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The data sets in the Anscombe's quartet are designed to have approximately the same linear regression line (as well as nearly identical means, standard deviations, and correlations) but are graphically very different. This illustrates the pitfalls of relying solely on a fitted model to understand the relationship between variables.
A drawback of polynomial bases is that the basis functions are "non-local", meaning that the fitted value of y at a given value x = x 0 depends strongly on data values with x far from x 0. [9] In modern statistics, polynomial basis-functions are used along with new basis functions, such as splines, radial basis functions, and wavelets. These ...
Benford's law, which describes the frequency of the first digit of many naturally occurring data. The ideal and robust soliton distributions. Zipf's law or the Zipf distribution. A discrete power-law distribution, the most famous example of which is the description of the frequency of words in the English language.
This data set gives average masses for women as a function of their height in a sample of American women of age 30–39. Although the OLS article argues that it would be more appropriate to run a quadratic regression for this data, the simple linear regression model is applied here instead.
All four sets have identical statistical parameters, but the graphs show them to be considerably different. Anscombe's quartet comprises four datasets 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.
The primary application of linear least squares is in data fitting. Given a set of m data points ,, …,, consisting of experimentally measured values taken at m values ,, …, of an independent variable (may be scalar or vector quantities), and given a model function = (,), with = (,, …,), it is desired to find the parameters such that the ...
For example, if the functional form of the model does not match the data, R 2 can be high despite a poor model fit. Anscombe's quartet consists of four example data sets with similarly high R 2 values, but data that sometimes clearly does not fit the regression line. Instead, the data sets include outliers, high-leverage points, or non-linearities.
Social statistics data (3 C, 30 P) Sports records and statistics (41 C, ... Pages in category "Statistical data sets" The following 32 pages are in this category, out ...