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Statistical modeling method
multivariate analysis. A generalization of linear regression is found in nonlinear regression. Linear regression is also a type of machine learning algorithm
Linear_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 method
real-world regression models involve multiple predictors, and basic descriptions of linear regression are often phrased in terms of the multiple regression model
Multiple_linear_regression
Set of statistical processes for estimating the relationships among variables
non-linear models (e.g., nonparametric regression). Regression analysis is primarily used for two conceptually distinct purposes. First, regression analysis
Regression_analysis
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
Statistical linear model
general linear model or general multivariate regression model is a compact way of simultaneously writing several multiple linear regression models. In
General_linear_model
Least squares approximation of linear functions to data
in linear regression, including variants for ordinary (unweighted), weighted, and generalized (correlated) residuals. Numerical methods for linear least
Linear_least_squares
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
Ordinary_least_squares
Concept in statistical mathematics
Segmented linear regression is segmented regression whereby the relations in the intervals are obtained by linear regression. Segmented linear regression with
Segmented_regression
Class of statistical models
generalized linear model (GLM) is a flexible generalization of ordinary linear regression. The GLM generalizes linear regression by allowing the linear model
Generalized_linear_model
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
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
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
Method for model fitting in statistics
squares (WLS), also known as weighted linear regression, is a generalization of ordinary least squares and linear regression in which knowledge of the unequal
Weighted_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
Specialized form of regression analysis, in statistics
In robust statistics, robust regression seeks to overcome some limitations of traditional regression analysis. A regression analysis models the relationship
Robust_regression
Topics referred to by the same term
heteroscedastic errors Simple linear regression, the simplest type of regression, involving only one explanatory variable General linear model for multivariate
Linear regression (disambiguation)
Linear_regression_(disambiguation)
Statistical method
squares (PLS) regression is a statistical method that bears some relation to principal components regression and is a reduced rank regression; instead of
Partial least squares regression
Partial_least_squares_regression
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
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
Regularization technique for ill-posed problems
estimators when linear regression models have some multicollinear (highly correlated) independent variables—by creating a ridge regression estimator (RR)
Ridge_regression
Statistical model for a binary dependent variable
an event as a linear combination of one or more independent variables. In regression analysis, logistic regression (or logit regression) estimates the
Logistic_regression
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
Type of numerical analysis
In statistics and numerical analysis, isotonic regression or monotonic regression is the technique of fitting a free-form line to a sequence of observations
Isotonic_regression
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
Regression analysis for modeling ordinal data
machine learning, ordinal regression may also be called ranking learning. Ordinal regression can be performed using a generalized linear model (GLM) that fits
Ordinal_regression
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
Theorem related to ordinary least squares
estimator across samples) within the class of linear unbiased estimators, if the errors in the linear regression model are uncorrelated, have equal variances
Gauss–Markov_theorem
Type of statistical model
seen as generalizations of linear models (in particular, linear regression), although they can also extend to non-linear models. These models became
Multilevel_model
Indicator for how well data points fit a line or curve
(2018) shows, several shrinkage estimators – such as Bayesian linear regression, ridge regression, and the (adaptive) lasso – make use of this decomposition
Coefficient_of_determination
2D graphic with logarithmic scales on both axes
forms appear approximately linear on the log–log scale, and simply evaluating the goodness of fit of a linear regression on logged data using the coefficient
Log–log_plot
Concept in statistical analysis
(possibly the independent variable) (see also correlation and simple linear regression). Bivariate analysis can be contrasted with univariate analysis in
Bivariate_analysis
Statistical hypothesis test
Case of Linear Regression Independent t-test as a linear model in R 2.9 Building Connections Between The 2-Sample t-test and Linear Regression Shieh, Gwowen
Student's_t-test
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
Category of regression analysis
function. Linear regression is a restricted case of nonparametric regression where m ( x ) {\displaystyle m(x)} is assumed to be a linear function of
Nonparametric_regression
Number of values in the final calculation of a statistic that are free to vary
regression methods, including regularized least squares (e.g., ridge regression), linear smoothers, smoothing splines, and semiparametric regression,
Degrees of freedom (statistics)
Degrees_of_freedom_(statistics)
General linear model that blends ANOVA and regression
Analysis of covariance (ANCOVA) is a general linear model that blends ANOVA and regression. ANCOVA evaluates whether the means of a dependent variable
Analysis_of_covariance
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
Collection of statistical models
notation in place, we now have the exact connection with linear regression. We simply regress response y k {\displaystyle y_{k}} against the vector X k
