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. Bivariate analysis can help determine to what extent it becomes easier to know and predict a value for one variable (possibly a dependent variable) if we know the value of the other variable (possibly the independent variable) (see also correlation and simple linear regression).

Bivariate analysis can be contrasted with univariate analysis in which only one variable is analysed. Like univariate analysis, bivariate analysis can be descriptive or inferential. It is the analysis of the relationship between the two variables. Bivariate analysis is a simple (two variable) special case of multivariate analysis (where multiple relations between multiple variables are examined simultaneously).

Regression is a statistical technique used to help investigate how variation in one or more variables predicts or explains variation in another variable. Bivariate regression aims to identify the equation representing the optimal line that defines the relationship between two variables based on a particular data set. This equation is subsequently applied to anticipate values of the dependent variable not present in the initial dataset. Through regression analysis, one can derive the equation for the curve or straight line and obtain the correlation coefficient.

Simple linear regression is a statistical method used to model the linear relationship between an independent variable and a dependent variable. It assumes a linear relationship between the variables and is sensitive to outliers. The best-fitting linear equation is often represented as a straight line to minimize the difference between the predicted values from the equation and the actual observed values of the dependent variable.

Equation: ${\displaystyle y=mx+b}$

${\displaystyle x}$: independent variable (predictor)

${\displaystyle y}$: dependent variable (outcome)