Question

match each correlation coefficient to the appropriate scatter plot. the line in each scatter plot is the least squares regression line.
r = 0.3
r = 0.8

Explanation:

Step1: Recall Correlation Coefficient Meaning

The correlation coefficient \( r \) measures the strength and direction of a linear relationship between two variables. A value closer to \( 1 \) (or \( -1 \)) indicates a stronger linear relationship, while a value closer to \( 0 \) indicates a weaker linear relationship.

Step2: Analyze Scatter Plot Clustering

• For \( r = 0.3 \): This is a weak positive correlation. The data points should be more spread out around the regression line.
• For \( r = 0.8 \): This is a strong positive correlation. The data points should be closer to the regression line.

Looking at the two scatter plots:

• The left scatter plot has points closer to the regression line, indicating a stronger relationship (so it matches \( r = 0.8 \)).
• The right scatter plot has points more spread out around the regression line, indicating a weaker relationship (so it matches \( r = 0.3 \)). Wait, no—wait, actually, wait: Wait, \( 0.8 \) is stronger than \( 0.3 \). So the plot with points closer to the line is \( r = 0.8 \), and the one with more spread is \( r = 0.3 \). Wait, let's recheck:

Wait, the left plot: points are more tightly clustered around the line. So left plot: \( r = 0.8 \); right plot: \( r = 0.3 \)? Wait, no, maybe I mixed up. Wait, the left plot's points are closer to the line, so that's a stronger correlation (higher \( r \)), so left is \( r = 0.8 \), right is \( r = 0.3 \)? Wait, no, wait the right plot: let's see the vertical spread. Wait, maybe I had it reversed. Wait, no: the correlation coefficient's magnitude (absolute value) tells the strength. So \( |r| = 0.8 \) is stronger than \( |r| = 0.3 \). So the scatter plot with points closer to the regression line is the one with \( r = 0.8 \), and the one with points more spread out is \( r = 0.3 \).

So:

• Left scatter plot (points closer to line): \( r = 0.8 \)
• Right scatter plot (points more spread): \( r = 0.3 \)

Wait, but let's confirm. Let's look at the two plots:

First plot (left): points are clustered more closely around the line. So that's a stronger linear relationship, so \( r = 0.8 \).

Second plot (right): points are more dispersed around the line, so weaker linear relationship, so \( r = 0.3 \).

Answer:

• \( r = 0.3 \) matches the right scatter plot.
• \( r = 0.8 \) matches the left scatter plot.

(Assuming the left plot is the first one, right is the second. So:

Left scatter plot: \( r = 0.8 \)

Right scatter plot: \( r = 0.3 \)