Final answer:
Correlation measures the degree of relationship between two variables without indicating causation. The correlation coefficient 'r' explains this relationship's strength and direction. Controlled experimentation with isolated variables and random assignment is necessary to establish causality.
Step-by-step explanation:
Correlation does not require variables to be classified strictly as explanatory and response variables, which is more typical in regression analysis. Instead, correlation assesses the degree and direction of a relationship between two variables. This statistical measure, known as the correlation coefficient, is represented by the symbol 'r' and ranges from -1 to 1. A value of 'r' close to 1 implies a strong positive correlation, while a value close to -1 indicates a strong negative correlation. However, correlation by itself should not be confused with causation. Despite a high correlation, it does not necessarily indicate that one variable causes the other to change.
Lurking variables or confounding variables can also influence the relationship between two variables of interest. Isolation of variables and random assignment are important in experimental design to demonstrate causality, rather than mere association. For example, a study might find a high correlation between fast-food restaurant density and obesity rates; however, this does not prove that one causes the other without controlled experimentation.
To further investigate the relationship between variables, one can:
- Determine the independent (explanatory) and dependent (response) variables in a study.
- Plot the data on a scatter plot to visually inspect any potential relationship.
- Use regression analysis to calculate the least-squares line of best fit and to find the correlation coefficient.
- Interpret the significance of the correlation coefficient and discuss whether it suggests a linear relationship or not.