Alternative descriptions of the model

The normal linear model describes the distribution of Y for any value of X:

Y  ~  normaly , σy)

where

μy  =  β0  +  β1x

σy  =  σ

An equivalent way to write the same model is...

y  =  β0  +  β1x  +  ε

where ε is called the model error and has a distribution

ε  ~  normal (0 , σ)

The error, ε , for a data point is the vertical distance between the cross on a scatterplot and the regression line.

Band containing about 95% of values

Applying the 70-95-100 rule of thumb to the errors, about 95% of them will be within 2 standard deviations of zero — i.e. between ±2σ.

Since the errors are vertical distances of data points to the regression line, a band 2σ on each side of it should contain about 95% of the crosses on a scatterplot of the data.