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  2. Polynomial regression - Wikipedia

    en.wikipedia.org/wiki/Polynomial_regression

    Although polynomial regression fits a nonlinear model to the data, as a statistical estimation problem it is linear, in the sense that the regression function E(y | x) is linear in the unknown parameters that are estimated from the data. For this reason, polynomial regression is considered to be a special case of multiple linear regression. [1]

  3. Linear least squares - Wikipedia

    en.wikipedia.org/wiki/Linear_least_squares

    Cubic, quartic and higher polynomials. For regression with high-order polynomials, the use of orthogonal polynomials is recommended. [15] Numerical smoothing and differentiation — this is an application of polynomial fitting. Multinomials in more than one independent variable, including surface fitting; Curve fitting with B-splines [12]

  4. Linear regression - Wikipedia

    en.wikipedia.org/wiki/Linear_regression

    Although polynomial regression fits a curve model to the data, as a statistical estimation problem it is linear, in the sense that the regression function E(y | x) is linear in the unknown parameters that are estimated from the data. For this reason, polynomial regression is considered to be a special case of multiple linear regression.

  5. Local regression - Wikipedia

    en.wikipedia.org/wiki/Local_regression

    Local regression or local polynomial regression, [1] also known as moving regression, [2] is a generalization of the moving average and polynomial regression. [3] Its most common methods, initially developed for scatterplot smoothing, are LOESS (locally estimated scatterplot smoothing) and LOWESS (locally weighted scatterplot smoothing), both pronounced / ˈ l oʊ ɛ s / LOH-ess.

  6. Regression analysis - Wikipedia

    en.wikipedia.org/wiki/Regression_analysis

    In linear regression, the model specification is that the dependent variable, is a linear combination of the parameters (but need not be linear in the independent variables). For example, in simple linear regression for modeling n {\displaystyle n} data points there is one independent variable: x i {\displaystyle x_{i}} , and two parameters, β ...

  7. Ordinary least squares - Wikipedia

    en.wikipedia.org/wiki/Ordinary_least_squares

    In statistics, ordinary least squares (OLS) is a type of linear least squares method for choosing the unknown parameters in a linear regression model (with fixed level-one [clarification needed] effects of a linear function of a set of explanatory variables) by the principle of least squares: minimizing the sum of the squares of the differences between the observed dependent variable (values ...

  8. Regularized least squares - Wikipedia

    en.wikipedia.org/wiki/Regularized_least_squares

    If the assumptions of OLS regression hold, the solution = (), with =, is an unbiased estimator, and is the minimum-variance linear unbiased estimator, according to the Gauss–Markov theorem. The term λ n I {\displaystyle \lambda nI} therefore leads to a biased solution; however, it also tends to reduce variance.

  9. Overfitting - Wikipedia

    en.wikipedia.org/wiki/Overfitting

    Figure 2. Noisy (roughly linear) data is fitted to a linear function and a polynomial function. Although the polynomial function is a perfect fit, the linear function can be expected to generalize better: If the two functions were used to extrapolate beyond the fitted data, the linear function should make better predictions. Figure 3.