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Statistical linear model
The general linear model or general multivariate regression model is a compact way of simultaneously writing several multiple linear regression models. In
General_linear_model
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 to
Generalized_linear_model
Type of statistical model
term linear model refers to any model which assumes linearity in the system. The most common occurrence is in connection with regression models and the
Linear_model
Statistical modeling method
variable) related via a linear combination. A linear model with exactly one explanatory variable is a simple linear regression; a model with two or more explanatory
Linear_regression
Mathematical model
log-linear model is a mathematical model that takes the form of a function whose logarithm equals a linear combination of the parameters of the model, which
Log-linear_model
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
Type of statistical model
are grouped. These models are also known as hierarchical linear models, linear mixed-effect models, mixed models, nested data models, random coefficient
Multilevel_model
Statistical model containing both fixed effects and random effects
discuss mainly linear mixed-effects models rather than generalized linear mixed models or nonlinear mixed-effects models. Linear mixed models (LMMs) are statistical
Mixed_model
Statistical model
statistics, a generalized linear mixed model (GLMM) is an extension to the generalized linear model (GLM) in which the linear predictor contains random
Generalized linear mixed model
Generalized_linear_mixed_model
Multiple linear regression is a special case, restricted to one dependent variable, of general linear models (also known as multivariate linear regression)
Multiple_linear_regression
Statistics model
In statistics, a linear probability model (LPM) is a special case of a binary regression model. Here the dependent variable for each observation takes
Linear_probability_model
Concept in statistics
of vector generalized linear models (VGLMs) was proposed to enlarge the scope of models catered for by generalized linear models (GLMs). In particular
Vector generalized linear model
Vector_generalized_linear_model
Type of statistical model
A partially linear model is a form of semiparametric model, since it contains parametric and nonparametric elements. Application of the least squares estimators
Partially_linear_model
Specialized form of regression analysis, in statistics
Google books Dawes, Robyn M. (1979). "The robust beauty of improper linear models in decision making". American Psychologist, volume 34, pages 571-582
Robust_regression
Statistical model for a binary dependent variable
In statistics, a logistic model (or logit model) is a statistical model that models the log-odds of an event as a linear combination of one or more independent
Logistic_regression
Statistical model used in time series analysis
model is typically denoted as ARMA(p, q), where p is the order of the autoregressive part and q is the order of the moving-average part. The general ARMA
Autoregressive moving-average model
Autoregressive_moving-average_model
Model for generating observable data in probability and statistics
generative model Energy based model Diffusion model Linear discriminant analysis If the observed data are truly sampled from the generative model, then fitting
Generative_model
Set of statistical processes for estimating the relationships among variables
estimate the conditional expectation across a broader collection of non-linear models (e.g., nonparametric regression). Regression analysis is primarily used
Regression_analysis
Topics referred to by the same term
explanatory variable General linear model for multivariate predictands Generalised linear model for non-normal distributions Bayesian linear regression, where
Linear regression (disambiguation)
Linear_regression_(disambiguation)
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
Approximation method in statistics
linear or ordinary least squares and nonlinear least squares, depending on whether or not the model functions are linear in all unknowns. The linear least-squares
Least_squares
Regression analysis
modeling see least squares and non-linear least squares. The assumption underlying this procedure is that the model can be approximated by a linear function
Nonlinear_regression
Matrix of values of explanatory variables
object. The design matrix is used in certain statistical models, e.g., the general linear model. It can contain indicator variables (ones and zeros) that
Design_matrix
Type of numerical analysis
that it is not constrained by any functional form, such as the linearity imposed by linear regression, as long as the function is monotonic increasing.
