Question

1. match each scatterplot and its regression line with the most appropriate correlation coefficient. choices: 0.62, -0.94, 0.97, -0.68

Explanation:

Step1: Understand correlation coefficient

The correlation coefficient \(r\) ranges from - 1 to 1. A positive \(r\) indicates a positive - linear relationship (as one variable increases, the other increases), and a negative \(r\) indicates a negative - linear relationship (as one variable increases, the other decreases). The closer \(|r|\) is to 1, the stronger the linear relationship.

Step2: Analyze first scatter - plot

The first scatter - plot has a negative slope for the regression line, indicating a negative linear relationship. The points are somewhat scattered but still show a clear linear trend. So, \(r=-0.68\) is a good fit as it is negative and not too close to - 1.

Step3: Analyze second scatter - plot

The second scatter - plot also has a negative slope for the regression line, and the points are very closely clustered around the regression line, indicating a strong negative linear relationship. So, \(r = - 0.94\) is appropriate as it is close to - 1.

Step4: Analyze third scatter - plot

The third scatter - plot has a positive slope for the regression line, and the points are closely clustered around the regression line, indicating a strong positive linear relationship. So, \(r = 0.97\) is a good choice as it is close to 1.

Answer:

First scatter - plot: - 0.68
Second scatter - plot: - 0.94
Third scatter - plot: 0.97