization. (Acad. Press) London 1972]

    Article  MATH  MathSciNet  Google Scholar 

  • 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 

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

    Google Scholar 

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

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  • 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 

  • 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 

  • 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 

  • Daniel, C., and Wood, F. S. (with J. W. Gorman): Fitting Equations to Data. Computer Analysis of Multifactor Data for Scientists and Engineers. (Wiley-Interscience, 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 

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

    Google Scholar 

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

    Google Scholar 

  • 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 

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

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  • 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), 114–122and 189–197

    Article  Google Scholar 

  • 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 

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

    Google Scholar 

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

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  • 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

    MATH  MathSciNet  Google Scholar 

  • Heald, M. A.: Least Squares made easy. Amer. J. Phys. 37(1969), 655–662

    Article  Google Scholar 

  • Hotelling, H.: (1) 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 [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]. (2) New light on the correlation coefficient and its transforms. J. Roy. Statist. Soc. B 15 (1953), 193–232

    Article  MATH  MathSciNet  Google Scholar 

  • 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

    Google Scholar 

  • Hoel, P. G.: Methods for comparing growth type curves. Biometrics 20(1964), 859–872

    Article  MATH  Google Scholar 

  • 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 

  • Kendali, M. G.: (1) A new measure of rank correlation. Biometrika 30(1938), 81–93. (2) Multivariate Analysis. (Griffin; pp. 210) London 1975. (3) Rank Correlation Methods, 3rd ed. London 1962, pp. 38–41 (4th ed. 1970). (4) Ronald Aylmer Fisher, 1890–1962. Biometrika 50 (1963), 1–15. (5) Time Series. (Griffin; pp. 197) London 1973

    Google Scholar 

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

    Article  Google Scholar 

  • Koller, S.: (1) Statistische Auswertung der Versuchsergebnisse. In Hoppe-Seyler/Thierfelder’s Handb. d. physiologisch-und pathologisch-chemischen Analyse, 10th edition, vol. II, pp. 931–1036, Berlin-Göttingen-Heidelberg 1955, pp. 1002–1004. (2) Typisierung korrelativer Zusammenhänge. Metrika 6 (1963), 65–75 [see also 17 (1971), 30–42]. (3) Systematik der statistischen Schlußfehler. Method. Inform. Med. 3 (1964), 113–117. (4) Graphische Tafeln zur Beurteilung statistischer Zahlen. 3rd edition. Darmstadt 1953 (4th edition 1969)

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Google Scholar 

  • 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 

  • Kres, H.: Statistische Tafeln zur Multivariaten Analysis. (Springer, 431 pages) Berlin, Heidelberg, New York 1975

    Google Scholar 

  • 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 

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

    Article  Google Scholar 

  • Lees, Ruth, W., and Lord, F. M.: (1) Nomograph for Computing partial correlation coefficients. J. Amer. Statist. Assoc. 56(1961), 995–997. (2) Corrigenda 57 (1962), 917–918

    Article  MATH  MathSciNet  Google Scholar 

  • Lieberson, S.: Non-graphic computation of KendalPs tau. Amer. Statist. 17 (Oct. 1961), 20–21

    Article  Google Scholar 

  • Linder, A.: (1) Statistische Methoden für Naturwissenschaftler, Mediziner und Ingenieure. 3rd edition. Basel 1960, page 172. (2) Anschauliche Deutung und Begründung des Trennverfahrens. Method. Inform. Med. 2 (1963), 30–33. (3) Trennverfahren bei qualitativen Merkmalen. Metrika 6 (1963), 76–83

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  • 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]

    Article  MATH  MathSciNet  Google Scholar 

  • Mandel, J.: (1) Fitting a straight line to certain types of cumulative data. J. Amer. Statist. Assoc. 52(1957), 552–566. (2) Estimation of weighting factors in linear regression and analysis of variance. Technometrics 6 (1964), 1–25

    Article  MATH  MathSciNet  Google Scholar 

  • 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 

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

    Article  Google Scholar 

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

    Google Scholar 

  • Morrison, D. F.: Multivariate Statistical Methods. 2nd ed. (McGraw-Hill, pp. 416), New York 1976

    Google Scholar 

  • 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 

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

    Google Scholar 

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

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Google Scholar 

  • Quenouille, M. H.: Rapid Statistical Calculations. Griffin, London 1959 Raatz, U.: Die Berechnung des SPEARMANschen Rangkorrelationskoeffizienten aus einer bivariaten Häufigkeitstabelle. Biom. Z. 13(1971), 208–214

