As an example, if we assume that data arise from a univariate Gaussian distribution, then we are assuming that . In this example, the dimension, , equals 2. As another example, suppose that the data consists of points (, ) that we assume are distributed according to a straight line with i.i.d. Gaussian residuals (with zero mean): this leads to the same statistical model as was used in the example with children's heights. The dimension of the statistical model is 3: the intercept of the line, the slope of the line, and the variance of the distribution of the residuals. (Note that in geometry, a straight line has dimension 1.) Although formally is a single parameter that has dimension , it is sometimes regarded as comprising separate parameters. For example, with the univariate Gaussian distribution, is formally a single parameter with dimension 2, but it is sometimes regarded as comprising 2 separate parameters—the mean and the standard deviation. A statistical model is nonparametric if the parameter set is infinite dimensional. A statistical model is semiparametric if it has both finite-dimensional and infinite-dimensional parameters. Formally, if is the dimension of and is the number of samples, both semiparametric and nonparametric models have as . If as , then the model is semiparametric; otherwise, the model is nonparametric. Parametric models are by far the most commonly used statistical models. Regarding semiparametric and nonparametric models, Sir David Cox has said, "These typically involve fewer assumptions of structure and distributional form but usually contain strong assumptions about independencies". Nested models Two statistical models are nested if the first model can be transformed into the second model by imposing constraints on the parameters of the first model. As an example, the set of all Gaussian distributions has, nested within it, the set of zero-mean Gaussian distributions: we constrain the mean in the set of all Gaussian distributions to get the zero-mean distributions. As a second example, the quadratic model has, nested within it, the linear model —we constrain the parameter to equal 0. In both those examples, the first model has a higher dimension than the second model (for the first example, the zero-mean model has dimension 1). Such is often, but not always, the case. As a different example, the set of positive-mean Gaussian distributions, which has dimension 2, is nested within the set of all Gaussian distributions. Comparing models Comparing statistical models is