Question

What would the scatter plot show for data that produce a Pearson correlation of r = +0.88?

a. Points clustered close to a line that slopes up to the right
b. Points clustered close to a line that slopes down to the right
c. Points widely scattered around a line that slopes up to the right
d. Points widely scattered around a line that slopes down to the right

Answer 1

The correct answer is:

a.Points clustered close to a line that slopes up to the right

The Pearson correlation coefficient, also known as Pearson's r, measures the strength and direction of association between two continuous variables. It ranges from -1.0 to +1.0. A positive coefficient indicates a positive linear relationship between the variables, and a negative coefficient indicates a negative linear relationship.

In this case, we have a Pearson correlation value of r = +0.88. This is a relatively high positive value, suggesting a strong positive linear relationship between the two variables.

A strong positive relationship is signified by a scatter plot with points tightly clustered around a line that slopes upwards from left to right. This is because as one variable increases, the other is also expected to increase, which is demonstrated by the upward slope. The close clustering of the points indicates the strength of the relationship - the closer the points are to the line, the stronger the relationship.

Therefore, given a r value of +0.88, the scatter plot would show points clustered close to a line that slopes up to the right. Hence, the correct answer is:

a. Points clustered close to a line that slopes up to the right.

Answer 2

The correct option is (a).

Explanation:

The Pearson's correlation coefficient is a statistical degree that computes the strength of the linear relationship amid the relative movements of the two variables (i.e. dependent and independent).It ranges from -1 to +1.

Positive correlation is an association amid two variables in which both variables change in the same direction. A positive correlation occurs when one variable declines as the other variable declines, or one variable escalates while the other escalates.

Negative correlation is a relationship amid two variables in which one variable rises as the other falls, and vice versa.

In this case, it is provided that the Pearson correlation coefficient is, r = +0.88.

A correlation coefficient between ±0.70 to ±1.00 are considered as strong positive correlation.

The scatter plot for correlation coefficient between +0.70 to +1.00 shows:

• A straight and upward moving trend of the point
• A straight line can be formed using these points that slopes up to the right
• Points clustered close to this line that slopes up to the right

Thus, the correct option is (a).