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Anscombe's Quartet
Anscombe's quartet comprises four data sets that have nearly identical simple descriptive statistics, yet have very different distributions and appear very different when graphed. Each dataset consists of eleven (''x'',''y'') points. They were constructed in 1973 by the statistician Francis Anscombe to demonstrate both the importance of graphing data when analyzing it, and the effect of outliers and other influential observations on statistical properties. He described the article as being intended to counter the impression among statisticians that "numerical calculations are exact, but graphs are rough." Data For all four datasets: * The first scatter plot (top left) appears to be a simple linear relationship, corresponding to two variables correlated where y could be modelled as gaussian with mean linearly dependent on ''x''. * The second graph (top right); while a relationship between the two variables is obvious, it is not linear, and the Pearson correlation co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Relationship
In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statistics it usually refers to the degree to which a pair of variables are ''linearly'' related. Familiar examples of dependent phenomena include the correlation between the height of parents and their offspring, and the correlation between the price of a good and the quantity the consumers are willing to purchase, as it is depicted in the so-called demand curve. Correlations are useful because they can indicate a predictive relationship that can be exploited in practice. For example, an electrical utility may produce less power on a mild day based on the correlation between electricity demand and weather. In this example, there is a causal relationship, because extreme weather causes people to use more electricity for heating or cooling. However ... [...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 * Shapiro–Wilk test *Chi-squared test *Akaike informat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exploratory Data Analysis
In statistics, exploratory data analysis (EDA) is an approach of analyzing data sets to summarize their main characteristics, often using statistical graphics and other data visualization methods. A statistical model can be used or not, but primarily EDA is for seeing what the data can tell us beyond the formal modeling and thereby contrasts traditional hypothesis testing. Exploratory data analysis has been promoted by John Tukey since 1970 to encourage statisticians to explore the data, and possibly formulate hypotheses that could lead to new data collection and experiments. EDA is different from initial data analysis (IDA), which focuses more narrowly on checking assumptions required for model fitting and hypothesis testing, and handling missing values and making transformations of variables as needed. EDA encompasses IDA. Overview Tukey defined data analysis in 1961 as: "Procedures for analyzing data, techniques for interpreting the results of such procedures, ways of pla ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conference On Human Factors In Computing Systems
The ACM Conference on Human Factors in Computing Systems (CHI) series of academic conferences is generally considered the most prestigious in the field of human–computer interaction and is one of the top-ranked conferences in computer science. It is hosted by ACM SIGCHI, the Special Interest Group on computer–human interaction. CHI has been held annually since 1982 and attracts thousands of international attendees. CHI 2020, which was originally planned to take place on April, was cancelled due to COVID-19, and CHI 2021 was held online as a virtual conference chaired by Yoshifumi Kitamura and Aaron Quigley. CHI 2021 “making waves, combining strengths” was originally scheduled to take place in Yokohama. History The CHI conference series started with the ''Human Factors in Computer Systems'' conference in Gaithersburg, Maryland, US in 1982, organized by Bill Curtis and Ben Shneiderman. During this meeting the formation of the ACM Special Interest Group on Computer–Huma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The American Statistician
''The American Statistician'' is a quarterly peer-reviewed scientific journal covering statistics published by Taylor & Francis on behalf of the American Statistical Association. It was established in 1947. The editor-in-chief is Daniel R. Jeske, a professor at the University of California, Riverside The University of California, Riverside (UCR or UC Riverside) is a public land-grant research university in Riverside, California. It is one of the ten campuses of the University of California system. The main campus sits on in a suburban distr .... External links * Taylor & Francis academic journals Statistics journals Publications established in 1947 English-language journals Quarterly journals 1947 establishments in the United States Academic journals associated with learned and professional societies of the United States {{math-journal-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Springer Science+Business Media
Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in Berlin, it expanded internationally in the 1960s, and through mergers in the 1990s and a sale to venture capitalists it fused with Wolters Kluwer and eventually became part of Springer Nature in 2015. Springer has major offices in Berlin, Heidelberg, Dordrecht, and New York City. History Julius Springer founded Springer-Verlag in Berlin in 1842 and his son Ferdinand Springer grew it from a small firm of 4 employees into Germany's then second largest academic publisher with 65 staff in 1872.Chronology ". Springer Science+Business Media. In 1964, Springer expanded its business internationally, o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
O'Reilly Media
O'Reilly Media (formerly O'Reilly & Associates) is an American learning company established by Tim O'Reilly that publishes books, produces tech conferences, and provides an online learning platform. Its distinctive brand features a woodcut of an animal on many of its book covers. Company Early days The company began in 1978 as a private consulting firm doing technical writing, based in the Cambridge, Massachusetts area. In 1984, it began to retain publishing rights on manuals created for Unix vendors. A few 70-page "Nutshell Handbooks" were well-received, but the focus remained on the consulting business until 1988. After a conference displaying O'Reilly's preliminary Xlib manuals attracted significant attention, the company began increasing production of manuals and books. The original cover art consisted of animal designs developed by Edie Freedman because she thought that Unix program names sounded like "weird animals". Global Network Navigator In 1993 O'Reilly Media creat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
High-leverage Point
In statistics and in particular in regression analysis, leverage is a measure of how far away the independent variable values of an observation are from those of the other observations. ''High-leverage points'', if any, are outliers with respect to the independent variables. That is, high-leverage points have no neighboring points in \mathbb^ space, where '''' is the number of independent variables in a regression model. This makes the fitted model likely to pass close to a high leverage observation. Hence high-leverage points have the potential to cause large changes in the parameter estimates when they are deleted i.e., to be influential points. Although an influential point will typically have high leverage, a high leverage point is not necessarily an influential point. The leverage is typically defined as the diagonal elements of the hat matrix. Definition and interpretations Consider the linear regression model _i = \boldsymbol_i^\boldsymbol+_i, i=1,\, 2,\ldots,\, n. That is, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Regression Line
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 t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coefficient Of Determination
In statistics, the coefficient of determination, denoted ''R''2 or ''r''2 and pronounced "R squared", is the proportion of the variation in the dependent variable that is predictable from the independent variable(s). It is a statistic used in the context of statistical models whose main purpose is either the prediction of future outcomes or the testing of hypotheses, on the basis of other related information. It provides a measure of how well observed outcomes are replicated by the model, based on the proportion of total variation of outcomes explained by the model. There are several definitions of ''R''2 that are only sometimes equivalent. One class of such cases includes that of simple linear regression where ''r''2 is used instead of ''R''2. When only an intercept is included, then ''r''2 is simply the square of the sample correlation coefficient (i.e., ''r'') between the observed outcomes and the observed predictor values. If additional regressors are included, ''R''2 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
