Question

4 - 70. the following scatterplots have correlations $r = - 0.9$, $r = - 0.6$, $r = 0.1$, and $r = 0.6$. which scatterplot has which correlation coefficient?

Explanation:

Step1: Understand the correlation coefficient

The correlation coefficient \(r\) measures the strength and direction of a linear relationship. \(r = 0.1\) is a weak positive correlation, \(r = 0.6\) is a moderate positive correlation, \(r=-0.6\) is a moderate negative correlation, and \(r = - 0.9\) is a strong negative correlation.

Step2: Analyze scatter - plot a

Scatter - plot a shows a negative linear relationship. The points are relatively close to the line of best - fit, so it has a stronger negative correlation. So \(r=-0.6\).

Step3: Analyze scatter - plot b

Scatter - plot b shows a weak positive relationship. The points are spread out, so \(r = 0.1\).

Step4: Analyze scatter - plot c

Scatter - plot c shows a moderate positive relationship. The points are moderately close to the line of best - fit, so \(r = 0.6\).

Step5: Analyze scatter - plot d

Scatter - plot d shows a strong negative relationship. The points are very close to the line of best - fit, so \(r=-0.9\).

Answer:

a. \(r=-0.6\), b. \(r = 0.1\), c. \(r = 0.6\), d. \(r=-0.9\)