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Rao, C. R.: (1) Multivariate analysis: an indispensable aid in applied research (with an 81 reference bibliography). Sankhya 22(1960), 317–338. (2) Linear Statistical Inference and Its Applications. New York 1965 (2nd ed. 1973). (3) Recent trends of research work in multivariate analysis. Biometrics 28 (1972), 3–22

    MATH  MathSciNet  Google Scholar 

  • 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  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Google Scholar 

  • Sachs, L.: Statistische Methoden. Ein Soforthelfer. 3rd revised edition. (Springer, 105 pages) Berlin, Heidelberg, New York 1976, pages 91–93 (5th revised edition 1982)

    Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

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

    Google Scholar 

  • Samiuddin, M.: On a test for an assigned value of correlation in a bivariate normal distribution. Biometrika 57(1970), 461–464[cf. K. Stange: Statist. Hefte 14 (1973), 206–236]

    MathSciNet  Google Scholar 

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

    MathSciNet  Google Scholar 

  • 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 

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

    Article  Google Scholar 

  • 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; Kowalski, Ch. J. and K. E. Guire, Growth 38 (1974), 131–169 as well as 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 

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

    Google Scholar 

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

    Google Scholar 

  • Spearman, C: (1) The proof and measurement of association between two things. Amer. J. Psychol. 15(1904), 72–101. (2) The method “of right and wrong cases” (“constant Stimuli”) without Gauss formulae. Brit. J. Phychol. 2 (1908), 227–242

    Article  Google Scholar 

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

    Article  Google Scholar 

  • 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

    Article  MATH  MathSciNet  Google Scholar 

  • Stuart, A.: Calculation of Spearman’s rho for ordered two-way classifications. American Statistician 17 (Oct. 1963), 23–24 Student: Probable error of a correlation coefficient. Biometrika 6 (1908), 302–310

    Article  Google Scholar 

  • Swanson, P., Leverton, R., Gram, M. R., Roberts, H., and Pesek, I.: Blood values of women: cholesterol. Journal of Gerontology 10(1955) 41–47, cited by Snedecor, G. W., Statistical Methods, 5th ed., Arnes 1959, p. 430

    Google Scholar 

  • Täte, R. F.: (1) Correlation between a discrete and a continuous variable. Pointbiserial correlation. Ann. Math. Statist. 25(1954), 603–607. (2) The theory of correlation between two continuous variables when one is dichotomized. Biometrika 42 (1955), 205–216. (3) Applications of correlation models for biserial data. J. Amer. Statist. Assoc. 50 (1955), 1078–1095. (4) Conditional-normal regression models. J. Amer. Statist. Assoc. 61 (1966), 477–489

    Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Google Scholar 

  • 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 

  • Walter, E.: Rangkorrelation und Quadrantenkorrelation. Züchter Sonderh. 6, Die Frühdiagnose in der Züchtung und Züchtungsforschung II (1963), 7-11

    Google Scholar 

  • 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 

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

    Google Scholar 

  • 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

    MATH  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  MATH  MathSciNet  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  MATH  MathSciNet  Google Scholar 

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

    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]

    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, III. 1970

    Google Scholar 

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

    Article  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

    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  MATH  MathSciNet  Google Scholar 

  • Anseombe, 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]

    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)]

    Article  Google Scholar 

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

    Google Scholar 

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

    Article  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]

    Article  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 

  • 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

    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  MATH  MathSciNet  Google Scholar 

  • Enderlein, G., Reiher, W., and Trommer, R.: Mehrfache lineare Regression, polynomiale 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

    Article  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

    Article  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 

  • Hamaker, H. C: On multiple regression analysis. Statistica Neerlandica 16(1962), 31–56

    Article  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  MATH  MathSciNet  Google Scholar 

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

    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]

    Article  Google Scholar 

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

    Article  MATH  MathSciNet  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 14 (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. Grifiin, pp. 120), London 1966

    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  MATH  MathSciNet  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  MATH  MathSciNet  Google Scholar 

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

    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  MATH  MathSciNet  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

  1. Abteilung Medizinische Statistik und Dokumentation im Klinikum, Universität Kiel, D-2300, Kiel 1, Federal Republic of Germany

    Lothar Sachs

Authors
  1. Lothar Sachs
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 1982 Springer-Verlag New York Inc.

About this chapter

Cite this chapter

Sachs, L. (1982). Measures of Association: Correlation and Regression. In: Applied Statistics. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-0123-3_8

Download citation

  • DOI: https://doi.org/10.1007/978-1-4684-0123-3_8

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4684-0125-7

  • Online ISBN: 978-1-4684-0123-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation