Question

The school’s guidance department compares the grade-point averages and standardized state test scores for 10 students in each grade. The table below shows the correlation coefficient for each data set.

Grade
Level
Correlation Coefficient
9th grade
0.3
10th grade
–0.1
11th grade
0.2
12th grade
–0.8


For which data set(s) is a linear regression model reasonable?
9th grade and 11th grade data sets
10th grade data set
10th grade and 12th grade data sets
12th grade data set

Answer 1

12th grade data set

Reason: Only the 12th grade has a correlation with large magnitude (|r| = 0.8), indicating a strong linear relationship. The others (0.3, −0.1, 0.2) are too close to 0 to justify a linear model.