Standard linear regression

Written by Ronny Gunnarsson and first published on August 8, 2014.
Last revised on September 9, 2019.

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Suggested pre-reading	What this web page adds
Introduction to statistics Observations and variables Inferential statistics Choosing statistical analysis Associations and predictions Regression and correlation	This web-page provides an introduction to standard linear regression. Reading this will give you an understanding of these concepts and how to use them.

The dependent variable in a standard linear regression is always a variable measured with an interval or ratio scale.

Simple standard linear regression

Simple standard linear regression also has other labels with exactly the same meaning:

Bivariate standard linear regression (using two variables, one dependent and one independent)
Univariate standard linear regression (using only one independent variable)
Unadjusted standard linear regression (not adjusting for other independent variables)

A standard linear regression with one dependent variable (Y) and one independent variable (x) can mathematically be described in several ways (all with exactly the same meaning):
Y = a + bx
can also be written as
Y = b₀ + b₁x
can also be written as
Y = b + mx

Look at this video by Steve Grambow introducing the idea behind simple standard linear regression:

Multiple standard linear regression

A standard linear regression with one dependent variable (Y) and several independent variables (several x) can be written as:
Y = a + b₁x₁ + b₂x₂ + b₃x₃ + … …b_nx_n

(This section is still under construction. Sorry for the inconvenience.)