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Non-linear regression method
Beta regression is a form of regression which is used when the response variable, y {\displaystyle y} , takes values within ( 0 , 1 ) {\displaystyle (0
Beta_regression
Set of statistical processes for estimating the relationships among variables
called regressors, predictors, covariates, explanatory variables or features). The most common form of regression analysis is linear regression, in which
Regression_analysis
Statistical model for a binary dependent variable
combination of one or more independent variables. In regression analysis, logistic regression (or logit regression) estimates the parameters of a logistic model
Logistic_regression
Statistical modeling method
regression; a model with two or more explanatory variables is a multiple linear regression. This term is distinct from multivariate linear regression
Linear_regression
Method for estimating the unknown parameters in a linear regression model
especially in the case of a simple linear regression, in which there is a single regressor on the right side of the regression equation. The OLS estimator is consistent
Ordinary_least_squares
Statistics concept
In statistics, polynomial regression is a form of regression analysis in which the relationship between the independent variable x and the dependent variable
Polynomial_regression
Statistical modeling technique
Quantile regression is a type of regression analysis used in statistics and econometrics. Whereas the method of least squares estimates the conditional
Quantile_regression
Statistical method
linear regression models. This simple case reveals a substantial amount about the estimator. These include its relationship to ridge regression and best
Lasso_(statistics)
Regularization technique for ill-posed problems
Ridge regression (also known as Tikhonov regularization, named for Andrey Tikhonov) is a method of estimating the coefficients of multiple-regression models
Ridge_regression
Linear regression model with a single explanatory variable
In statistics, simple linear regression (SLR) is a linear regression model with a single explanatory variable. That is, it concerns two-dimensional sample
Simple_linear_regression
Statistical model for count data
Poisson regression is a generalized linear model form of regression analysis used to model count data and contingency tables. Poisson regression assumes
Poisson_regression
Regression for more than two discrete outcomes
In statistics, multinomial logistic regression is a classification method that generalizes logistic regression to multiclass problems, i.e. with more than
Multinomial logistic regression
Multinomial_logistic_regression
Moving average and polynomial regression method for smoothing data
Local regression or local polynomial regression, also known as moving regression, is a generalization of the moving average and polynomial regression. Its
Local_regression
Least squares approximation of linear functions to data
^{\mathsf {T}}\mathbf {y} .} Optimal instruments regression is an extension of classical IV regression to the situation where E[εi | zi] = 0. Total least
Linear_least_squares
Estimates from regression analysis on data with unit variance
standardized (regression) coefficients, also called beta coefficients or beta weights, are the estimates resulting from a regression analysis where the
Standardized_coefficient
Statistical phenomenon
In statistics, regression toward the mean (also called regression to the mean, reversion to the mean, and reversion to mediocrity) is the phenomenon where
Regression_toward_the_mean
Statistical bias in linear regressions
Regression dilution, also known as regression attenuation, is the biasing of the linear regression slope towards zero (the underestimation of its absolute
Regression_dilution
Statistical technique
used for estimating the unknown regression coefficients in a standard linear regression model. In PCR, instead of regressing the dependent variable on the
Principal component regression
Principal_component_regression
Algorithm for the line of best fit for a two-dimensional dataset
data-sources; however the regression procedure takes no account for possible errors in estimating this ratio. The Deming regression is only slightly more
Deming_regression
Class of statistical models
(GLM) is a flexible generalization of ordinary linear regression. The GLM generalizes linear regression by allowing the linear model to be related to the
Generalized_linear_model
Indicator for how well data points fit a line or curve
remaining 51% of the variability is still unaccounted for. For regression models, the regression sum of squares, also called the explained sum of squares,
Coefficient_of_determination
Second letter of the Greek alphabet
predictor X. In statistics, beta may represent type II error, or regression slope. Dirichlet beta function Some uses of beta in physics and engineering
Beta
Regression analysis
In statistics, nonlinear regression is a form of regression analysis in which observational data are modeled by a function which is a nonlinear combination
Nonlinear_regression
Continuous probability distribution on the unit interval
models for continuous proportional data, proposed as an alternative to beta regression. The special case λ = 1 {\displaystyle \lambda =1} coincides with the
Continuous binomial distribution
Continuous_binomial_distribution
Method of statistical analysis
Bayesian linear regression is a type of conditional modeling in which the mean of one variable is described by a linear combination of other variables
