# Correlation and Regression

JoVE Core
Analytical Chemistry
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JoVE Core Analytical Chemistry
Correlation and Regression

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Regression and correlation are statistical techniques that examine the relationship between two variables.

While regression is used to understand the change in one variable caused by the alteration in another, correlation measures the strength and the direction of the linear correlation between the two variables.

Linear Regression establishes the relationship between two variables by fitting a line to the data points. The equation of the line reliably predicts the value of one unknown variable based on a known variable.

Linear correlation is expressed using the Pearson correlation coefficient, 'r,' which ranges from −1 to +1. A value closer to −1 or +1 suggests a strong correlation between variables, whereas a zero value indicates no correlation.

## Correlation and Regression

In statistics, correlation describes the degree of association between two variables. In the subfield of linear regression, correlation is mathematically expressed by the correlation coefficient, which describes the strength and direction of the relationship between two variables. The coefficient is symbolically represented by 'r' and ranges from -1 to +1. A positive value indicates a positive correlation where the two variables move in the same direction. A negative value suggests a negative correlation, where the two variables move in opposite directions. A value closer to +1 or −1 suggests that the two variables are strongly correlated, directly or inversely. A value close to zero implies no linear correlation between the two variables.

To obtain the correlation coefficient and the best-fit equation, statisticians use the method of linear regression. The best-fit equation can be used subsequently to predict the value of a signal ('y' in the linear equation) or calculate the concentration of the substance giving the signal ('x' in the linear equation).