Question

which correlation coefficient does not belong with the other three? explain your reasoning.
r = -0.98 r = 0.96 r = -0.09 r = 0.97
(handwritten explanation about r = -0.09 being weak, others strong)

1. which regression model would best fit the following scatterplots below?

(three scatterplot images: u - shaped, curve - like, and scattered points)

Explanation:

Step1: Analyze Correlation Strength

Correlation coefficients (\(r\)) with absolute values close to 1 indicate strong linear relationships (either positive or negative). Values close to 0 indicate weak relationships.

• \(|r = -0.98| = 0.98\) (strong negative)
• \(|r = 0.96| = 0.96\) (strong positive)
• \(|r = -0.09| = 0.09\) (weak negative)
• \(|r = 0.97| = 0.97\) (strong positive)

Step2: Identify the Outlier

\(r = -0.09\) has a much smaller absolute value (weaker relationship) than the other three, which have strong linear relationships.

Answer:

\(r = -0.09\) does not belong. The other three (\(r = -0.98\), \(r = 0.96\), \(r = 0.97\)) have absolute values close to 1 (strong linear relationships), while \(r = -0.09\) has an absolute value close to 0 (weak linear relationship).