# Correlation: Dependent and independent variables

## Correlation: An Overview

• Correlation is a statistical technique used to determine the relationship between two or more variables.
• Correlation measures the degree to which two variables move in relation to each other.
• It provides quantitative measurements of the statistical dependence between these variables.

## Dependent and Independent Variables

• In correlation analysis, the variables are classified as either dependent or independent.
• A dependent variable is the one being tested or measured in a study. Its value depends on other variables.
• An independent variable is the one that is manipulated or changed in a study. Its values are independent.
• For example, in an experiment studying the effect of hours of study on exam scores, hours of study would be the independent variable and exam scores the dependent variable.

## Types of Correlations

• Positive Correlation: Both variables increase or decrease together. A value close to +1 indicates a strong positive correlation.
• Negative Correlation: As one variable increases, the other decreases. A value close to -1 indicates a strong negative correlation.
• Zero or No Correlation: There is no relationship between the variables. A value close to 0 indicates no correlation.

## Pearson’s Correlation Coefficient

• The most commonly used method to measure correlation is the Pearson correlation coefficient, also termed as Pearson’s r.
• It provides a value between -1 and +1, inclusive.
• Pearson’s correlation coefficient assumes that the relationship between the variables is linear and that both variables are normally distributed.

## Limitations of Correlation

• Correlation does not imply causation. Just because two variables are correlated, doesn’t mean that changes in one variable causes changes in the other.
• It may not be able to detect non-linear relationships. Just because a correlation is near 0, doesn’t mean that no relationship exists.
• Correlation doesn’t handle multiple relationships well. There might be other variables affecting the dependent variable that are not considered.

## Correlation and Further Mathematics

• Understanding correlation and the difference between dependent and independent variables is fundamental in statistics.
• It’s important to know when to use correlation, interpret its results, and understand its limitations.
• Mastering this concept cultivates skills in data analysis, statistical reasoning, and critical thinking.