Understand correlation vs causation; interpret trends and regression lines qualitatively.
Correlation shows association, not causation, and a regression line describes the overall trend.
核心知识
A positive or negative trend shows association, not automatic cause. A regression line summarizes the overall pattern, but it does not mean every point lies on the line or that one variable causes the other.
深入理解
Rule: Scatterplots and regression lines help you describe direction, form, and rough strength of a relationship. If the line slopes upward, larger values of one variable tend to go with larger values of the other. If it slopes downward, larger values of one variable tend to go with smaller values of the other.
The key word is tend. A regression line is a model of the overall pattern, not a guarantee for every individual. Just as important, correlation alone does not prove causation. A lurking variable, reverse direction, or simple coincidence may explain the association.
分步讲解
- State the direction of the association from the trend or regression line.
- Describe the relationship as a tendency, not as a rule with no exceptions.
- Use the graph to support prediction only within a reasonable range of the data.
- Do not claim cause unless the study design justifies it.
常见误解
- Treating correlation as proof of cause.
- Assuming every point lies exactly on the regression line.
- Using the trend to make exact predictions far outside the data range.
示例解析
A scatterplot of weekly study hours and ACT math score for 60 students shows a positive linear trend, and the fitted regression line slopes upward. Which conclusion is best supported?
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