Question

This table illustrates the relationship between the number of absences and the average final grade, showing a general decline in grades as absences increase.
Number of Absences 0 1 2 3 4 5 6 7 8 9
Average Final Grade 89.2 86.4 83.5 81.1 78.2 73.9 64.3 71.8 65.5 66.2
Use the data to report a bivariate data analysis. The correlation coefficient is r=−0.95
. Which of the following best reports the relationship between the number of absences and the final grade?

Answer 1

Best description: a strong negative linear relationship.

Details:
- Correlation r = −0.95 indicates a very strong negative linear association: as absences increase, final grades tend to decrease.
- Least-squares regression line: ŷ = 88.77 − 2.84(x), where x = number of absences and ŷ = predicted final grade.
- Interpretation of slope: each additional absence is associated with an average drop of about 2.84 points in the final grade.
- Coefficient of determination: R^2 = r^2 ≈ 0.9025, so about 90% of the variability in final grades is explained by the number of absences.
- Caveat: correlation does not prove causation; other factors could influence grades.