Isotonic_regression
Procedure for comparing multivariate sample means
general linear model, containing the group and the covariates, and substitute Y ¯ {\textstyle {\bar {Y}}} with the predictions of the general linear model
Multivariate analysis of variance
Multivariate_analysis_of_variance
Method for estimating the unknown parameters in a linear regression model
least squares (OLS) is a type of linear least squares method for choosing the unknown parameters in a linear regression model by the principle of least squares:
Ordinary_least_squares
Concept in statistical mathematics
regressors on the right-hand-side. The SUR model can be viewed as either the simplification of the general linear model where certain coefficients in matrix
Seemingly unrelated regressions
Seemingly_unrelated_regressions
Class of statistical survival models
Poisson model] is true, but simply use it as a device for deriving the likelihood." McCullagh and Nelder's book on generalized linear models has a chapter
Proportional_hazards_model
Type of statistical model
\Gamma ^{-1}+U\Gamma ^{-1}=X\Pi +V.\,} This is already a simple general linear model, and it can be estimated for example by ordinary least squares. Unfortunately
Simultaneous_equations_model
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
Statistical hypothesis test
Likelihood-ratio tests in general statistical modelling, for testing whether there is evidence of the need to move from a simple model to a more complicated
Chi-squared_test
Method to solve optimization problems
lowest cost) in a mathematical model whose requirements and objective are represented by linear relationships. Linear programming is a special case of
Linear_programming
Statistical technique to aid interpretation of data
in an external factor. Linear trend estimation essentially creates a straight line on a graph of data that models the general direction that the data
Linear_trend_estimation
Collection of statistical models
case of linear regression which in turn is a special case of the general linear model. All consider the observations to be the sum of a model (fit) and
Analysis_of_variance
Value that appears most often in a set of data
concept of median does not apply. The median makes sense when there is a linear order on the possible values. Generalizations of the concept of median to
Mode_(statistics)
Statistics concept
model is linear in the parameters to be estimated. In general, we can model the expected value of y as an nth degree polynomial, yielding the general
Polynomial_regression
Numerical measure of a statistical relationship between variables
correlation coefficient is a numerical measure of some type of linear correlation, meaning a linear function between two variables. The variables may be two
Correlation_coefficient
Type of mathematical model
being 1.5 meters tall. We could formalize that relationship in a linear regression model, like this: heighti = b0 + b1agei + εi, where b0 is the intercept
Statistical_model
Statistical regression where the dependent variable can take only two values
using similar techniques. When viewed in the generalized linear model framework, the probit model employs a probit link function. It is most often estimated
Probit_model
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
Weighted_least_squares
Type of chart
in, because the area contained becomes proportional to the square of the linear measures. For example, in a chart with 5 variables that range from 1 to
Radar_chart
Simultaneous observation and analysis of more than one outcome variable
simultaneously to changes in others. For linear relations, regression analyses here are based on forms of the general linear model. Some suggest that multivariate
Multivariate_statistics
Parametric model in survival analysis
\theta } . This reduces the accelerated failure time model to regression analysis (typically a linear model) where − log ( θ ) {\displaystyle -\log(\theta
Accelerated failure time model
Accelerated_failure_time_model
Unit of information
"Evidence of unreliable data and poor data provenance in clinical prediction model research and clinical practice". BMC Medicine. doi:10.1186/s12916-026-04981-y
Data
Approximation method in statistics
Non-linear least squares is the form of least squares analysis used to fit a set of m observations with a model that is non-linear in n unknown parameters
Non-linear_least_squares
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
Regression models accounting for possible errors in independent variables
samples. For simple linear regression the effect is an underestimate of the coefficient, known as the attenuation bias. In non-linear models the direction of
Errors-in-variables_model
Task of selecting a statistical model from a set of candidate models
Analysis Log-linear analysis Model identification Occam's razor Optimal design Parameter identification problem Scientific modelling Statistical model validation
Model_selection
Statistics concept
Applied linear models with SAS (Online-Ausg. ed.). Cambridge: Cambridge University Press. ISBN 978-0-521-76159-8. "7.3: Types of Outliers in Linear Regression"
Errors_and_residuals
Main model used in radioprotection to minimize radiation exposures
The linear no-threshold model (LNT) is a dose-response model used in radiation protection to estimate stochastic health effects such as radiation-induced
Linear_no-threshold_model
Mathematical relation assigning a probability event to a cost
including t-tests, regression models, design of experiments, and much else, use least squares methods applied using linear regression theory, which is based
Loss_function
Metric for fit of statistical models
The goodness of fit of a statistical model describes how well it fits a set of observations. Measures of goodness of fit typically summarize the discrepancy
Goodness_of_fit
Type of statistical measure over subsets of a dataset
applications in image signal processing. In a moving average regression model, a variable of interest is assumed to be a weighted moving average of unobserved
Moving_average
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
Table that displays the frequency of variables
ISBN 978-0-262-02113-5. MR 0381130. Christensen, Ronald (1997). Log-linear models and logistic regression. Springer Texts in Statistics (Second ed.).
