Three parameters of the normal linear model
A normal linear model,
μy = β0 + β1x
σy = σ
involves 3 parameters, β0, β1 and σ. These parameters provide considerable flexibility to the model.
Interpreting the model's slope and intercept
Esimating the parameters by eye
The regression line (i.e. the straight line showing how the mean depends on x) and the band that is 2σ above and below it are a good way to understand the normal linear model. Indeed they can be used as an informal way to estimate the parameters of the model 'by eye'. (We will give better methods in the next section.)