Abstract
The rather curious name regression was given to a statistical methodology by British scientist Sir Francis Galton, who analyzed the heights of sons and the average heights of their parents. From his observations, Galton (Fig. 16.1a) concluded that sons of very tall (or short) parents were generally taller (shorter) than average, but not as tall (short) as their parents. The results were published in 1886 under the title Regression Towards Mediocrity in Hereditary Stature. In the course of time the word regression became synonymous with the statistical study of the functional relationship between two or more variables. The data set illustrating Darwin’s finding and used by Pearson is given in pearson.dat. The scatterplot and regression fits are analyzed in galton.m and summarized in Fig. 16.1b. The circles correspond to pairs of father-son heights, the black line is the line y Æ x, the red line is the regression line, and the green line is the regression line constrained to pass through the origin. Darwin’s findings can be summarized by the observation that the slope of the regression (red) line was significantly smaller than the slope of the 45°-line.
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Vidakovic, B. (2011). Regression. In: Statistics for Bioengineering Sciences. Springer Texts in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0394-4_16
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DOI: https://doi.org/10.1007/978-1-4614-0394-4_16
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