Normal linear model for the response
A regression model for the response in a bivariate data set describes how the response distribution depends on X. The most commonly used regression model is a normal linear model. This model involves:
The last two properties of the normal linear model can be expressed as
σy = σ
μy = β0 + β1x
Note: only the response is modelled
A normal linear model does not try to explain the distribution of x-values.
Example of a normal linear model
A typical normal linear model is shown below.
Drag the slider to see how the distribution of Y depends on the value of X. Observe that...
The centre of the response's distribution is the green line on the diagram, called the regression line. In this example, it is described by the equation
μy = 2.5 + 1.5x
The spread of the response distribution is the same for all X,
σy = 0.8
Click Take sample a few times to observe typical data from this model when 5 response measurements are made at each of X = 1, 2, 3 and 4.
The model can also be used in situations where the values of X are not repeated. Select the option Regular X then take a few more samples to see typical data if the values of X are chosen to be 0.6, 0.8, 1.0, ..., 4.4.
Select the option Random X and take a few more samples to see typical data if the values of X are irregularly spaced.