three scatterplots are shown, along with their best - fit lines and correlation coefficients, $r_1$, $r_2$…

three scatterplots are shown, along with their best - fit lines and correlation coefficients, $r_1$, $r_2$, and $r_3$. choose the correct statement.\na $r_1<r_2<r_3$\nb $r_2<r_1<r_3$\nc $r_3<r_2<r_1$\nd $r_1<r_3<r_2$\ne $r_2<r_3<r_1$

three scatterplots are shown, along with their best - fit lines and correlation coefficients, $r_1$, $r_2$, and $r_3$. choose the correct statement.\na $r_1<r_2<r_3$\nb $r_2<r_1<r_3$\nc $r_3<r_2<r_1$\nd $r_1<r_3<r_2$\ne $r_2<r_3<r_1$

Answer

Explanation:

Step1: Recall correlation - coefficient concept

The closer the data points are to the best - fit line, the closer the absolute value of the correlation coefficient is to 1.

Step2: Analyze scatter - plots

In scatter - plot with $r_1$, the data points are very close to the best - fit line. In scatter - plot with $r_2$, the data points are more spread out from the best - fit line compared to $r_1$. In scatter - plot with $r_3$, the data points are more spread out than in $r_1$ but less spread out than in $r_2$.

Step3: Compare correlation coefficients

Since the data points in the plot with $r_1$ are closest to the line, $|r_1|$ is the largest. Among $r_2$ and $r_3$, $|r_3|>|r_2|$ as the points in the plot with $r_3$ are closer to the line than those in the plot with $r_2$. And since all the relationships seem to be positive (the best - fit lines have positive slopes), we have $r_2 < r_3 < r_1$.

Answer:

E. $r_2 < r_3 < r_1$