Questions: The linear correlation coefficient "r" tells us how strong the linear relationship is; in general, the closer it is to 1, the stronger the linear relationship, while the closer it is to 0, the weaker the linear relationship. Match each scatterplot with its most reasonable r-value.

The linear correlation coefficient "r" tells us how strong the linear relationship is; in general, the closer it is to 1, the stronger the linear relationship, while the closer it is to 0, the weaker the linear relationship. Match each scatterplot with its most reasonable r-value.

Transcript text: The linear correlation coefficient "$r$" tells us how strong the linear relationship is; in general, the closer it is to 1, the stronger the linear relationship, while the closer it is to 0, the weaker the linear relationship. Match each scatterplot with its most reasonable $r$-value.

Solution

Solution Steps

Step 1: Understand the Problem

The problem requires matching each scatterplot with its most reasonable r-value. The r-value, or correlation coefficient, measures the strength and direction of a linear relationship between two variables. The value ranges from -1 to 1.

Step 2: Analyze the Scatterplots

First Scatterplot: The points are widely scattered with no clear linear pattern. This suggests a weak or no correlation.
Second Scatterplot: The points show a downward trend, indicating a negative correlation.
Third Scatterplot: The points are closely clustered around a line, indicating a strong positive correlation.

Step 3: Match Scatterplots to r-values

First Scatterplot: Since the points are widely scattered, the r-value is close to 0.
Second Scatterplot: The downward trend suggests a negative r-value, likely around -0.7 to -0.9.
Third Scatterplot: The close clustering around a line suggests a strong positive r-value, likely around 0.7 to 0.9.