regression analysis, the form of the function must be specified. Sometimes the form of this function is based on knowledge about the relationship between and that does not rely on the data. If no such knowledge is available, a flexible or convenient form for is chosen. For example, a simple univariate regression may propose , suggesting that the researcher believes to be a reasonable approximation for the statistical process generating the data. Once researchers determine their preferred statistical model, different forms of regression analysis provide tools to estimate the parameters . For example, least squares (including its most common variant, ordinary least squares) finds the value of that minimizes the sum of squared errors . A given regression method will ultimately provide an estimate of , usually denoted to distinguish the estimate from the true (unknown) parameter value that generated the data. Using this estimate, the researcher can then use the fitted value for prediction or to assess the accuracy of the model in explaining the data. Whether the researcher is intrinsically interested in the estimate or the predicted value will depend on context and their goals. As described in ordinary least squares, least squares is widely used because the estimated function approximates the conditional expectation . However, alternative variants (e.g., least absolute deviations or quantile regression) are useful when researchers want to model other functions . It is important to note that there must be sufficient data to estimate a regression model. For example, suppose that a researcher has access to rows of data with one dependent and two independent variables: . Suppose further that the researcher wants to estimate a bivariate linear model via least squares: . If the researcher only has access to data points, then they could find infinitely many combinations that explain the data equally well: any combination can be chosen that satisfies , all of which lead to and are therefore valid solutions that minimize the sum of squared residuals. To understand why there are infinitely many options, note that the system of equations is to be solved for 3 unknowns, which makes the system underdetermined. Alternatively, one can visualize infinitely many 3-dimensional planes that go through fixed points. More generally, to estimate a least squares model with distinct parameters, one must have distinct data points. If , then there does not generally exist a set of parameters that will perfectly fit the data.