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# Chapter3Bwd - 118 Chapter Number and Title ction New York...

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118 Chapter Number and Title SIR FRANCIS GALTON Correlation, Regression, and Heredity The least-squares method will happily fit a straight line to any two-variable data. It is an old method, going back to the French mathematician Legendre in about 1805. Legendre invented least squares for use on data from astronomy and surveying. It was Sir Francis Galton (1822–1911), however, who turned “regression” into a general method for understanding relationships. He even invented the word. While he was at it, he also invented “correlation,” both the word and the definition of r. Galton was one of the last gentleman scientists, an upper-class Englishman who studied medicine at Cambridge and explored Africa before turning to the study of heredity. He was well connected here also: Charles Darwin, who published The Origin of Species in 1859, was his cousin. Galton was full of ideas but was no mathematician. He didn’t even use least squares, preferring to avoid unpleasant computations. But Galton was the first to apply regression ideas to biological and psychological data. He asked: If people’s heights are distributed normally in every generation, and height is inherited, what is the rela- tionship between generations? He discovered a straight-line relationship between the heights of parent and child and found that tall parents tended to have children who were taller than average but less tall than their parents. He called this “regression toward medi- ocrity.” The name “regression” came to be applied to the statistical method. Galton was full of ideas but was no mathematician. He didn’t even use least squares, preferring to avoid unpleasant computations. The Granger Collection, New York

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Examining Relationships Introduction 3.1 Scatterplots 3.2 Correlation 3.3 Least-Squares Regression Chapter Review c h e r a p t 3
120 Chapter 3 Examining Relationships ACTIVITY 3 SAT/ACT Scores Materials: Pencil, grid paper Is there an association between SAT Math scores and SAT Verbal scores? If a student performs well on the Math part of the SAT exam, will he or she do well on the Verbal part, too? If a student performs well on one part, does that suggest that the student will not do as well on the other? Is it rare or fairly common for students to score about the same on both parts of the SAT? In this activity you will collect, anonymously of course, the SAT Math and SAT Verbal scores for each member of the class who has taken the SAT exam. You will then plot these data and inspect the graph to see if a pattern is evident. If your school is in a state where the ACT exam is the principal college placement test, then use ACT scores. 1. Begin by writing your Math score and Verbal score on an index card or similar uniform “ballot.” Label your Math score M, and your Verbal score V. A selected student should collect the folded index cards in a box or other container. When all of the index cards have been placed in the box, mix them without looking, so that each student’s privacy is protected.

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Chapter3Bwd - 118 Chapter Number and Title ction New York...

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