match each correlation coefficient to the appropriate scatter plot. the line in each scatter plot is the…

match each correlation coefficient to the appropriate scatter plot. the line in each scatter plot is the least squares regression line. r = -1 r = 0.4

match each correlation coefficient to the appropriate scatter plot. the line in each scatter plot is the least squares regression line. r = -1 r = 0.4

Answer

Explanation:

Step1: Understand correlation coefficient properties

The correlation coefficient $r$ ranges from - 1 to 1. A value of $r=-1$ indicates a perfect negative linear - relationship (all data points lie on a straight line with a negative slope). A value of $r = 0.4$ indicates a positive, but not perfect, linear relationship.

Step2: Analyze the first scatter - plot

In the first scatter - plot, all the data points lie exactly on a straight line with a negative slope. So, the correlation coefficient for this scatter - plot is $r=-1$.

Step3: Analyze the second scatter - plot

In the second scatter - plot, the data points show a positive linear trend, but they do not lie exactly on a straight line. So, the correlation coefficient for this scatter - plot is $r = 0.4$.

Answer:

The scatter - plot with all points on a negative - sloped line corresponds to $r=-1$. The scatter - plot with a positive, non - perfect linear trend corresponds to $r = 0.4$.