Question

Graphing Scatterplots and Trend Lines
You just found a positive trend line showing a strong relationship between homework scores and test scores for five students. Explain what this means.

Answer 1

A positive trend line means that, for these five students, higher homework scores are associated with higher test scores — the line slopes upward from left to right. In other words, as homework scores increase, test scores tend to increase too.

A “strong” relationship means the five data points lie close to that trend line (the scatter is small), so the line fits the data well. Practically that implies:
- You could use the trend-line equation (y = mx + b) to make reasonably accurate predictions of a student’s test score from their homework score: the slope (m) is the average change in test score for each one-unit increase in homework score, and the intercept (b) is the predicted test score when the homework score is zero.
- A high correlation coefficient (r close to +1) or a high R² value would quantify that strength: R² near 1 means most of the variation in test scores is explained by homework scores.

Cautions:
- Correlation is not causation. The relationship doesn’t prove that doing more homework causes better test scores — other factors (ability, study habits, class time, etc.) could cause both.
- The sample is very small (five students), so results may not generalize. Adding more data and checking for outliers or confounding variables would strengthen confidence in the finding.