Regression versus Correlation
Idea of the linear regression. Auxiliary material - straight lines in Cartesian geometry. The concept of distance – geometrical distance and equivalent distances in two orthogonal directions – as a prerequisite to the concept of two regression lines. Frequent errors in interpreting two regression lines. The least square concept - Adrien Marie Legendre, Francis Galton, Karl Pearson . Formal derivation of the two regression lines. Correlation coefficient as a geometrical mean of the two directional coefficients of regression lines. Which in fact measures the correlation coefficient? Udny Yule  and his warnings regarding abuse of correlation analysis. Further reading [3-4], [6-9].
KeywordsRegression Line Turbulence Intensity Atmospheric Turbulence Class Frequency Auxiliary Line
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- 1.Yule, G.U.: An Introduction to the Theory of Statistics. Charles Griffin and Co., London (1911); 2-nd Edition translated into Polish by Z. Limanowski: Wstęp do Teorji Statystyki, Gebethner i Wolff, Warszawa 1921; pp. 1–446. VI-th Edition of 1922 accessible by Internet, pp. 1–415. 14-th edition, co-author M.G. Kendall, 1950 translated into Polish as Wstęp do Teorii Statystyki. PWN, Warszawa (1966)Google Scholar
- 3.Weinberg, G.H., Schumaker, J.A., Oltman, D.: Statistics – An Intuitive Approach, 4th edn., pp. 1–447. Brooks/Cole, Monterey (1981)Google Scholar
- 4.Fisher, R.A.: The design of experiments. Oliver & Boyd, Edinburg (1935)Google Scholar
- 6.Laudański, L.M.: Statystyka nie tylko dla licencjatów (in Polish: Statistics not only for the undergraduates), Part 1 and 2, 2nd edn. Publishing House of the Rzeszow TU (2009)Google Scholar
- 7.Soper, H.E.: On the Probable Error of the Correlation Coefficient to a Second Approximation. Biometrica IX, 91–115 (1913)Google Scholar
- 8.Fisher, R.A.: Frequency Distribution of the Values of the Correlation Coefficient in Samples from Indefinitely Large Population. Biometrica X, 507–521 (1915) Google Scholar
- 10.Pearson, K., assisted by Lee, A.: On the Laws of Inheritance in Man. Biometrica 2(4), 357–462 (1903) Google Scholar