te negative linear association −0.75 < r 6 −0.50 strong negative linear association −1 6 r 6 −0.75 Classifying the strength of a linear relationship using the correlation coefficient Classify the strength of each of the following values of the correlation coefficient according to the previous table: a r = −0.08 b r = 0.80 c r = 0.56 d r = −0.3 Uncorrected 2nd sample pages • Cambridge University Press and Assessment © Lipson, et al 2025 • 978-1-009-57800-4 • Ph 03 8671 140055:T66f,42 Chapter 1 Bivariate data analysis 1 Solution Explanation a No linear association r = −0.08 lies in the interval −0.25 < r < 0.25 b Strong positive linear r = 0.80 lies in the interval 0.75 ≤ r ≤ 1 association r = 0.56 lies in the interval 0.50 ≤ r < 0.75 U N SA C O M R PL R E EC PA T E G D ES c Moderate positive linear association d Weak negative linear r = −0.3 lies in the interval −0.50 < r ≤ −0.25 association Section Summary I Pearson’s correlation coefficient r is a measure of the strength of a linear association when the variables are numeric and the association is linear. I Assumptions when using Pearson’s correlation coefficient, r are: B the data from both variables are numerical. B the association is linear. I Pearson’s correlation coefficient, r: B has a value between –1 and +1, with larger values indicating stronger associations. B is close to zero if there is no association. B is positive if the direction of the linear association is positive. B is negative if the direction of the linear association is negative. I The strength of the correlation coefficient is classified according to the following table: 0.75 ≤ r ≤ 1 strong positive association 0.50 6 r < 0.75 moderate positive association 0.25 6 r < 0.50 weak positive association −0.25 < r < 0.25 no association −0.50 < r 6 −0.25 weak negative association −0.75 < r 6 −0.50 moderate negative association −1 6 r 6 −0.75 strong negative association Uncorrected 2nd sample pag