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Various methods have been proposed for measuring influence. [3] [4] Assume an estimated regression = +, where is an n×1 column vector for the response variable, is the n×k design matrix of explanatory variables (including a constant), is the n×1 residual vector, and is a k×1 vector of estimates of some population parameter .
A model with exactly one explanatory variable is a simple linear regression; a model with two or more explanatory variables is a multiple linear regression. [1] This term is distinct from multivariate linear regression, which predicts multiple correlated dependent variables rather than a single dependent variable. [2]
In statistical modeling, regression analysis is a set of statistical processes for estimating the relationships between a dependent variable (often called the outcome or response variable, or a label in machine learning parlance) and one or more error-free independent variables (often called regressors, predictors, covariates, explanatory ...
The basic form of a linear predictor function () for data point i (consisting of p explanatory variables), for i = 1, ..., n, is = + + +,where , for k = 1, ..., p, is the value of the k-th explanatory variable for data point i, and , …, are the coefficients (regression coefficients, weights, etc.) indicating the relative effect of a particular explanatory variable on the outcome.
In statistics, explained variation measures the proportion to which a mathematical model accounts for the variation of a given data set.Often, variation is quantified as variance; then, the more specific term explained variance can be used.
The explanatory variable is the diet pill and the response variable is the amount of weight loss. Although the sex of the patient is not the main focus of the experiment—the effect of the drug is—it is possible that the sex of the individual will affect the amount of weight lost.
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 of values of explanatory variables of a set of objects. Each row represents an individual object, with the successive columns corresponding to the variables and their specific values for ...
In 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 are either 0 or 1. The probability of observing a 0 or 1 in any one case is treated as depending on one or more explanatory variables.