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Pearson correlation coefficient. Several sets of ( x , y) points, with the correlation coefficient of x and y for each set. The correlation reflects the strength and direction of a linear relationship (top row), but not the slope of that relationship (middle), nor many aspects of nonlinear relationships (bottom).
Canonical commutation rule for position q and momentum p variables of a particle, 1927. pq − qp = h / (2 πi ). Uncertainty principle of Heisenberg, 1927. The uncertainty principle, also known as Heisenberg's indeterminacy principle, is a fundamental concept in quantum mechanics. It states that there is a limit to the precision with which ...
Example graph of a logistic regression curve fitted to data. The curve shows the estimated probability of passing an exam (binary dependent variable) versus hours studying (scalar independent variable). See Example for worked details. In statistics, the 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 ...
Principal component analysis (PCA) is a linear dimensionality reduction technique with applications in exploratory data analysis, visualization and data preprocessing. The data is linearly transformed onto a new coordinate system such that the directions (principal components) capturing the largest variation in the data can be easily identified.
- History
- Regression Model
- Underlying Assumptions
- Linear Regression
- Nonlinear Regression
- Prediction
- Power and Sample Size Calculations
- Other Methods
- Software
- Further Reading
The earliest form of regression was the method of least squares, which was published by Legendre in 1805, and by Gauss in 1809. Legendre and Gauss both applied the method to the problem of determining, from astronomical observations, the orbits of bodies about the Sun (mostly comets, but also later the then newly discovered minor planets). Gauss pu...
In practice, researchers first select a model they would like to estimate and then use their chosen method (e.g., ordinary least squares) to estimate the parameters of that model. Regression models involve the following components: 1. The unknown parameters, often denoted as a scalar or vector β {\\displaystyle \\beta } . 2. The independent variables...
By itself, a regression is simply a calculation using the data. In order to interpret the output of regression as a meaningful statistical quantity that measures real-world relationships, researchers often rely on a number of classical assumptions. These assumptions often include: 1. The sample is representative of the population at large. 2. The i...
In linear regression, the model specification is that the dependent variable, y i {\\displaystyle y_{i}} is a linear combination of the parameters (but need not be linear in the independent variables). For example, in simple linear regression for modeling n {\\displaystyle n} data points there is one independent variable: x i {\\displaystyle x_{i}} , ...
When the model function is not linear in the parameters, the sum of squares must be minimized by an iterative procedure. This introduces many complications which are summarized in Differences between linear and non-linear least squares.
Regression models predict a value of the Y variable given known values of the X variables. Prediction within the range of values in the dataset used for model-fitting is known informally as interpolation. Prediction outside this range of the data is known as extrapolation. Performing extrapolation relies strongly on the regression assumptions. The ...
There are no generally agreed methods for relating the number of observations versus the number of independent variables in the model. One method conjectured by Good and Hardin is N = m n {\\displaystyle N=m^{n}} , where N {\\displaystyle N} is the sample size, n {\\displaystyle n} is the number of independent variables and m {\\displaystyle m} is the ...
Although the parameters of a regression model are usually estimated using the method of least squares, other methods which have been used include: 1. Bayesian methods, e.g. Bayesian linear regression 2. Percentage regression, for situations where reducing percentageerrors is deemed more appropriate. 3. Least absolute deviations, which is more robus...
All major statistical software packages perform least squares regression analysis and inference. Simple linear regression and multiple regression using least squares can be done in some spreadsheetapplications and on some calculators. While many statistical software packages can perform various types of nonparametric and robust regression, these me...
William H. Kruskal and Judith M. Tanur, ed. (1978), "Linear Hypotheses," International Encyclopedia of Statistics. Free Press, v. 1,
In mathematical analysis, the Dirac delta function (or δ distribution ), also known as the unit impulse, [1] is a generalized function on the real numbers, whose value is zero everywhere except at zero, and whose integral over the entire real line is equal to one.
The Navier–Stokes equations ( / nævˈjeɪ stoʊks / nav-YAY STOHKS) are partial differential equations which describe the motion of viscous fluid substances. They were named after French engineer and physicist Claude-Louis Navier and the Irish physicist and mathematician George Gabriel Stokes. They were developed over several decades of ...
