which is most likely the correlation coefficient for the set of data shown? -0.65 -0.19 0.19 0.75

Explanation:

Step1: Analyze the scatter - plot trend

The data points in the scatter - plot show a positive linear trend. As the value of (x) increases, the value of (y) also tends to increase. So, the correlation coefficient (r) should be positive. This eliminates the options (- 0.65) and (-0.19).

Step2: Evaluate the strength of the linear relationship

The data points are not very closely clustered around the line of best - fit. A correlation coefficient of (r = 0.75) indicates a relatively strong positive linear relationship, while (r=0.19) indicates a weak positive linear relationship. Since the points are somewhat scattered, the correlation is weak. So, (r = 0.19) is the most appropriate.

Answer:

0.19