Contingency_table
Measure of linear correlation
unqualified correlation coefficient, is a correlation coefficient that measures linear correlation between two sets of data. It is the ratio between the covariance
Pearson correlation coefficient
Pearson_correlation_coefficient
Mathematical model used for classification or regression
Discriminative models, also referred to as conditional models, are a class of models frequently used for classification. In machine learning, it typically models the
Discriminative_model
Relative measure of dispersion expressed as the ratio of standard deviation to the mean
error in the production process). However, data that are linear or even logarithmically non-linear and include a continuous range for the independent variable
Coefficient_of_variation
Measure of statistical dispersion
data set is divided into quartiles, or four rank-ordered even parts via linear interpolation. These quartiles are denoted by Q1 (also called the lower
Interquartile_range
Design of tasks
weights and experimental measurements may be represented with a general linear model, with the design matrix W {\displaystyle W} having entries from {
Design_of_experiments
Statistical model
discriminate between the fixed and the random effects models. Consider the linear unobserved effects model for N {\displaystyle N} observations and T {\displaystyle
Fixed_effects_model
Diagnostic plot of binary classifier ability
z-score of an ROC curve is always linear, as assumed, except in special situations. The Yonelinas familiarity-recollection model is a two-dimensional account
Receiver operating characteristic
Receiver_operating_characteristic
Complete set of items that share at least one property in common
hands in a game of poker). In statistical inference, the population is modelled by a probability distribution with unknown parameters. By analyzing a subset
Statistical_population
Statistical technique
wavelet transformation. Parametric statistical models are assumed at each voxel, using the general linear model to describe the data variability in terms of
Statistical parametric mapping
Statistical_parametric_mapping
Branch of statistics
study. Cox models may be extended for such time-varying covariates. The Cox PH regression model is a linear model. It is similar to linear regression
Survival_analysis
Method of data analysis
a general attitude toward property and home ownership. The index, or the attitude questions it embodied, could be fed into a General Linear Model of
Principal_component_analysis
Statistical hypothesis test
data set in a regression analysis follows the simpler of two proposed linear models that are nested within each other. Multiple-comparison testing is conducted
F-test
Method of statistical inference
Kiona; Tucker, Colin; Cable, Jessica M. (2014-01-01). "Beyond simple linear mixing models: process-based isotope partitioning of ecological processes". Ecological
Bayesian_inference
Statistical test comparing two probability distributions
Ord, Keith; Arnold, Steven [F.] (1999). Classical Inference and the Linear Model. Kendall's Advanced Theory of Statistics. Vol. 2A (Sixth ed.). London:
Kolmogorov–Smirnov_test
Statistic which divides a data set into 100 parts and analyzes it as a percentage
subscript i, linearly interpolating v between adjacent nodes. There are two ways in which the variant approaches differ. The first is in the linear relationship
Percentile
Least squares approximation of linear functions to data
Linear least squares (LLS) is the least squares approximation of linear functions to data. It is a set of formulations for solving statistical problems
Linear_least_squares
Middle quantile of a data set or probability distribution
the model Y = X + Z {\displaystyle Y=X+Z} where Z {\displaystyle Z} is standard normal independent of X {\displaystyle X} , the estimator is linear if
Median
Generates a forecast of future values of a time series
Seasonal, Holt's Linear Trend, Brown's Linear Trend, Damped Trend, Winters' Additive, and Winters' Multiplicative in the Time-Series modeling procedure within
Exponential_smoothing
Statistical phenomenon
such a line that minimizes the sum of squared residuals of the linear regression model. In other words, numbers α and β solve the following minimization
Regression_toward_the_mean
distribution frequency domain frequentist inference general linear model generalized linear model grouped data histogram An approximate graphical representation
Glossary of probability and statistics
Glossary_of_probability_and_statistics
Probabilistic problem-solving algorithm
space models". Journal of Computational and Graphical Statistics. 5 (1): 1–25. doi:10.2307/1390750. JSTOR 1390750. Del Moral, Pierre (1996). "Non Linear Filtering:
Monte_Carlo_method
Conditional probability used in Bayesian statistics
hypothesis, or parameter values), given prior knowledge and a mathematical model describing the observations available at a particular time. After the arrival
Posterior_probability
Method of modeling the behavior of a viscoelastic material
The standard linear solid (SLS), also known as the Zener model after Clarence Zener, is a method of modeling the behavior of a viscoelastic material using
Standard_linear_solid_model
Interpretation of probability
