Question

deja and michael each created a scatter plot and found the correlation coefficient as shown below. what must deja and michaels scatter plots have in common? deja $r=-0.98$ michael $r = 0.97$ a. both scatter plots have strong association. b. both scatter plots display causation. c. both scatter plots have negative association. d. both scatter plots increase from left to right.

Explanation:

Step1: Recall the property of correlation coefficient

The correlation coefficient \( r \) measures the strength and direction of a linear relationship between two variables. The value of \( r \) ranges from \( - 1\) to \(1\). When \(|r|\) is close to \(1\) (e.g., \(|r|\geq0.7\)), it indicates a strong linear association.
For Deja, \(r=-0.98\), and \(|r| = 0.98\). For Michael, \(r = 0.97\), and \(|r|=0.97\).

Step2: Analyze each option

• Option A:

Since \(|r| = 0.98\) for Deja and \(|r|=0.97\) for Michael, and both \(0.98\) and \(0.97\) are close to \(1\), both scatter - plots have a strong association.

• Option B:

A correlation coefficient only measures the linear relationship between two variables, not causation. Just because \(|r|\) is close to \(1\) does not mean there is a cause - and - effect relationship.

• Option C:

Deja has a negative association (\(r=-0.98<0\)), while Michael has a positive association (\(r = 0.97>0\)). So, they do not both have a negative association.

• Option D:

Deja's scatter - plot (with \(r=-0.98\)) has a decreasing trend (as \(x\) increases, \(y\) decreases), while Michael's scatter - plot (with \(r = 0.97\)) has an increasing trend (as \(x\) increases, \(y\) increases).

Answer:

A. Both scatter plots have strong association.