Aaliyah, Julio, Dan, and Miriam are each studying sets of data. Aaliyah is working with 14 data pairs with a correlation coefficient of 0.9. Julio is working with 13 data pairs with a correlation coefficient of –0.8. Dan is working with 10 data pairs with a correlation coefficient of 0.1. Miriam is working with 15 data pairs with a correlation coefficient of –0.2. For which two data sets is a linear regression model reasonable?

A linear regression model is most reasonable when the data have a strong linear relationship, indicated by a correlation coefficient close to 1 or –1. Aaliyah’s coefficient is 0.9 and Julio’s is –0.8, so both indicate strong linear relationships. Dan’s 0.1 and Miriam’s –0.2 are close to 0 and indicate weak relationships. Therefore, Aaliyah’s and Julio’s data sets are the best choices.

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