Regresi linear

Dalam perangkaan, regresi linear ialah satu pendekatan linear untuk memodelkan hubungan antara respons skalar dengan satu atau lebih pembolehubah penjelasan (juga dikenali sebagai pembolehubah bersandar dan tidak bersandar). Kes satu pembolehubah penjelasan dipanggil regresi linear mudah; untuk lebih daripada satu, proses itu dipanggil regresi linear berganda.^[1] Istilah ini berbeza daripada regresi linear multivariat, di mana berbilang pembolehubah bersandar berkorelasi diramalkan, bukannya pembolehubah skalar tunggal.^[2]

Dalam regresi linear, hubungan dimodelkan menggunakan fungsi peramal linear di mana parameter modelnya yang tidak diketahui adalah dianggarkan daripada data. Model sedemikian dipanggil model linear.^[3] Lazimnya, min bersyarat bagi respons yang diberikan nilai pembolehubah penjelasan (atau peramal) diandaikan sebagai fungsi afine bagi nilai tersebut; kadangkala median bersyarat atau beberapa kuantil lain digunakan. Seperti semua bentuk analisis regresi, regresi linear memfokuskan pada taburan kebarangkalian bersyarat respons tersebut yang diberikan nilai peramal, bukannya pada taburan kebarangkalian bersama semua pembolehubah ini, yang merupakan domain analisis multivariat.

Rujukan

Petikan

^ David A. Freedman (2009). Statistical Models: Theory and Practice. Cambridge University Press. m/s. 26. A simple regression equation has on the right hand side an intercept and an explanatory variable with a slope coefficient. A multiple regression e right hand side, each with its own slope coefficient
^ Rencher, Alvin C.; Christensen, William F. (2012), "Chapter 10, Multivariate regression – Section 10.1, Introduction", Methods of Multivariate Analysis, Wiley Series in Probability and Statistics, 709 (ed. 3rd), John Wiley & Sons, m/s. 19, ISBN 9781118391679.
^ Hilary L. Seal (1967). "The historical development of the Gauss linear model". Biometrika. 54 (1/2): 1–24. doi:10.1093/biomet/54.1-2.1. JSTOR 2333849.

Sumber

Cohen, J., Cohen P., West, S.G., & Aiken, L.S. (2003). Applied multiple regression/correlation analysis for the behavioral sciences. (2nd ed.) Hillsdale, NJ: Lawrence Erlbaum Associates
Charles Darwin. The Variation of Animals and Plants under Domestication. (1868) (Chapter XIII describes what was known about reversion in Galton's time. Darwin uses the term "reversion".)
Draper, N.R.; Smith, H. (1998). Applied Regression Analysis (ed. 3rd). John Wiley. ISBN 978-0-471-17082-2.
Francis Galton. "Regression Towards Mediocrity in Hereditary Stature," Journal of the Anthropological Institute, 15:246-263 (1886). (Facsimile at: [1])
Robert S. Pindyck and Daniel L. Rubinfeld (1998, 4h ed.). Econometric Models and Economic Forecasts, ch. 1 (Intro, incl. appendices on Σ operators & derivation of parameter est.) & Appendix 4.3 (mult. regression in matrix form).

Bacaan lanjut

Pedhazur, Elazar J (1982). Multiple regression in behavioral research: Explanation and prediction (ed. 2nd). New York: Holt, Rinehart and Winston. ISBN 978-0-03-041760-3.
Mathieu Rouaud, 2013: Probability, Statistics and Estimation Chapter 2: Linear Regression, Linear Regression with Error Bars and Nonlinear Regression.
National Physical Laboratory (1961). "Chapter 1: Linear Equations and Matrices: Direct Methods". Modern Computing Methods. Notes on Applied Science. 16 (ed. 2nd). Her Majesty's Stationery Office.

Pautan luar

Least-Squares Regression, PhET Interactive simulations, University of Colorado at Boulder
DIY Linear Fit

[Freedman09-1] David A. Freedman (2009). Statistical Models: Theory and Practice. Cambridge University Press. m/s. 26. A simple regression equation has on the right hand side an intercept and an explanatory variable with a slope coefficient. A multiple regression e right hand side, each with its own slope coefficient

[2] Rencher, Alvin C.; Christensen, William F. (2012), "Chapter 10, Multivariate regression – Section 10.1, Introduction", Methods of Multivariate Analysis, Wiley Series in Probability and Statistics, 709 (ed. 3rd), John Wiley & Sons, m/s. 19, ISBN 9781118391679.

[3] Hilary L. Seal (1967). "The historical development of the Gauss linear model". Biometrika. 54 (1/2): 1–24. doi:10.1093/biomet/54.1-2.1. JSTOR 2333849.

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