variables, or more generally unknown quantities, to model all sources of uncertainty in statistical models including uncertainty resulting from lack of information
Bayesian_probability
Form of causal modeling that fit networks of constructs to data
structures and the concerns motivating economic models. Judea Pearl extended SEM from linear to nonparametric models, and proposed causal and counterfactual interpretations
Structural_equation_modeling
Measure of covariance of components of a random vector
\mathbb {R} ^{n}} Proof Indeed, from the property 4 it follows that under linear transformation of random variable X {\displaystyle \mathbf {X} } with covariation
Covariance_matrix
Nonparametric measure of rank correlation
Pearson's correlation assesses linear relationships, Spearman's correlation assesses monotonic relationships (whether linear or not). If there are no repeated
Spearman's rank correlation coefficient
Spearman's_rank_correlation_coefficient
Plot using the dispersal of scattered dots to show the relationship between variables
determined by established best-fit procedures. For a linear correlation, the best-fit procedure is known as linear regression and is guaranteed to generate a correct
Scatter_plot
shape-flexible, has simple closed forms, and can be parameterized with data using linear least squares. The Marchenko–Pastur distribution is important in the theory
List of probability distributions
List_of_probability_distributions
Statistical hypothesis test
Special 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
Student's_t-test
Family of statistical methods based on sampling of available data
The bootstrap estimate of model prediction bias is more precise than jackknife estimates with linear models such as linear discriminant function or multiple
Resampling_(statistics)
Branch of statistics
techniques that are commonly used in statistics include mathematical analysis, linear algebra, stochastic analysis, differential equations, and measure theory
Mathematical_statistics
Class of statistical tests
One application of normality tests is to the residuals from a linear regression model. If they are not normally distributed, the residuals should not
Normality_test
Probabilistic model
A graphical model or probabilistic graphical model (PGM) or structured probabilistic model is a probabilistic model for which a graph expresses the conditional
Graphical_model
Time series model
ISBN 9781107661455. Lanne, Markku; Saikkonen, Pentti (July 2005). "Non-linear GARCH models for highly persistent volatility" (PDF). The Econometrics Journal
Autoregressive conditional heteroskedasticity
Autoregressive_conditional_heteroskedasticity
Number of values in the final calculation of a statistic that are free to vary
the context of linear models (linear regression, analysis of variance), where certain random vectors are constrained to lie in linear subspaces, and the
Degrees of freedom (statistics)
Degrees_of_freedom_(statistics)
Algorithmically generated data that have a similar distribution as sampled data
constructing a statistical model. In a linear regression line example, the original data can be plotted, and a best fit linear line can be created from
Synthetic_data
Method of estimating the parameters of a statistical model
This is both because these estimators are optimal under squared-error and linear-error loss respectively—which are more representative of typical loss functions—and
Maximum a posteriori estimation
Maximum_a_posteriori_estimation
Regularization technique for ill-posed problems
problem of multicollinearity in linear regression, which commonly occurs in models with large numbers of parameters. In general, the method provides improved
Ridge_regression
Range to estimate an unknown parameter
distribution (also here) Confidence interval for the parameters of a simple linear regression Confidence interval for the difference of means (based on data
Confidence_interval
Dividing things between two categories
Neural networks Logistic regression Probit model Genetic Programming Multi expression programming Linear genetic programming Each classifier is best
Binary_classification
Statistical method for handling multiple comparisons
{\displaystyle q=5\%} ) may still not be very costly. Controlling the FDR using the linear step-up BH procedure, at level q, has several properties related to the
False_discovery_rate
Method of quality control
degraded functionality of the cams and pulleys may lead to a non-random linear pattern of increasing cereal box weights. We call this common cause variation
Statistical_process_control
Regression for more than two discrete outcomes
logit model and numerous other methods, models, algorithms, etc. with the same basic setup (the perceptron algorithm, support vector machines, linear discriminant
Multinomial logistic regression
Multinomial_logistic_regression
Statistical test that compares goodness of fit
Karl-Rudolf (1988). Parameter Estimation and Hypothesis Testing in Linear Models. New York: Springer. p. 306. ISBN 0-387-18840-1. Silvey, S.D. (1970)
Likelihood-ratio_test
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GENERAL LINEAR-MODEL
GENERAL LINEAR-MODEL
GENERAL LINEAR-MODEL
GENERAL LINEAR-MODEL
GENERAL LINEAR-MODEL
GENERAL LINEAR-MODEL
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