EXAMPLE 3.1.7

This graph shows the relationship between high school GPA and college GPA for a certain group of students.

Select the statement that is correct, according to the data shown.

A. Higher high school GPAs tend to be associated with higher college GPAs.

B. Higher college GPAs tend to be associated with lower high school GPAs.

C. Higher high school GPAs cause higher college GPAs.

D. There is no apparent association between college GPA and high school GPA.

SOLUTION

The scatter plots shows a slight rising tendency as we look to right; there are several correct ways to express this. The following six statements are all correct according to the trend shown by the scatter plot:

1. Higher high school GPAs tend to be associated with higher college GPAs.

2. Higher college GPAs tend to be associated with higher high school GPAs.

3. Lower high school GPAs tend to be associated with lower college GPAs.

4. Lower college GPAs tend to be associated with lower high school GPAs.

5. There is a positive association between high school GPA and college GPA.

6. There is a positive correlation between high school GPA and college GPA.

In the multiple-choice question, we see that the correct choice is A.

Statements like C, which infer a cause/effect relationship between the two quantities, are not justified.