Interpretation of regression lines
If separate regression lines are fitted by least squares in the different groups, these lines will usually have both different slopes and intercepts. By forcing these regression lines to be parallel, differences between the groups are easier to understand.
Least squares
The principle behind fitting parallel lines to two or more groups is the same as in ordinary simple regression — we choose the parameters to minimise the sum of squared residuals. The formulae for the resulting lines are much harder to express algebraically and will therefore not be described here, but most statistical software will do the calculations for you, so the precise details are of little importance.
Gas consumption and insulation