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Regression
Regression or regressions may refer to: Science * Marine regression, coastal advance due to falling sea level, the opposite of marine transgression * Regression (medicine), a characteristic of diseases to express lighter symptoms or less extent (mainly for tumors), without disappearing totally * Regression (psychology), a defensive reaction to some unaccepted impulses * Nodal regression, the movement of the nodes of an object in orbit, in the opposite direction to the motion of the object Statistics * Regression analysis, a statistical technique for estimating the relationships among variables. There are several types of regression: ** Linear regression ** Simple linear regression ** Logistic regression ** Nonlinear regression ** Nonparametric regression ** Robust regression ** Stepwise regression * Regression toward the mean, a common statistical phenomenon Computing * Software regression, the appearance of a bug which was absent in a previous revision ** Regression testing, a s ...
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Regression (film)
''Regression'' is a 2015 psychological thriller horror mystery film directed and written by Alejandro Amenábar. The film stars Ethan Hawke and Emma Watson, with David Thewlis, Lothaire Bluteau, Dale Dickey, David Dencik, Peter MacNeill, Devon Bostick, and Aaron Ashmore in supporting roles. The film had its world premiere at the San Sebastián International Film Festival on September 18, 2015. It was released in the United States on October 9, 2015, by The Weinstein Company under the banner RADiUS-TWC. The film received mostly negative reviews from critics. Plot The film takes place in Minnesota, in 1990. Detective Bruce Kenner (Ethan Hawke) investigates the case of John Gray (David Dencik), who admits to sexually abusing his 17-year-old daughter Angela (Emma Watson) but has no recollection of the abuse. They seek the help of Professor Kenneth Raines (David Thewlis) to use recovered-memory therapy on John Gray to retrieve his memories, and come to suspect that their colleagu ...
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Regression Analysis
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 independent variables (often called 'predictors', 'covariates', 'explanatory variables' or 'features'). The most common form of regression analysis is linear regression, in which one finds the line (or a more complex linear combination) that most closely fits the data according to a specific mathematical criterion. For example, the method of ordinary least squares computes the unique line (or hyperplane) that minimizes the sum of squared differences between the true data and that line (or hyperplane). For specific mathematical reasons (see linear regression), this allows the researcher to estimate the conditional expectation (or population average value) of the dependent variable when the independent variables take on a given ...
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Logistic Regression
In statistics, the logistic model (or logit model) is a statistical model that models the probability of an event taking place by having the log-odds for the event be a linear function (calculus), linear combination of one or more independent variables. In regression analysis, logistic regression (or logit regression) is estimation theory, estimating the parameters of a logistic model (the coefficients in the linear combination). Formally, in binary logistic regression there is a single binary variable, binary dependent variable, coded by an indicator variable, where the two values are labeled "0" and "1", while the independent variables can each be a binary variable (two classes, coded by an indicator variable) or a continuous variable (any real value). The corresponding probability of the value labeled "1" can vary between 0 (certainly the value "0") and 1 (certainly the value "1"), hence the labeling; the function that converts log-odds to probability is the logistic function, h ...
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Linear Regression
In statistics, linear regression is a linear approach for modelling the relationship between a scalar response and one or more explanatory variables (also known as dependent and independent variables). The case of one explanatory variable is called '' simple linear regression''; for more than one, the process is called multiple linear regression. This term is distinct from multivariate linear regression, where multiple correlated dependent variables are predicted, rather than a single scalar variable. In linear regression, the relationships are modeled using linear predictor functions whose unknown model parameters are estimated from the data. Such models are called linear models. Most commonly, the conditional mean of the response given the values of the explanatory variables (or predictors) is assumed to be an affine function of those values; less commonly, the conditional median or some other quantile is used. Like all forms of regression analysis, linear regression focuses on ...
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Regression Toward The Mean
In statistics, regression toward the mean (also called reversion to the mean, and reversion to mediocrity) is the fact that if one sample of a random variable is extreme, the next sampling of the same random variable is likely to be closer to its mean. Furthermore, when many random variables are sampled and the most extreme results are intentionally picked out, it refers to the fact that (in many cases) a second sampling of these picked-out variables will result in "less extreme" results, closer to the initial mean of all of the variables. Mathematically, the strength of this "regression" effect is dependent on whether or not all of the random variables are drawn from the same distribution, or if there are genuine differences in the underlying distributions for each random variable. In the first case, the "regression" effect is statistically likely to occur, but in the second case, it may occur less strongly or not at all. Regression toward the mean is thus a useful concept to ...
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Regressions (album)
''Regressions'' is the first Album#Studio album, studio album by Cleric (band), Cleric, released on April 27, 2010, by Web of Mimicry. Recording Cleric recorded ''Regressions'' in Queens, New York, with the producer Colin Marston. The music was recorded at The Thousand Caves, Marston's studio, and put guitar, drums, and bass guitar simultaneously on reel-to-reel tape. In contrast to the rest of the album, the music that "The Fiberglass Cheesecake" comprises was assembled in the studio rather than performed, making it difficult to reproduce in a live setting. In crafting the track, the band used a sound replacer, recording the drummer, Larry Kwartowitz, using his hands to play a part on his lap and then replacing the sounds of his hands with drums. Marston commented on the album's recording process in an interview with ''American Aftermath'': "''Regressions'' by Cleric took waaaaaay longer than any other record I’ve ever worked on. It's also probably the most dense in terms of th ...