Bayesian_linear_regression
Theorem in statistics and econometrics
is the double residual regression. With a linear regression of the form y = X β ^ + Z δ ^ + e ^ {\displaystyle y=X{\hat {\beta }}+Z{\hat {\delta }}+{\hat
Frisch–Waugh–Lovell_theorem
Expected change in price of a stock relative to the whole market
\beta _{i}} of an asset i {\displaystyle i} , observed on t {\displaystyle t} occasions, is defined by (and best obtained via) a linear regression of
Beta_(finance)
Statistical technique
Conditional logistic regression is an extension of logistic regression that allows one to account for stratification and matching. Its main field of application
Conditional logistic regression
Conditional_logistic_regression
Statistical linear model
model or general multivariate regression model is a compact way of simultaneously writing several multiple linear regression models. In that sense it is
General_linear_model
Class of statistical survival models
itself be described as a regression model. There is a relationship between proportional hazards models and Poisson regression models which is sometimes
Proportional_hazards_model
Regression analysis technique
In statistics, binomial regression is a regression analysis technique in which the response (often referred to as Y) has a binomial distribution: it is
Binomial_regression
Technique in statistics
explanatory variables (covariates) are correlated with the error terms in a regression model. Such correlation may occur when: changes in the dependent variable
Instrumental_variables
Regression models accounting for possible errors in independent variables
error model is a regression model that accounts for measurement errors in the independent variables. In contrast, standard regression models assume that
Errors-in-variables_model
Method for estimating parameters
asset pricing model Standard errors in regression analysis IHS EViews (2014). "Fama-MacBeth Two-Step Regression" (PDF). Fama, Eugene F.; MacBeth, James
Fama–MacBeth_regression
Type of plot in applied statistics
i {\displaystyle \beta _{i}} , where β i {\displaystyle \beta _{i}} corresponds to the regression coefficient for Xi of a regression of Y on all of the
Partial_regression_plot
Statistical method
parametric (normally polynomial regression). The most common non-parametric method used in the RDD context is a local linear regression. This is of the form: Y
Regression discontinuity design
Regression_discontinuity_design
Statistical regression method
particular, in the fitting of linear or logistic regression models, the elastic net is a regularized regression method that linearly combines the L1 and L2
Elastic_net_regularization
Approximation method in statistics
as the least angle regression algorithm. One of the prime differences between Lasso and ridge regression is that in ridge regression, as the penalty is
Least_squares
Regression models that combine parametric and nonparametric models
In statistics, semiparametric regression includes regression models that combine parametric and nonparametric models. They are often used in situations
Semiparametric_regression
Regression algorithm
In statistics, least-angle regression (LARS) is an algorithm for fitting linear regression models to high-dimensional data, developed by Bradley Efron
Least-angle_regression
Type of regression analysis
Functional regression is a version of regression analysis when responses or covariates include functional data. Functional regression models can be classified
Functional_regression
Method for model fitting in statistics
(WLS), also known as weighted linear regression, is a generalization of ordinary least squares and linear regression in which knowledge of the unequal variance
Weighted_least_squares
In statistics, unit-weighted regression is a simplified and robust version (Wainer & Thissen, 1976) of multiple regression analysis where only the intercept
Unit-weighted_regression
Statistical technique
taken into account. It is a generalization of Deming regression and also of orthogonal regression, and can be applied to both linear and non-linear models
Total_least_squares
Concept in statistical mathematics
Zellner in (1962), is a generalization of a linear regression model that consists of several regression equations, each having its own dependent variable
Seemingly unrelated regressions
Seemingly_unrelated_regressions
Checking software against expectations
test. Regression testing focuses on finding defects after a major code change has occurred. Specifically, it seeks to uncover software regressions, as degraded
Software_testing
Spatial prediction technique
applied statistics and geostatistics, regression-kriging (RK) is a spatial prediction technique that combines a regression of the dependent variable on auxiliary
Regression-kriging
Type of statistical model
can be seen as generalizations of linear models (in particular, linear regression), although they can also extend to non-linear models. These models became
Multilevel_model
Method for dimension reduction in statistics
Sliced inverse regression (SIR) is a tool for dimensionality reduction in the field of multivariate statistics. In statistics, regression analysis is a
Sliced_inverse_regression
Regression model for ordinal dependent variables
logit model or proportional odds logistic regression is an ordinal regression model—that is, a regression model for ordinal dependent variables—first
Ordered_logit
Method for solving certain optimization problems
