Statistical Model - An Example

An Example

Length and age are probabilistically distributed over humans. They are stochastically related, when you know that a person is of age 7, this influences the chance of this person being 6 feet tall. You could formalize this relationship in a linear regression model of the following form: length_i = b₀ + b₁age_i + ε_i, where b₀ is the intercept, b₁ is a parameter that age is multiplied by to get a prediction of length, ε is the error term, and i is the subject. This means that length starts at some value, there is a minimum length when someone is born, and it is predicted by age to some amount. This prediction is not perfect as error is included in the model. This error contains variance that stems from sex and other variables. When sex is included in the model, the error term will become smaller, as you will have a better idea of the chance that a particular 16-year-old is 6 feet tall when you know this 16-year-old is a girl. The model would become length_i = b₀ + b₁age_i + b₂sex_i + ε_i, where the variable sex is dichotomous. This model would presumably have a higher R2. The first model is nested in the second model: the first model is obtained from the second when b₂ is restricted to zero.