Abstract
The multiple linear regression model is the most commonly applied statistical technique for relating a set of two or more variables. In Chapter 3 the concept of a regression model was introduced to study the relationship between two quantitative variables X and Y. In the latter part of Chapter 3, the impact of another explanatory variable Z on the regression relationship between X and Y was also studied. It was shown that by extending the regression to include the explanatory variable Z, the relationship between Y and X can be studied while controlling or taking into account Z. In a multivariate setting, the regression model can be extended so that Y can be related to a set of p explanatory variables X 1, X 2, …, X p . In this chapter, an extensive outline of the multiple linear regression model and its applications will be presented. A data set to be used as a multiple regression example is described next.
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References
Andrews, D.F. and Pregibon, D. (1978). “Finding the Outliers that Matter.” Journal of the Royal Statistical Society, Series B 40, 85–93.
Atkinson, A.C. (1985). Plots, Transformations, and Regression. Oxford: Clarendon Press.
Belsey, D.A., Kuh, E., and Welsch, R.E. (1980). Regression Diagnostics: Identifying Influential Data and Sources of Collinearity. New York: John Wiley and Sons, Inc.
Belsey, D.A. (1984). “Demeaning Conditioning Diagnostics Through Centering (with Discussion).” The American Statistician 38, 73–77.
Berk, K.N. (1977). “Tolerance and Condition in Regression Computations.” Journal of the American Statistical Association 72, 46–53.
Box, G.E.P., Hunter, W.G. and Hunter, J.S. (1978). Statistics For Experimenters: An Introduction to Design, Data Analysis and Model Building. New York: John Wiley and Sons, Inc.
Breusch, T. and Pagan, A. (1979). “A Simple Test for Heteroscedasticity and Random Coefficient Variation.” Econometrica 47, 1287–1294.
Chatterjee, S. and Hadi, A.S. (1988). Sensitivity Analysis in Linear Regression. New York: John Wiley and Sons, Inc.
Cook, R.D. and Weisberg, S. (1982). Residuals and Influence in Regression. New York: Chapman and Hall.
Draper, N.R. and John, J.A. (1981). “Influential Observations and Outliers in Regression.” Technometrics 23, 21–26.
Fomby, T.B., Hill, R.C. and Johnson, S.R. (1984). Advanced Econometric Methods. New York: Springer-Verlag.
Freedman, D.A. (1983). “A Note on Screening Regression Equations.” American Statistician 37, 152–155.
Fuller, W.A. and Battese, G.E. (1974). “Estimation of Linear Models with Crossed Error Structure.” Journal of Econometrics 2, 67–78.
Furnival, G.M. and Wilson, R.B. (1974). “Regressions by Leaps and Bounds.” Technometrics 16, 499–511.
Gallant, A.R. and Fuller, W.A. (1973). “Fitting Segmented Polynomial Regression Models Whose Join Points have to be Estimated.” Journal of the American Statistical Association 68, 144–147.
Gibbons, D.I., McDonald, G.C. and Gunst, R.F. (1987). “The Complementary Use of Regression Diagnostics and Robust Estimators.” Naval Research Logistics 34, 109–131.
Goldfeld, S.M. and Quandt, R.E. (1965). “Some Tests for Homoscedasticity.” Journal of the American Statistical Association 60, 539–547.
Gray, J.B. and Ling, R.F. (1984). “K-Clustering as a Detection Tool for Influential Subsets in Regression.” Technometrics 26, 305–318.
Graybill, F.A. (1976). Theory and Application of the Linear Model. Boston: Duxbury Press.
Gunst, R.F. and Mason, R.L. (1980). Regression Analysis and its Applications. New York: Marcel Dekker.
Hocking, R.R. (1976). “The Analysis and Selection of Variables in Linear Regression.” Biometrics 32, 1–49.
Jobson, J.D. and Fuller, W.A. (1980). “Least Squares Estimation when the Covariance Matrix and Parameter Vector are Functionally Related.” Journal of the American Statistical Association 75, 176–181.
Judge, G.G., Griffiths, W.E., Hill, R.C., Lütkepohl, H. and Lee, T. (1985). The Theory and Practice of Econometrics, Second Edition. New York: John Wiley and Sons, Inc.
Kerlinger, F.N. and Pedhauzer, E.J. (1973). Multiple Regression in Behavioral Research. New York: Holt, Rinehart and Winston, Inc.
Lovell, M.C. (1983). “Data Mining.” The Review of Economics and Statistics 65, 1–12.
Mallows, C.L. (1986). “Augmented Partial Residuals.” Technometrics 28, 313–319.
Mansfield, E.R. and Conerly, M.D. (1987). “Diagnostic Value of Residual and Partial Residual Plots.” American Statistician 41, 107–116.
Marasingle, M.G. (1985). “A Multistage Procedure for Detecting Several Outliers in Linear Regression.” Technometrics 27, 395–399.
Montgomery, D.C. (1984). Design and Analysis of Experiments,Second Edition. New York: John Wiley and Sons, Inc.
Montgomery, D.C. and Peck, E.A. (1982). Introduction to Linear Regression Analysis. New York: John Wiley and Sons, Inc.
Myers, R.H. (1976). Response Surface Methodology. Ann Arbor, Michigan: Edwards Brothers, Inc.
Myers, R.H. (1986). Classical and Modern Regression With Applications. Boston: Duxbury Press.
Neter, J., Wasserman, W. and Kutner, M.H. (1983). Applied Linear Regression Models. Homewood, Illinois: Richard D. Irwin, Inc.
Rawlings, J.O. (1988). Applied Regression Analysis: A Research Tool. Pacific Grove, California: Wadsworth & Brooks/Cole.
Smith, P.L. (1979). “Splines as a Convenient and Useful Statistical Tool.” American Statistician 33, 57–62.
Theil, H. (1971). Principles of Econometrics. New York: John Wiley and Sons, Inc.
Thompson, M.L. (1978). “Selection of Variables in Multiple Regression: Part I. A Review and Evaluation and Part II. Chosen Procedures, Computations and Examples.” International Statistical Review 46, 119, 129–146.
Transport Canada (1985). Fuel Consumption Guide. Ottawa, Canada.
Weisberg, S. (1980). Applied Linear Regression, Second Edition. New York: John Wiley and Sons, Inc.
Welsch, R.E. (1982). “Influence Functions and Regression Diagnostics,” in Modern Data Analysis, eds. R. Laurier and A. Siegel. New York: Academic Press.
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Jobson, J.D. (1991). Multiple Linear Regression. In: Applied Multivariate Data Analysis. Springer Texts in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0955-3_4
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DOI: https://doi.org/10.1007/978-1-4612-0955-3_4
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