An Example
Height 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: heighti = b0 + b1agei + εi, where b0 is the intercept, b1 is a parameter that age is multiplied by to get a prediction of height, ε is the error term, and i is the subject. This means that height starts at some value, there is a minimum height 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 heighti = b0 + b1agei + b2sexi + εi, 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.
Read more about this topic: Statistical Models
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“Our intellect is not the most subtle, the most powerful, the most appropriate, instrument for revealing the truth. It is life that, little by little, example by example, permits us to see that what is most important to our heart, or to our mind, is learned not by reasoning but through other agencies. Then it is that the intellect, observing their superiority, abdicates its control to them upon reasoned grounds and agrees to become their collaborator and lackey.”
—Marcel Proust (1871–1922)