Question

which is most likely the correlation coefficient for the set of data shown? -0.83 -0.21 0.21 0.83

Explanation:

Step1: Determine the sign of the correlation coefficient

The line of best - fit has a negative slope. So, the correlation coefficient \(r\) is negative. This eliminates the options \(0.21\) and \(0.83\).

Step2: Analyze the strength of the negative correlation

The data points are not extremely close to the line of best - fit (but also not very scattered). A correlation coefficient of \(- 0.21\) indicates a weak negative correlation, while \(-0.83\) indicates a relatively strong negative correlation. Since the points follow the general trend of the line more closely than a weak correlation would suggest, \(-0.83\) is a better fit.

Answer:

\(-0.83\)