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If the data points are normally distributed with mean 0 and variance , then the residual sum of squares has a scaled chi-squared distribution (scaled by the factor ), with n − 1 degrees of freedom. The degrees-of-freedom, here a parameter of the distribution, can still be interpreted as the dimension of an underlying vector subspace.
Previously when assessing a dataset before running a linear regression, the possibility of outliers would be assessed using histograms and scatterplots. Both methods of assessing data points were subjective and there was little way of knowing how much leverage each potential outlier had on the results data.
Computations or tables of the Wilks' distribution for higher dimensions are not readily available and one usually resorts to approximations. One approximation is attributed to M. S. Bartlett and works for large m [2] allows Wilks' lambda to be approximated with a chi-squared distribution
Exploratory analysis of Bayesian models is an adaptation or extension of the exploratory data analysis approach to the needs and peculiarities of Bayesian modeling. In the words of Persi Diaconis: [17] Exploratory data analysis seeks to reveal structure, or simple descriptions in data. We look at numbers or graphs and try to find patterns.
This distribution for a = 0, b = 1 and c = 0.5—the mode (i.e., the peak) is exactly in the middle of the interval—corresponds to the distribution of the mean of two standard uniform variables, that is, the distribution of X = (X 1 + X 2) / 2, where X 1, X 2 are two independent random variables with standard uniform distribution in [0, 1]. [1]
Shoelace scheme for determining the area of a polygon with point coordinates (,),..., (,). The shoelace formula, also known as Gauss's area formula and the surveyor's formula, [1] is a mathematical algorithm to determine the area of a simple polygon whose vertices are described by their Cartesian coordinates in the plane. [2]
The origin of the phrase "Lies, damned lies, and statistics" is unclear, but Mark Twain attributed it to Benjamin Disraeli [1] "Lies, damned lies, and statistics" is a phrase describing the persuasive power of statistics to bolster weak arguments, "one of the best, and best-known" critiques of applied statistics. [2]
Decimal degrees (DD) is a notation for expressing latitude and longitude geographic coordinates as decimal fractions of a degree.DD are used in many geographic information systems (GIS), web mapping applications such as OpenStreetMap, and GPS devices.