 |
Linear Regression
In statistics, linear regression is a statistical model, model that estimates the relationship between a Scalar (mathematics), scalar response (dependent variable) and one or more explanatory variables (regressor or independent variable). 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. This term is distinct from multivariate linear regression, which predicts multiple correlated dependent variables rather than a single dependent variable. In linear regression, the relationships are modeled using linear predictor functions whose unknown model parameters are estimation theory, estimated from the data. 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, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
 |
Simple Linear Regression
In statistics, simple linear regression (SLR) 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. In this case, the slope of the fitted line is equal to the corre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
 |
Statistics
Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of statistical survey, surveys and experimental design, experiments. When census data (comprising every member of the target population) cannot be collected, statisticians collect data by developing specific experiment designs and survey sample (statistics), samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
 |
Norm (mathematics)
In mathematics, a norm is a function (mathematics), function from a real or complex vector space to the non-negative real numbers that behaves in certain ways like the distance from the Origin (mathematics), origin: it Equivariant map, commutes with scaling, obeys a form of the triangle inequality, and zero is only at the origin. In particular, the Euclidean distance in a Euclidean space is defined by a norm on the associated Euclidean vector space, called the #Euclidean norm, Euclidean norm, the #p-norm, 2-norm, or, sometimes, the magnitude or length of the vector. This norm can be defined as the square root of the inner product of a vector with itself. A seminorm satisfies the first two properties of a norm but may be zero for vectors other than the origin. A vector space with a specified norm is called a normed vector space. In a similar manner, a vector space with a seminorm is called a ''seminormed vector space''. The term pseudonorm has been used for several related meaning ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
|
Goodness Of Fit
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 between observed values and the values expected under the model in question. Such measures can be used in statistical hypothesis testing, e.g. to test for normality of residuals, to test whether two samples are drawn from identical distributions (see Kolmogorov–Smirnov test), or whether outcome frequencies follow a specified distribution (see Pearson's chi-square test). In the analysis of variance, one of the components into which the variance is partitioned may be a lack-of-fit sum of squares. Fit of distributions In assessing whether a given distribution is suited to a data-set, the following tests and their underlying measures of fit can be used: * Bayesian information criterion * Kolmogorov–Smirnov test * Cramér–von Mises criterion * Anderson–Darling test * Berk-Jones tests * Shapiro–Wilk test * Chi-s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
|
 |
Least Squares
The method of least squares is a mathematical optimization technique that aims to determine the best fit function by minimizing the sum of the squares of the differences between the observed values and the predicted values of the model. The method is widely used in areas such as regression analysis, curve fitting and data modeling. The least squares method can be categorized into linear and nonlinear forms, depending on the relationship between the model parameters and the observed data. The method was first proposed by Adrien-Marie Legendre in 1805 and further developed by Carl Friedrich Gauss. History Founding The method of least squares grew out of the fields of astronomy and geodesy, as scientists and mathematicians sought to provide solutions to the challenges of navigating the Earth's oceans during the Age of Discovery. The accurate description of the behavior of celestial bodies was the key to enabling ships to sail in open seas, where sailors could no longer rely on la ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
 |
Data Set
A data set (or dataset) is a collection of data. In the case of tabular data, a data set corresponds to one or more table (database), database tables, where every column (database), column of a table represents a particular Variable (computer science), variable, and each row (database), row corresponds to a given Record (computer science), record of the data set in question. The data set lists values for each of the variables, such as for example height and weight of an object, for each member of the data set. Data sets can also consist of a collection of documents or files. In the open data discipline, a dataset is a unit used to measure the amount of information released in a public open data repository. The European data.europa.eu portal aggregates more than a million data sets. Properties Several characteristics define a data set's structure and properties. These include the number and types of the attributes or variables, and various statistical measures applicable to the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
|
Forecasting
Forecasting is the process of making predictions based on past and present data. Later these can be compared with what actually happens. For example, a company might Estimation, estimate their revenue in the next year, then compare it against the actual results creating a variance actual analysis. Prediction is a similar but more general term. Forecasting might refer to specific formal statistical methods employing time series, cross-sectional data, cross-sectional or longitudinal study, longitudinal data, or alternatively to less formal judgmental methods or the process of prediction and assessment of its accuracy. Usage can vary between areas of application: for example, in hydrology the terms "forecast" and "forecasting" are sometimes reserved for estimates of values at certain specific future times, while the term "prediction" is used for more general estimates, such as the number of times floods will occur over a long period. Risk and uncertainty are central to forecasting an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
|
 |
Prediction
A prediction (Latin ''præ-'', "before," and ''dictum'', "something said") or forecast is a statement about a future event or about future data. Predictions are often, but not always, based upon experience or knowledge of forecasters. There is no universal agreement about the exact difference between "prediction" and " estimation"; different authors and disciplines ascribe different connotations. Future events are necessarily uncertain, so guaranteed accurate information about the future is impossible. Prediction can be useful to assist in making plans about possible developments. Opinion In a non-statistical sense, the term "prediction" is often used to refer to an informed guess or opinion. A prediction of this kind might be informed by a predicting person's abductive reasoning, inductive reasoning, deductive reasoning, and experience; and may be useful—if the predicting person is a knowledgeable person in the field. The Delphi method is a technique for elicitin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
 |
Variance Reduction
In mathematics, more specifically in the theory of Monte Carlo methods, variance reduction is a procedure used to increase the precision of the estimates obtained for a given simulation or computational effort. Every output random variable from the simulation is associated with a variance which limits the precision of the simulation results. In order to make a simulation statistically efficient, i.e., to obtain a greater precision and smaller confidence intervals for the output random variable of interest, variance reduction techniques can be used. The main variance reduction methods are * common random numbers * antithetic variates * control variates * importance sampling * stratified sampling * moment matching * conditional Monte Carlo * and quasi random variables (in Quasi-Monte Carlo method) For simulation with black-box models subset simulation and line sampling can also be used. Under these headings are a variety of specialized techniques; for example, parti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
 |
Supervised Learning
In machine learning, supervised learning (SL) is a paradigm where a Statistical model, model is trained using input objects (e.g. a vector of predictor variables) and desired output values (also known as a ''supervisory signal''), which are often human-made labels. The training process builds a function that maps new data to expected output values. An optimal scenario will allow for the algorithm to accurately determine output values for unseen instances. This requires the learning algorithm to Generalization (learning), generalize from the training data to unseen situations in a reasonable way (see inductive bias). This statistical quality of an algorithm is measured via a ''generalization error''. Steps to follow To solve a given problem of supervised learning, the following steps must be performed: # Determine the type of training samples. Before doing anything else, the user should decide what kind of data is to be used as a Training, validation, and test data sets, trainin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
 |
Algorithm
In mathematics and computer science, an algorithm () is a finite sequence of Rigour#Mathematics, mathematically rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can use Conditional (computer programming), conditionals to divert the code execution through various routes (referred to as automated decision-making) and deduce valid inferences (referred to as automated reasoning). In contrast, a Heuristic (computer science), heuristic is an approach to solving problems without well-defined correct or optimal results.David A. Grossman, Ophir Frieder, ''Information Retrieval: Algorithms and Heuristics'', 2nd edition, 2004, For example, although social media recommender systems are commonly called "algorithms", they actually rely on heuristics as there is no truly "correct" recommendation. As an e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |