Question

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?

aaliyahs and julios data sets
julios and miriams data sets
dans and miriams data sets
miriams and aaliyahs data sets

Explanation:

Identify the correlation coefficients

We are given the correlation coefficients (\(r\)) for four different data sets:

• Aaliyah: \(r = 0.9\)
• Julio: \(r = -0.8\)
• Dan: \(r = 0.1\)
• Miriam: \(r = -0.2\)

Analyze linear model suitability

A linear regression model is reasonable when there is a strong linear relationship between the variables. The strength of a linear relationship is determined by the absolute value of the correlation coefficient, \(|r|\):

• An \(|r|\) value close to \(1\) indicates a strong linear relationship (either positive or negative).
• An \(|r|\) value close to \(0\) indicates a weak or non-existent linear relationship.

Let's calculate the absolute values:

• Aaliyah: \(|0.9| = 0.9\) (Strong positive linear relationship)
• Julio: \(|-0.8| = 0.8\) (Strong negative linear relationship)
• Dan: \(|0.1| = 0.1\) (Very weak linear relationship)
• Miriam: \(|-0.2| = 0.2\) (Very weak linear relationship)

Determine the best two data sets

Comparing the strengths:

• Aaliyah's and Julio's data sets have the highest absolute correlation coefficients (\(0.9\) and \(0.8\)), indicating strong linear relationships.
• Therefore, a linear regression model is reasonable for Aaliyah's and Julio's data sets.

Answer:

• Aaliyah's and Julio's data sets (Correct answer)
• Julio's and Miriam's data sets
• Dan's and Miriam's data sets
• Miriam's and Aaliyah's data sets