{\beta }}){\big |}^{2}.} IRLS is used to find the maximum likelihood estimates of a generalized linear model, and in robust regression to find an
Iteratively reweighted least squares
Iteratively_reweighted_least_squares
Statistical regression where the dependent variable can take only two values
In statistics, a probit model is a type of regression where the dependent variable can take only two values, for example married or not married. The word
Probit_model
Statistical regression technique
multilevel regression with poststratification model involves the following pair of steps: MRP step 1 (multilevel regression): The multilevel regression model
Multilevel regression with poststratification
Multilevel_regression_with_poststratification
Statistical test for model misspecification
statistics, the Ramsey Regression Equation Specification Error Test (RESET) test is a general specification test for the linear regression model. More specifically
Ramsey_RESET_test
Statistical model
characterized. Step 1 and step 2 use simple regression analysis, whereas step 3 uses multiple regression analysis. How you were parented (i.e., independent
Mediation_(statistics)
Method for nonparametric multiple regression
In statistics, projection pursuit regression (PPR) is a statistical model developed by Jerome H. Friedman and Werner Stuetzle that extends additive models
Projection_pursuit_regression
Continuous probability distribution
standard linear regression is used for modeling continuous variables (e.g., income or population). Specifically, logistic regression models can be phrased
Logistic_distribution
Probability distribution
^{2}(2\beta -1)+\beta ^{2}(\beta +1)-2\alpha \beta (\beta +2)]}{\alpha \beta (\alpha +\beta +2)(\alpha +\beta +3)}}\\&={\frac {6[(\alpha -\beta )^{2}(\alpha
Beta_distribution
Bayesian approach to multivariate linear regression
Bayesian multivariate linear regression is a Bayesian approach to multivariate linear regression, i.e. linear regression where the predicted outcome is
Bayesian multivariate linear regression
Bayesian_multivariate_linear_regression
Matrix of values of explanatory variables
In statistics and in particular in regression analysis, a design matrix, also known as model matrix or regressor matrix and often denoted by X, is a matrix
Design_matrix
Statistical measure in mathematical model
the regression of Xj on the other covariates (a regression that does not involve the response variable Y) and β ^ j {\displaystyle {\hat {\beta }}_{j}}
Variance_inflation_factor
Theorem related to ordinary least squares
f(\beta _{0},\beta _{1},\dots ,\beta _{p})=\sum _{i=1}^{n}(y_{i}-\beta _{0}-\beta _{1}x_{i1}-\dots -\beta _{p}x_{ip})^{2}} for a multiple regression model
Gauss–Markov_theorem
Statistical technique
{\beta }}(X_{0})\\\end{aligned}}} Savitzky–Golay filter Kernel methods Kernel density estimation Local regression Kernel regression Li, Q. and
Kernel_smoother
Statistics models class
specified parametric form (for example a polynomial, or an un-penalized regression spline of a variable) or may be specified non-parametrically, or semi-parametrically
Generalized_additive_model
Statistical measure of the discrepancy between data and an estimation model
is the hat matrix, or the projection matrix in linear regression. The least-squares regression line is given by y = a x + b , {\displaystyle y=ax+b,}
Residual_sum_of_squares
Statistical estimation method
In statistics, specifically regression analysis, a binary regression estimates a relationship between one or more explanatory variables and a single output
Binary_regression
Statistical optimality criterion
the idea of least absolute deviations regression is just as straightforward as that of least squares regression, the least absolute deviations line is
Least_absolute_deviations
Probability distribution
income distribution, stock returns, as well as in regression analysis. The exponential generalized beta (EGB) distribution follows directly from the GB
Generalized_beta_distribution
Statistical hypothesis test
the linear regression to the result from the t-test. From the t-test, the difference between the group means is 6-2=4. From the regression, the slope
Student's_t-test
Asymptotic variances under heteroskedasticity
the linear regression model for the scalar y {\displaystyle y} . y = x ⊤ β + ε , {\displaystyle y=\mathbf {x} ^{\top }{\boldsymbol {\beta }}+\varepsilon
Heteroskedasticity-consistent standard errors
Heteroskedasticity-consistent_standard_errors
Type of statistical model
occurrence is in connection with regression models and the term is often taken as synonymous with linear regression model. However, the term is also used
Linear_model
Statistical model for censored regressands
In statistics, a tobit model is any of a class of regression models in which the observed range of the dependent variable is censored in some way. The
Tobit_model
Quantile Regression Averaging (QRA) is a forecast combination approach to the computation of prediction intervals. It involves applying quantile regression to
Quantile_regression_averaging
Linear function of explanatory variables used to predict a dependent variable
This sort of function usually comes in linear regression, where the coefficients are called regression coefficients. However, they also occur in various
Linear_predictor_function
Empirical statistical testing of economic theories
the multiple linear regression model. In modern econometrics, other statistical tools are frequently used, but linear regression is still the most frequently
Econometrics
Empirical law on the variance of species in a habitat
