The Basic Practice of Statistics 7th Edition

Published by W. H. Freeman
ISBN 10: 1-46414-253-X
ISBN 13: 978-1-46414-253-6

Chapter 4 - Scatterplots and Correlation - Apply Your Knowledge: 4.10b

Answer

r = -1

Work Step by Step

$ r = \frac{1}{(n-1)}$ $ r = \frac{1}{(n-1)} * (\frac{(x_{1}-mean)}{standard deviation}*\frac{(y_{1}-mean)}{standard deviation}+\frac{(x_{2}-mean)}{standard deviation}*\frac{(y_{2}-mean)}{standard deviation}+\frac{(x_{3}-mean)}{standard deviation}*\frac{(y_{3}-mean)}{standard deviation}+\frac{(x_{4}-mean)}{standard deviation}*\frac{(y_{4}-mean)}{standard deviation}+\frac{(x_{5}-mean)}{standard deviation}*\frac{(y_{5}-mean)}{standard deviation}+\frac{(x_{6}-mean)}{standard deviation}*\frac{(y_{6}-mean)}{standard deviation}+\frac{(x_{7}-mean)}{standard deviation}*\frac{(y_{7}-mean)}{standard deviation})$ $mean_{x} = (29.68+29.87+30.16+30.22+30.48+30.65+30.9)/7$ $mean_{x} = 211.96/7$ $mean_{x} = 30.28$ $mean_{y} = (2.63+2.58+2.68+2.6+2.48+2.38+2.26)/7$ $mean_{y} = 17.61/7$ $mean_{y} = 2.515 = 2.52$ $deviation_{x} = .43 $ (calculated via Microsoft Excel) $deviation_{y} = .15 $ (calculated via Microsoft Excel) $ r = \frac{1}{(7-1)} * (\frac{29.68-30.28}{.43}*\frac{2.63-2.52}{.13}+\frac{(29.87-30.28)}{.43}*\frac{2.58-2.52}{.13}+\frac{30.16-30.28}{.43}*\frac{2.68-2.52}{.13}+\frac{30.22-30.28}{.43}*\frac{2.6-2.52}{.13}+\frac{30.48-30.28}{.43}*\frac{2.48-2.52}{.13}+\frac{30.65-30.28}{.43}*\frac{2.38-2.52}{.13}+\frac{30.9-30.28}{.43}*\frac{2.26-2.52}{.13})$ $ r = \frac{1}{6}* (\frac{-.6}{.43}*\frac{.11}{.13}+\frac{-.41}{.43}*\frac{.06}{.13}+\frac{-.12}{.43}*\frac{.16}{.13}+\frac{-.06}{.43}*\frac{.08}{.13}+\frac{.2}{.43}*\frac{-.04}{.13}+\frac{.37}{.43}*\frac{-.14}{.13}+\frac{.62}{.43}*\frac{-.26}{.13})$ $ r = \frac{1}{6}* (-1.395*.846+(-.953)*.462+(-.279)*1.23+(-.139)*.615+.465*(-.307)+.86*-1.077+1.442*-2)$ $ r = \frac{1}{6}* (-1.4*.85+(-.95)*.46+(-.28)*1.23+(-.14)*.62+.47*(-.31)+.86*-1.08+1.44*-2)$ $ r = \frac{1}{6}* (-1.19+(-.437)+(-.3444)+(-.0868)+(-.1457)+(-.9288)+(-2.88)$ $ r = \frac{1}{6}* (-1.19+(-.44)+(-.34)+(-.09)+(-.15)+(-.93)+(-2.88)$ $ r = \frac{1}{6} * (-6.02)$ $ r = -1.0033 = -1$
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