Which of the following can be used to show a cause-and-effect relationship between two variables?

• A. A controlled experiment
• B. A scatterplot with a linear pattern
• C. A high correlation coefficient $r$
• D. A regression line $y=a+bx$

Answer: (A)

Verified step by step guidance

1. Understand the difference between correlation and causation: Correlation measures the strength and direction of a relationship between two variables, but it does not imply that one variable causes the other.
2. Recognize that a scatterplot with a linear pattern visually shows a relationship between two variables, but it cannot prove cause and effect on its own.
3. Know that a high correlation coefficient quantifies the strength of a linear relationship but does not establish causality.
4. Learn that a regression line models the relationship between variables and can predict values, but it also does not prove cause and effect by itself.
5. Identify that a controlled experiment is designed to test cause-and-effect relationships by manipulating one variable (independent variable) and observing the effect on another variable (dependent variable) while controlling other factors.