Basics of Bivariate Analysis

Bivariate analysis is one of the simplest forms of quantitative (statistical) analysis. It involves the analysis of two variables (often denoted as X, Y), for the purpose of determining the empirical relationship between them.
Bivariate analysis can be helpful in testing simple hypotheses of association.

Data Representation

Scatter plots are an effective way to visualise the relationship between two variables. They plot paired data points on an x-y axis.
Important patterns can often be seen in the plot, such as positive or negative correlation, or no correlation. Relationships between variables can further be described as linear, non-linear, or random.

Correlation

Correlation is a statistic that measures the degree to which two variables move in relation to each other.
The correlation coefficient, often represented by ‘r’, is a numerical measure of correlation, ranging from -1 to 1. A value of -1 suggests a perfect negative linear relationship, a value of 1 suggests a perfect positive linear relationship, and a value of 0 suggests no linear correlation.

Regression Analysis

Linear regression is a statistical method that is used to study the correlation between two variables.
Regression analysis builds upon correlation to add prediction capabilities. The variable you want to predict (Y) is called the dependent variable, and the variable you are using to predict (X) is called the independent variable.
Regression analysis allows you to quantify the strength of the relationship between variables, control for confounding variables, check for interaction effects, and make predictions.

Remember, correlation does not imply causation. Just because two variables are correlated, it does not automatically follow that changing one variable will change the other.