Question

what is the best estimate of the correlation coefficient for the data set? a -0.9 b -0.3 c 0.3 d 0.9

Explanation:

Step1: Analyze the scatter plot trend

The points in the scatter plot show a negative linear trend (as x increases, y tends to decrease), so the correlation coefficient should be negative, eliminating options C and D.

Step2: Assess the strength of correlation

The points are somewhat close to a straight line but not perfectly aligned. A correlation coefficient of -0.9 indicates a very strong negative linear relationship (points almost on a line), while -0.5 is a moderate negative relationship. The scatter here is more consistent with a strong but not extremely strong negative correlation, but among the options, -0.9 is a stronger negative, and the pattern looks like a strong negative linear association. Wait, actually, let's re - evaluate. Wait, if the points are forming a relatively tight negative linear pattern, -0.9 is a strong negative. But let's check the options again. Wait, maybe I made a mistake. Wait, the scatter plot: when x increases, y decreases, so negative. Now, the spread: if the points are close to a line, the correlation is close to -1. Among the options, -0.9 is closer to -1 than -0.5. Wait, but maybe the plot has a strong negative trend. So the best estimate is -0.9? Wait, no, wait. Wait, maybe the plot is such that the points are in a negative linear trend, and the correlation coefficient's magnitude: -0.9 is a very strong negative, -0.5 is moderate. Let's think about the scatter plot's appearance. If the points are forming a clear negative line, then -0.9 is better. But let's check the options. The options are A: -0.9, B: -0.5, C: 0.5, D: 0.9. Since it's a negative trend, C and D are out. Now, between -0.9 and -0.5. If the points are tightly clustered around a negative line, -0.9 is correct. So the best estimate is -0.9.

Answer:

A. -0.9