Slope and intercept
A normal linear model,
μy = β0 + β1x
σy = σ
involves 3 parameters, β0, β1 and σ. The model's slope, β1, and intercept, β0, can be interpreted in a similar way to the slope and intercept of a least squares line.
Examples of interpretation
Context | Interpretation of β1 | Interpretation of β0 |
---|---|---|
Y = Yield of wheat per acre X = Fertiliser (kg per m2) |
Increase in mean yield per acre for each additional kg/m2 of fertiliser | Mean yield per acre if no fertiliser is used |
Y = Exam mark X = Hours of study by student before exam |
Increase in expected mark for each additional hour of study | Expected mark if there is no study |
Y = Hospital stay (days) X = Age of patient |
Average extra days in hospital per extra year of age | Average days in hospital at age 0. Not particularly meaningful here. |