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Regression Testing
Regression testing (rarely, ''non-regression testing'') is re-running functional and non-functional tests to ensure that previously developed and tested software still performs as expected after a change. If not, that would be called a '' regression''. Changes that may require regression testing include bug fixes, software enhancements, configuration changes, and even substitution of electronic components. As regression test suites tend to grow with each found defect, test automation is frequently involved. Sometimes a change impact analysis is performed to determine an appropriate subset of tests (''non-regression analysis''). Background As software is updated or changed, or reused on a modified target, emergence of new faults and/or re-emergence of old faults is quite common. Sometimes re-emergence occurs because a fix gets lost through poor revision control practices (or simple human error in revision control). Often, a fix for a problem will be "fragile" in that it fi ...
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Software Regression
A software regression is a type of software bug where a feature that has worked before stops working. This may happen after changes are applied to the software's source code, including the addition of new features and bug fixes. They may also be introduced by changes to the environment in which the software is running, such as system upgrades, system patching or a change to daylight saving time. A software performance regression is a situation where the software still functions correctly, but performs more slowly or uses more memory or resources than before. Various types of software regressions have been identified in practice, including the following: * ''Local'' – a change introduces a new bug in the changed module or component. * ''Remote'' – a change in one part of the software breaks functionality in another module or component. * ''Unmasked'' – a change unmasks an already existing bug that had no effect before the change. Regressions are often caused by encompassed bu ...
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Robust Regression
In robust statistics, robust regression seeks to overcome some limitations of traditional regression analysis. A regression analysis models the relationship between one or more independent variables and a dependent variable. Standard types of regression, such as ordinary least squares, have favourable properties if their underlying assumptions are true, but can give misleading results otherwise (i.e. are not robust to assumption violations). Robust regression methods are designed to limit the effect that violations of assumptions by the underlying data-generating process have on regression estimates. For example, least squares estimates for regression models are highly sensitive to outliers: an outlier with twice the error magnitude of a typical observation contributes four (two squared) times as much to the squared error loss, and therefore has more leverage over the regression estimates. The Huber loss function is a robust alternative to standard square error loss that reduces ...
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Stepwise Regression
In statistics, stepwise regression is a method of fitting regression models in which the choice of predictive variables is carried out by an automatic procedure. In each step, a variable is considered for addition to or subtraction from the set of explanatory variables based on some prespecified criterion. Usually, this takes the form of a forward, backward, or combined sequence of ''F''-tests or ''t''-tests. The frequent practice of fitting the final selected model followed by reporting estimates and confidence intervals without adjusting them to take the model building process into account has led to calls to stop using stepwise model building altogetherFlom, P. L. and Cassell, D. L. (2007) "Stopping stepwise: Why stepwise and similar selection methods are bad, and what you should use," NESUG 2007. or to at least make sure model uncertainty is correctly reflected.Chatfield, C. (1995) "Model uncertainty, data mining and statistical inference," J. R. Statist. Soc. A 158, Part 3, ...
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Nonlinear Regression
In statistics, nonlinear regression is a form of regression analysis in which observational data are modeled by a function which is a nonlinear combination of the model parameters and depends on one or more independent variables. The data are fitted by a method of successive approximations. General In nonlinear regression, a statistical model of the form, : \mathbf \sim f(\mathbf, \boldsymbol\beta) relates a vector of independent variables, \mathbf, and its associated observed dependent variables, \mathbf. The function f is nonlinear in the components of the vector of parameters \beta, but otherwise arbitrary. For example, the Michaelis–Menten model for enzyme kinetics has two parameters and one independent variable, related by f by: : f(x,\boldsymbol\beta)= \frac This function is nonlinear because it cannot be expressed as a linear combination of the two ''\beta''s. Systematic error may be present in the independent variables but its treatment is outside the scope of ...
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Simple Linear Regression
In statistics, simple linear regression is a linear regression model with a single explanatory variable. That is, it concerns two-dimensional sample points with one independent variable and one dependent variable (conventionally, the ''x'' and ''y'' coordinates in a Cartesian coordinate system) and finds a linear function (a non-vertical straight line) that, as accurately as possible, predicts the dependent variable values as a function of the independent variable. The adjective ''simple'' refers to the fact that the outcome variable is related to a single predictor. It is common to make the additional stipulation that the ordinary least squares (OLS) method should be used: the accuracy of each predicted value is measured by its squared '' residual'' (vertical distance between the point of the data set and the fitted line), and the goal is to make the sum of these squared deviations as small as possible. Other regression methods that can be used in place of ordinary least square ...
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