two sets of data are graphed here. they are identical, except for the addition of point q in the second set…

two sets of data are graphed here. they are identical, except for the addition of point q in the second set. if their correlation coefficients are $r_1$ (for the first set) and $r_2$ (for the second set), choose the correct statement.\na $r_1 < r_2$\nb $r_2 < r_1$\nc $r_1 = r_2$\nd $r_1 + r_2>0$

two sets of data are graphed here. they are identical, except for the addition of point q in the second set. if their correlation coefficients are $r_1$ (for the first set) and $r_2$ (for the second set), choose the correct statement.\na $r_1 < r_2$\nb $r_2 < r_1$\nc $r_1 = r_2$\nd $r_1 + r_2>0$

Answer

Explanation:

Step1: Understand correlation coefficient

The correlation coefficient $r$ measures the strength and direction of a linear relationship between two variables. A value close to 1 indicates a strong positive linear - relationship, a value close to - 1 indicates a strong negative linear relationship, and a value close to 0 indicates a weak or no linear relationship.

Step2: Analyze the first set of data

The first set of data points appears to have a relatively strong positive linear relationship, so $r_1$ is a positive value close to 1.

Step3: Analyze the second set of data

The addition of point Q in the second set makes the data less linear. Point Q is an out - lier that disrupts the linear pattern. So, the linear relationship in the second set is weaker than in the first set, and $r_2$ is a positive value but smaller than $r_1$.

Answer:

B. $r_2 < r_1$