Bivariate regression analysis

Bivariate regression analysis is a type of statistical analysis that can be used during the analysis and reporting stage of quantitative market research. It is often considered the simplest form of regression analysis, and is also known as Ordinary Least-Squares regression or linear regression.

Essentially, bivariate regression analysis involves analysing two variables to establish the strength of the relationship between them. The two variables are frequently denoted as X and Y, with one being an independent variable (or explanatory variable), while the other is a dependent variable (or outcome variable).

In order to determine the relationship, bivariate regression analysis uses a linear regression line (because the relationship between the variables is assumed to be linear) in order to help measure how the two variables change together, simultaneously. This will take the form of a line of best fit placed on a scatter chart through the plotted values of the independent variable (X-axis), against the dependent variable (Y-axis).

Uses of bivariate regression analysis include testing simple hypotheses, particularly of association and causality. In this way it can be seen how much easier it becomes to know and predict a value of the dependent variable having known the independent variable. It can be very helpful to researchers with limited sample information and who therefore need to make predictions in order to make key judgements.

An example could be looking at the relationship between income and happiness. The researcher could then predict a participant’s happiness score, if they know their income.

The equation of the line of best fit which describes a positive relationship between the independent and dependent variables is denoted as y=bx+a. y is the dependent variable, x is the independent variable, a is the point where the line of best fit intersects the y-axis and b is the angle of the line.

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Bivariate regression analysis