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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 error-free independent variables (often called ''regressors'', ''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 i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Machine Learning
Machine learning (ML) is a field of study in artificial intelligence concerned with the development and study of Computational statistics, statistical algorithms that can learn from data and generalise to unseen data, and thus perform Task (computing), tasks without explicit Machine code, instructions. Within a subdiscipline in machine learning, advances in the field of deep learning have allowed Neural network (machine learning), neural networks, a class of statistical algorithms, to surpass many previous machine learning approaches in performance. ML finds application in many fields, including natural language processing, computer vision, speech recognition, email filtering, agriculture, and medicine. The application of ML to business problems is known as predictive analytics. Statistics and mathematical optimisation (mathematical programming) methods comprise the foundations of machine learning. Data mining is a related field of study, focusing on exploratory data analysi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Regression Toward The Mean
In statistics, regression toward the mean (also called regression to the mean, reversion to the mean, and reversion to mediocrity) is the phenomenon where 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Francis Galton
Sir Francis Galton (; 16 February 1822 – 17 January 1911) was an English polymath and the originator of eugenics during the Victorian era; his ideas later became the basis of behavioural genetics. Galton produced over 340 papers and books. He also developed the statistical concept of correlation and widely promoted regression toward the mean. He was the first to apply statistical methods to the study of human differences and inheritance of intelligence, and introduced the use of questionnaires and Statistical survey, surveys for collecting data on human communities, which he needed for genealogical and biographical works and for his anthropometrics, anthropometric studies. He popularised the phrase "nature versus nurture". His book ''Hereditary Genius'' (1869) was the first social scientific attempt to study genius and greatness. As an investigator of the human mind, he founded psychometrics and differential psychology, as well as the lexical hypothesis of personality. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gauss–Markov Theorem
In statistics, the Gauss–Markov theorem (or simply Gauss theorem for some authors) states that the ordinary least squares (OLS) estimator has the lowest sampling variance within the class of linear unbiased estimators, if the errors in the linear regression model are uncorrelated, have equal variances and expectation value of zero. The errors do not need to be normal, nor do they need to be independent and identically distributed (only uncorrelated with mean zero and homoscedastic with finite variance). The requirement that the estimator be unbiased cannot be dropped, since biased estimators exist with lower variance. See, for example, the James–Stein estimator (which also drops linearity), ridge regression, or simply any degenerate estimator. The theorem was named after Carl Friedrich Gauss and Andrey Markov, although Gauss' work significantly predates Markov's. But while Gauss derived the result under the assumption of independence and normality, Markov r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
C/1769 P1
C/1769 P1 (Messier) is a long-period comet that was visible to the naked eye at its last apparition in 1769. The comet is classified as a great comet due to its superlative brightness. Discovery and observations At the Naval Observatory in Paris, late in the evening of 8 August 1769 Charles Messier in his routine telescope search for comets saw a small nebulosity just above the horizon in the constellation Aries. On the next evening he saw the nebulosity by unassisted eye and confirmed it to be a comet due to its motion in the sky. On 15 August Messier estimated the length of the comet's tail to be 6°. Giovanni Domenico Maraldi and César François Cassini de Thury saw the comet for the first time on 22 August by telescope and later by unassisted eye. Chinese observers reported a "broom star" appearing on 24 August in the southeastern sky. Jean-François-Marie de Surville observed the comet in the pre-dawn of 26 August from a ship off the Philippines and reported the comet ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carl Friedrich Gauss
Johann Carl Friedrich Gauss (; ; ; 30 April 177723 February 1855) was a German mathematician, astronomer, geodesist, and physicist, who contributed to many fields in mathematics and science. He was director of the Göttingen Observatory and professor of astronomy from 1807 until his death in 1855. While studying at the University of Göttingen, he propounded several mathematical theorems. As an independent scholar, he wrote the masterpieces '' Disquisitiones Arithmeticae'' and ''Theoria motus corporum coelestium''. Gauss produced the second and third complete proofs of the fundamental theorem of algebra. In number theory, he made numerous contributions, such as the composition law, the law of quadratic reciprocity and the Fermat polygonal number theorem. He also contributed to the theory of binary and ternary quadratic forms, the construction of the heptadecagon, and the theory of hypergeometric series. Due to Gauss' extensive and fundamental contributions to science ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adrien-Marie Legendre
Adrien-Marie Legendre (; ; 18 September 1752 – 9 January 1833) was a French people, French mathematician who made numerous contributions to mathematics. Well-known and important concepts such as the Legendre polynomials and Legendre transformation are named after him. He is also known for his contributions to the Least squares, method of least squares, and was the first to officially publish on it, though Carl Friedrich Gauss had discovered it before him. Life Adrien-Marie Legendre was born in Paris on 18 September 1752 to a wealthy family. He received his education at the Collège Mazarin in Paris, and defended his thesis in physics and mathematics in 1770. He taught at the École Militaire in Paris from 1775 to 1780 and at the École Normale Supérieure, École Normale from 1795. At the same time, he was associated with the Bureau des Longitudes. In 1782, the Prussian Academy of Sciences, Berlin Academy awarded Legendre a prize for his treatise on projectiles in resistant m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Method Of 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] |
Princeton University Press
Princeton University Press is an independent publisher with close connections to Princeton University. Its mission is to disseminate scholarship within academia and society at large. The press was founded by Whitney Darrow, with the financial support of Charles Scribner, as a printing press to serve the Princeton community in 1905. Its distinctive building was constructed in 1911 on William Street in Princeton. Its first book was a new 1912 edition of John Witherspoon's ''Lectures on Moral Philosophy.'' History Princeton University Press was founded in 1905 by a recent Princeton graduate, Whitney Darrow, with financial support from another Princetonian, Charles Scribner II. Darrow and Scribner purchased the equipment and assumed the operations of two already existing local publishers, that of the ''Princeton Alumni Weekly'' and the Princeton Press. The new press printed both local newspapers, university documents, '' The Daily Princetonian'', and later added book publishing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tobias Mayer
Tobias Mayer (17 February 172320 February 1762) was a German astronomer famous for his studies of the Moon. He was born at Marbach, in Württemberg, and brought up at Esslingen in poor circumstances. A self-taught mathematician, he earned a living by teaching mathematics while still a youth. He had already published two original geometrical works when, in 1746, he entered J. B. Homann's cartographic establishment at Nuremberg. Here he introduced many improvements in mapmaking, and gained a scientific reputation which led (in 1751) to his election to the chair of economy and mathematics at the University of Göttingen. In 1754 he became superintendent of the observatory, where he worked until his death in 1762. He has been credited with developing an early form of regression analysis in 1750, though 50 years earlier Isaac Newton had used similar methods. Career Mayer's first important astronomical work was a careful investigation of the libration of the Moon (''Kosmographisc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equinox
A solar equinox is a moment in time when the Sun appears directly above the equator, rather than to its north or south. On the day of the equinox, the Sun appears to rise directly east and set directly west. This occurs twice each year, around 20 March and 23 September. An equinox is equivalently defined as the time when the plane of Earth's equator passes through the geometric center of the Sun's disk. This is also the moment when Earth's rotation axis is directly perpendicular to the Sun-Earth line, tilting neither toward nor away from the Sun. In modern times, since the Moon (and to a lesser extent the planets) causes Earth's orbit to vary slightly from a perfect ellipse, the equinox is officially defined by the Sun's more regular ecliptic longitude rather than by its declination. The instants of the equinoxes are currently defined to be when the apparent geocentric longitude of the Sun is 0° and 180°. The word is derived from the Latin ', from ' (equal) and ' ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
