Abstract
There is a very large literature on methods of choosing a regression model but, in spite of this, there is little clear guidance on what to do in a specific case. For access to the literature see Hocking (1976,1983), Mosteller and Tukey (1977), Seber (1977), Thompson, (1978), Daniel and Wood (1980), and Miller (1984). This chapter presents a review of the main points and for further details these references should be consulted.
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References
Allen, D. M. (1974) The relationship between variable selection and data augmentation and a method for prediction. Technometrics, 16, 125–127.
Anscombe, R. J. (1981) Computing in Statistical Science Through APL. Springer-Verlag, New York.
Beale, E. M. L, Kendall, M. G. and Mann, D. W. (1967) The discarding of variables in multivariate analysis. Biometrika, 54, 357–366.
Belsley, D., Kuh, E. and Welsch, R. E. (1980) Regression Diagnostics: Identifying Influential Data and Sources of Collinearity. Wiley, New York.
Berk, K. N., (1978) Comparing subset regression procedures. Technometrics, 20, 1–6.
Clarke, M. R. B. (1981) A given algorithm for moving from one linear model to another without going back to the data. Algorithm AS 153. Appl. Statist., 30, 198–203.
Clarke, M. R. B. (1982) The Gauss-Jordan sweep operator with detection of collinearity. Algorithm AS178. Appl. Statist., 31, 166–168.
Copas, J. B. (1983) Regression, prediction and shrinkage. J. Roy. Statist. Soc. B, 45, 311–354.
Daniel, C. and Wood, F. S. (1980) Fitting Equations to Data. Wiley, New York.
Forsythe, A. B., Engelman, L., Jennrich, R. and May, P. R. A. (1973) A stopping rule for variable selection in multiple regression. J. Amer. Statist. Assoc., 68, 75–77.
Freedman, D. A. (1983) A note on screening regression equations. Amer. Statist., 37, 147–151.
Furnival, G. M. (1971) All possible regressions with less computation. Technometrics, 13, 403–408.
Furnival, G. M. and Wilson, R. W., Jr. (1974) Regression by leaps and bounds. Technometrics, 16, 499–512.
Gorman, J. W. and Toman, R. J. (1966) Selection of variables for fitting equations to data. Technometrics, 8, 27–51.
Henderson, H. V. and Vellman, P. F. (1981) Building multiple regression models interactively. Biometrics, 37, 391–411.
Hocking, R. R. (1976) The analysis, and selection of variables in linear regression. Biometrics, 32, 1–49.
Hocking R. R. (1983) Developments of linear regression methodology: 1959–1983. Technometrics, 25, 219–249.
Hocking, R. R. and Leslie, R. N. (1967) Selection of the best subset in regression analysis. Technometrics, 9, 531–540.
Judge, G. G., Griffiths, W. E., Hill, R. C. and Lee, Tsoung-Chao (1980) The Theory and Practice of Econometrics. Wiley, New York.
Mallows, C. L. (1973) Some comments on C p . Technometrics, 15, 661–675.
Miller, A. J. (1984) Selection of subsets of regression variables. J. Roy. Statist. Soc. A, 147, 389–425.
Morgan, J. A. and Tatar, J. F. (1972) Calculation of the residual sum of squares for all possible regressions. Technometrics, 14, 317–325.
Mosteller, F. and Tukey, J. W. (1977) Data Analysis and Regression, Addison-Wesley, Reading, MA.
Newton, R. G. and Spurrell, D. J. (1967a) A development of multiple regression for the analysis of routine data. Appl. Statist., 16, 51–65.
Newton, R. G. and Spurrell, D. J. (1967b) Examples of the use of elements for clarifying regression analysis. Appl. Statist., 16, 165–171.
Pope, P. T. and Webster, J. T. (1972) The use of an F-statistic in stepwise regression procedures. Technometrics, 14, 327–340.
Preece, D. A. (1981) Distribution of final digits in data. The Statistician, 30, 31–60.
Rencher, A. C. and Pun, F. C. (1980) Inflation of R 2 in best subset regression. Technometrics, 22, 49–54.
Seber, G. A. F. (1977) Linear Regression Analysis. Wiley, New York.
Spjøtvoll, E. (1972a) Multiple comparison of regression functions. Ann. Math. Statist., 43, 1076–1088.
Spjøtvoll, E. (1972b) A note on a theorem of Forsythe and Golub. SIAM J. Appl. Math., 23, 307–311.
Stone, M. (1974) Cross-validatory choice and assessment of statistical predictions. J. Roy. Statist. Soc. B, 36, 111–147.
Thompson, M. L. (1978) Selection of variables in multiple regression. Part I. A review and evaluation. Part II. Chosen procedures, computations and examples. Int. Statist. Rev., 46, 1–19 and 129–146.
Wilkinson, L. and Dallal, G. E. (1981) Tests of significance in forward selection regression with an F-to enter stopping rule. Technometrics, 23, 377–380.
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© 1986 G. Barrie Wetherill
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Barrie Wetherill, G., Duncombe, P., Kenward, M., Köllerström, J., Paul, S.R., Vowden, B.J. (1986). Choosing a regression model. In: Regression Analysis with Applications. Monographs on Statistics and Applied Probability. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4105-2_11
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DOI: https://doi.org/10.1007/978-94-009-4105-2_11
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