{\exp(a+(b-2)[\alpha -\beta \log _{e}(p_{0})])}{n}}} where MSE is the mean square error of the regression, α and β are the constant and slope of the regression respectively
Taylor's_law
Estimation procedure for correlated data
unmeasured correlation between observations from different timepoints. Regression beta coefficient estimates from the Liang-Zeger GEE are consistent, unbiased
Generalized estimating equation
Generalized_estimating_equation
Continuous probability distribution
make it a more flexible alternative for a quantile regression model against the classical Beta regression model. The r {\displaystyle r} th raw moment of
Unit_Weibull_distribution
Statistical method
interaction term; it is not framed as a regression model. By contrast, the Blinder–Oaxaca (OB) decomposition is regression-based, typically at the mean, and
Kitagawa–Oaxaca–Blinder decomposition
Kitagawa–Oaxaca–Blinder_decomposition
Medication class with multiple uses
Beta blockers, also spelled β-blockers and also sometimes known as β-adrenergic receptor antagonists, are a class of medications predominantly used to
Beta_blocker
Statistical test
present. Suppose that we estimate the regression model y = β 0 + β 1 x + u , {\displaystyle y=\beta _{0}+\beta _{1}x+u,\,} and obtain from this fitted
Breusch–Pagan_test
Statistical hypothesis test for the presence of serial correlation
autocorrelation in the errors in a regression model. It makes use of the residuals from the model being considered in a regression analysis, and a test statistic
Breusch–Godfrey_test
Concept in mathematical modeling, statistical modeling and experimental sciences
dependent variable. If included in a regression, it can improve the fit of the model. If it is excluded from the regression and if it has a non-zero covariance
Dependent and independent variables
Dependent_and_independent_variables
Concept in regression analysis mathematics
least-angle regression algorithm. An important difference between lasso regression and Tikhonov regularization is that lasso regression forces more entries
Regularized_least_squares
Type of statistical bias
bias to exist in linear regression: the omitted variable must be a determinant of the dependent variable (i.e., its true regression coefficient must not
Omitted-variable_bias
Type of statistical regression analysis
Non-homogeneous Gaussian regression (NGR) is a type of statistical regression analysis used in the atmospheric sciences as a way to convert ensemble forecasts
Nonhomogeneous Gaussian regression
Nonhomogeneous_Gaussian_regression
Mathematical functions
instance, binary regression analysis has been used to predict endoscopic lesions in iron deficiency anemia. In addition, binary regression was applied to
Hyperbolastic_functions
Approximation method in statistics
the probit regression, (ii) threshold regression, (iii) smooth regression, (iv) logistic link regression, (v) Box–Cox transformed regressors ( m ( x ,
Non-linear_least_squares
Concept that permeates much of inferential statistics and descriptive statistics
Given a linear regression model y i = β 0 + β 1 x i 1 + ⋯ + β p x i p + ε i {\displaystyle y_{i}=\beta _{0}+\beta _{1}x_{i1}+\cdots +\beta _{p}x_{ip}+\varepsilon
Partition_of_sums_of_squares
Part of the process of building a statistical model
+ ρ s + β 1 x + β 2 x 2 + ε {\displaystyle \ln y=\ln y_{0}+\rho s+\beta _{1}x+\beta _{2}x^{2}+\varepsilon } where ε {\displaystyle \varepsilon } is the
Statistical model specification
Statistical_model_specification
Mathematical concept
{\beta }}} and is therefore equivalent to Bayesian linear regression. Regularized least squares: the elements of β {\displaystyle {\boldsymbol {\beta }}}
Constrained_least_squares
Statistical test of variance
⋯ = βk vs. at least one pair βj ≠ βj′ in Multiple linear regression or in Logistic regression. Usually, it tests more than two parameters of the same type
Omnibus_test
Statistical term
Consider the linear regression model y i = x i ⊤ β + ε i {\displaystyle {y}_{i}={\boldsymbol {x}}_{i}^{\top }{\boldsymbol {\beta }}+{\varepsilon }_{i}}
Leverage_(statistics)
Statistics model
statistics, a linear probability model (LPM) is a special case of a binary regression model. Here the dependent variable for each observation takes values which
Linear_probability_model
Type of probability distribution used in statistics
statistics, the g-prior is an objective prior for the regression coefficients of a multiple regression. It was introduced by Arnold Zellner. It is a key tool
G-prior
Statistics concept
regression analysis, are acceptable as descriptions of the data. The validation process can involve analyzing the goodness of fit of the regression,
Regression_validation
Technique for the generative modeling of a continuous probability distribution
1 ) {\displaystyle \beta _{1},...,\beta _{T}\in (0,1)} are fixed constants. α t := 1 − β t {\displaystyle \alpha _{t}:=1-\beta _{t}} α ¯ t := α 1 ⋯ α
Diffusion_model
Statistical regression model
In statistics, an additive model (AM) is a nonparametric regression method. It was suggested by Jerome H. Friedman and Werner Stuetzle (1981) and is an
Additive_model
Test statistic
when using OLS regression gretl: Automatically calculated when using OLS regression Stata: the command estat dwatson, following regress in time series
Durbin–Watson_statistic
Regression method in econometrics
data in the regression, which solves the problems of losing potentially useful information and including mis-specification. A simple regression example has
Mixed-data_sampling
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