Analysis_of_variance
Type of statistical model
the term linear model refers to any model which assumes linearity in the system. The most common occurrence is in connection with regression models and
Linear_model
Method used in statistics, pattern recognition, and other fields
categorical dependent variable (i.e. the class label). Logistic regression and probit regression are more similar to LDA than ANOVA is, as they also explain
Linear_discriminant_analysis
Concept in probability theory and statistics
for a constant term in the regression. Solving the linear regression problem amounts to finding (n+1)-dimensional regression coefficient vectors w X ∗
Partial_correlation
Approximation method in statistics
to state that the least-squares approach to regression analysis is optimal in the sense that in a linear model where the errors have a mean of zero, are
Least_squares
Non-parametric regression technique
adaptive regression splines (MARS) is a form of regression analysis introduced by Jerome H. Friedman in 1991. It is a non-parametric regression technique
Multivariate adaptive regression spline
Multivariate_adaptive_regression_spline
Statistical technique
to use the weighted average for the estimation. The idea of local linear regression is to fit locally a straight line (or a hyperplane for higher dimensions)
Kernel_smoother
Bayesian approach to multivariate linear regression
statistics, Bayesian multivariate linear regression is a Bayesian approach to multivariate linear regression, i.e. linear regression where the predicted outcome
Bayesian multivariate linear regression
Bayesian_multivariate_linear_regression
Degradation of AI models trained on synthetic data
shown. In the case of a linear regression model, scaling laws and bounds on learning can be obtained. In the case of a linear softmax classifier for next
Model_collapse
Method for solving certain optimization problems
find the maximum likelihood estimates of a generalized linear model, and in robust regression to find an M-estimator, as a way of mitigating the influence
Iteratively reweighted least squares
Iteratively_reweighted_least_squares
Type of artificial neural network
with linear activation functions. It was trained by the least squares method for minimising mean squared error, also known as linear regression. Legendre
Feedforward_neural_network
Mathematical model
the model, which makes it possible to apply (possibly multivariate) linear regression. That is, it has the general form exp ( c + ∑ i w i f i ( X ) )
Log-linear_model
Application of a function to each point in a data set
with linear regression if the original data violates one or more assumptions of linear regression. For example, the simplest linear regression models
Data transformation (statistics)
Data_transformation_(statistics)
Optimization algorithm
gradient descent and batched gradient descent. In general, given a linear regression y ^ = ∑ k ∈ 1 : m w k x k {\displaystyle {\hat {y}}=\sum _{k\in 1:m}w_{k}x_{k}}
Stochastic_gradient_descent
Type of mathematical function
published. If partitions, and then breakpoints, are already known, linear regression can be performed independently on these partitions. However, continuity
Piecewise_linear_function
Statistics concept
distinction is most important in regression analysis, where the concepts are sometimes called the regression errors and regression residuals and where they lead
Errors_and_residuals
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
Omnibus_test
Four data sets with the same descriptive statistics, yet very different distributions
relationship is linear, but should have a different regression line (a robust regression would have been called for). The calculated regression is offset by
Anscombe's_quartet
Empirical statistical testing of economic theories
which it is used today. A basic tool for econometrics is the multiple linear regression model. Econometric theory uses statistical theory and mathematical
Econometrics
Extension of evidence theory to continuous variables of interest
the later. We can use the linear regression model — Y = XA + b + E — to illustrate the property. As we mentioned, the regression model may be considered
Linear_belief_function
Information-theoretic measure
cross-entropy loss for logistic regression is equal to the gradient of the squared-error loss for linear regression (up to a constant factor). To see
Cross-entropy
Statistical estimation method
outputting a single value, as in linear regression. Binary regression is usually analyzed as a special case of binomial regression, with a single outcome ( n
Binary_regression
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
Simultaneous observation and analysis of more than one outcome variable
problems involving multivariate data, for example simple linear regression and multiple regression, are not usually considered to be special cases of multivariate
Multivariate_statistics
Flaw in mathematical modelling
"one in ten rule"). In the process of regression model selection, the mean squared error of the random regression function can be split into random noise
Overfitting
Concept in statistical mathematics
unrelated regressions (SUR) or seemingly unrelated regression equations (SURE) model, proposed by Arnold Zellner in (1962), is a generalization of a linear regression
Seemingly unrelated regressions
Seemingly_unrelated_regressions
Statistical method for fitting a line
robustly fitting a line to sample points in the plane (a form of simple linear regression) by choosing the median of the slopes of all lines through pairs of
Theil–Sen_estimator
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
Linear function of explanatory variables used to predict a dependent variable
comes in linear regression, where the coefficients are called regression coefficients. However, they also occur in various types of linear classifiers
Linear_predictor_function
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 measure of fit
of fit and when a likelihood function is used to fit a model. In linear regression, the squared multiple correlation, R2 is used to assess goodness of
Pseudo-R-squared
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
