Question

1. consider the following three scatterplots:

what is the relationship between r1, r2, and r3, the correlation coefficients of each scatterplot?
(a) r1 < r2 < r3
(b) r1 < r3 < r2
(c) r2 < r3 < r1
(d) r2 < r1 < r3
(e) r3 < r1 < r2

Explanation:

Step1: Recall the property of correlation coefficient

The correlation coefficient \(r\) measures the strength and direction of a linear relationship. The closer \(|r|\) is to \(1\), the stronger the linear relationship.

Step2: Analyze \(r_2\)

For \(r_2\), the points are very scattered, indicating a very weak linear relationship. So \(|r_2|\) is close to \(0\).

Step3: Analyze \(r_1\)

For \(r_1\), there is a somewhat discernible (but not extremely strong) negative linear trend. So \(|r_1|\) is greater than \(|r_2|\) but less than \(|r_3|\).

Step4: Analyze \(r_3\)

For \(r_3\), the points follow a clear negative linear path. So \(|r_3|\) is close to \(1\). Since all the relationships are negative (points going down - ward from left - to - right), \(r_2

Answer:

D. \(r_2 < r_1 < r_3\)