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
Process of using data analysis for predicting population data from sample data
characteristics of the observations. For example, model-free simple linear regression is based either on: a random design, where the pairs of observations
Statistical_inference
Set of methods for supervised statistical learning
have better predictive performance than other linear models, such as logistic regression and linear regression. Classifying data is a common task in machine
Support_vector_machine
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
Algorithm for the line of best fit for a two-dimensional dataset
compute than the simple linear regression. Most statistical software packages used in clinical chemistry offer Deming regression. The model was originally
Deming_regression
Statistical relationship
data. It usually refers to the extent to which a pair of quantities are linearly related. More generally, an arbitrary relationship between variables is
Correlation
Statistical techniques analyzing facts to make predictions about unknown events
authors list (link) "Linear Regression". www.stat.yale.edu. Retrieved 2022-05-06. Kinney, William R.; Salamon, Gerald L. (1982). "Regression Analysis in Auditing:
Predictive_analytics
Statistical method
for linear regression models. This simple case reveals a substantial amount about the estimator. These include its relationship to ridge regression and
Lasso_(statistics)
Statistical quantity
general regression model with n observations and k explanators, the first of which is a constant unit vector whose coefficient is the regression intercept
Explained_sum_of_squares
Topics referred to by the same term
Look up regression, regressions, or régression in Wiktionary, the free dictionary. Regression or regressions may refer to: Regression (film), a 2015 horror
Regression
Sequence of data points over time
Using Linear and Nonlinear Regression: A Practical Guide to Curve Fitting. Oxford University Press. ISBN 978-0-19-803834-4.[page needed] Regression Analysis
Time_series
Transforming data by taking the logarithm
with linear regression if the original data violates one or more assumptions of linear regression. For example, the simplest linear regression models
Log transformation (statistics)
Log_transformation_(statistics)
Theorem in statistics and econometrics
method of estimating coefficients in a linear regression where a single dependent variable is modeled as a linear function of one or more explanatory variables
Frisch–Waugh–Lovell_theorem
Measurable property or characteristic
that of explanatory variables used in statistical techniques such as linear regression. In feature engineering, two types of features are commonly used:
Feature_(machine_learning)
Index of articles associated with the same name
distance: Simple linear regression Resistance to outliers: Robust simple linear regression Perpendicular distance: Orthogonal regression (this is not scale-invariant
Line_fitting
Concept that permeates much of inferential statistics and descriptive statistics
this broad principle to inferential statistics. Theorem. 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
Partition_of_sums_of_squares
Branch of statistics mathematics
functional nonlinear regression models. Functional polynomial regression models may be viewed as a natural extension of the Functional Linear Models (FLMs) with
Functional_data_analysis
Machine learning technique
boosted models as Multiple Additive Regression Trees (MART); Elith et al. describe that approach as "Boosted Regression Trees" (BRT). A popular open-source
Gradient_boosting
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
Research field that lies at the intersection of machine learning and computer security
adversarial training of a linear regression model with input perturbations restricted by the 2-norm closely resembles Ridge regression. Adversarial deep reinforcement
Adversarial_machine_learning
Model for generating observable data in probability and statistics
necessarily perform better than generative models at classification and regression tasks. The two classes are seen as complementary or as different views
Generative_model
Type of activation function
context of artificial neural networks, the rectifier or ReLU (rectified linear unit) activation function is an activation function defined as the non-negative
Rectified_linear_unit
Measure of the joint variability
random variables. The sign of the covariance shows the tendency in the linear relationship between the variables. Covariance is positive when variables
Covariance
crystallization (e.g., liquidus temperature) or phase separation, linear regression can be applied using common polynomial functions up to the third degree
Calculation of glass properties
Calculation_of_glass_properties
Family of statistical methods based on sampling of available data
"self-influence". For comparison, in regression analysis methods such as linear regression, each y value draws the regression line toward itself, making the
Resampling_(statistics)
How many standard deviations apart from the mean an observed datum is
to multiple regression analysis is sometimes used as an aid to interpretation. (page 95) state the following. "The standardized regression slope is the
Standard_score
Mathematical data production model with limited structure
special form such as a linear regression or neural network. These have special analysis methods. In particular linear regression techniques are much more
Grey_box_model
Measure of covariance of components of a random vector
}\operatorname {K} _{\mathbf {XX} }^{-1}} is known as the matrix of regression coefficients, while in linear algebra K Y | X {\displaystyle \operatorname {K} _{\mathbf
Covariance_matrix
Statistical hypothesis test
that a proposed regression model fits the data well. See Lack-of-fit sum of squares. The hypothesis that a data set in a regression analysis follows
F-test
Statistical model validation technique
context of linear regression is also useful in that it can be used to select an optimally regularized cost function.) In most other regression procedures
Cross-validation_(statistics)
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