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# Projection matrix

In statistics, the projection matrix \mathbf, sometimes also called the influence matrix or hat matrix \mathbf, maps the vector of response values (dependent variable values) to the vector of fitted values (or predicted values). [1]

## Cambridge University Press

Cambridge University Press (CUP) is the publishing business of the University of Cambridge.

## Christmas

Christmas is an annual festival commemorating the birth of Jesus Christ,Martindale, Cyril Charles.

## Christmas and holiday season

The Christmas season, also called the festive season, or the holiday season (mainly in the U.S. and Canada; often simply called the holidays),, is an annually recurring period recognized in many Western and Western-influenced countries that is generally considered to run from late November to early January.

## Christmas Eve

Christmas Eve is the evening or entire day before Christmas Day, the festival commemorating the birth of Jesus.

Christmas traditions vary from country to country.

## Circumflex

The circumflex is a diacritic in the Latin, Greek and Cyrillic scripts that is used in the written forms of many languages and in various romanization and transcription schemes.

## Cook's distance

In statistics, Cook's distance or Cook's D is a commonly used estimate of the influence of a data point when performing a least-squares regression analysis.

## Covariance

In probability theory and statistics, covariance is a measure of the joint variability of two random variables.

## Covariance matrix

In probability theory and statistics, a covariance matrix (also known as dispersion matrix or variance–covariance matrix) is a matrix whose element in the i, j position is the covariance between the i-th and j-th elements of a random vector.

## David A. Freedman

David Amiel Freedman (5 March 1938 – 17 October 2008) was Professor of Statistics at the University of California, Berkeley.

## Dependent and independent variables

In mathematical modeling, statistical modeling and experimental sciences, the values of dependent variables depend on the values of independent variables.

## Design matrix

In statistics, a design matrix, also known as model matrix or regressor matrix, is a matrix of values of explanatory variables of a set of objects, often denoted by X. Each row represents an individual object, with the successive columns corresponding to the variables and their specific values for that object.

## Eigenvalues and eigenvectors

In linear algebra, an eigenvector or characteristic vector of a linear transformation is a non-zero vector that changes by only a scalar factor when that linear transformation is applied to it.

## Errors and residuals

In statistics and optimization, errors and residuals are two closely related and easily confused measures of the deviation of an observed value of an element of a statistical sample from its "theoretical value".

## Fixed effects model

In statistics, a fixed effects model is a statistical model in which the model parameters are fixed or non-random quantities.

## Idempotent matrix

In linear algebra, an idempotent matrix is a matrix which, when multiplied by itself, yields itself.

## Identity matrix

In linear algebra, the identity matrix, or sometimes ambiguously called a unit matrix, of size n is the n × n square matrix with ones on the main diagonal and zeros elsewhere.

## Independent and identically distributed random variables

In probability theory and statistics, a sequence or other collection of random variables is independent and identically distributed (i.i.d. or iid or IID) if each random variable has the same probability distribution as the others and all are mutually independent.

## Influential observation

In statistics, an influential observation is an observation for a statistical calculation whose deletion from the dataset would noticeably change the result of the calculation.

## Kernel regression

Kernel regression is a non-parametric technique in statistics to estimate the conditional expectation of a random variable.

## Leverage (statistics)

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.

## Linear algebra

Linear algebra is the branch of mathematics concerning linear equations such as linear functions such as and their representations through matrices and vector spaces.

## Linear filter

Linear filters process time-varying input signals to produce output signals, subject to the constraint of linearity.

## Linear least squares (mathematics)

In statistics and mathematics, linear least squares is an approach to fitting a mathematical or statistical model to data in cases where the idealized value provided by the model for any data point is expressed linearly in terms of the unknown parameters of the model.

## Linear model

In statistics, the term linear model is used in different ways according to the context.

## Local regression

LOESS and LOWESS (locally weighted scatterplot smoothing) are two strongly related non-parametric regression methods that combine multiple regression models in a ''k''-nearest-neighbor-based meta-model.

## Mathematical model

A mathematical model is a description of a system using mathematical concepts and language.

## Mean and predicted response

In linear regression, mean response and predicted response are values of the dependent variable calculated from the regression parameters and a given value of the independent variable.

## New Year

New Year is the time or day at which a new calendar year begins and the calendar's year count increments by one.

## New Year's Day

New Year's Day, also called simply New Year's or New Year, is observed on January 1, the first day of the year on the modern Gregorian calendar as well as the Julian calendar.

## New Year's Eve

In the Gregorian calendar, New Year's Eve (also known as Old Year's Day or Saint Sylvester's Day in many countries), the last day of the year, is on 31 December which is the seventh day of Christmastide.

## Projection (linear algebra)

In linear algebra and functional analysis, a projection is a linear transformation P from a vector space to itself such that.

## Propagation of uncertainty

In statistics, propagation of uncertainty (or propagation of error) is the effect of variables' uncertainties (or errors, more specifically random errors) on the uncertainty of a function based on them.

## Rank (linear algebra)

In linear algebra, the rank of a matrix A is the dimension of the vector space generated (or spanned) by its columns.

## Robust statistics

Robust statistics are statistics with good performance for data drawn from a wide range of probability distributions, especially for distributions that are not normal.

## Row and column spaces

In linear algebra, the column space (also called the range or '''image''') of a matrix A is the span (set of all possible linear combinations) of its column vectors.

## Smoothing spline

Smoothing splines are function estimates, \hat f(x), obtained from a set of noisy observations y_i of the target f(x_i), in order to balance a measure of goodness of fit of \hat f(x_i) to y_i with a derivative based measure of the smoothness of \hat f(x).

## Sparse matrix

In numerical analysis and computer science, a sparse matrix or sparse array is a matrix in which most of the elements are zero.

## Statistics

Statistics is a branch of mathematics dealing with the collection, analysis, interpretation, presentation, and organization of data.

## Studentized residual

In statistics, a studentized residual is the quotient resulting from the division of a residual by an estimate of its standard deviation.

## Symmetric matrix

In linear algebra, a symmetric matrix is a square matrix that is equal to its transpose.

## 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.

## Trace (linear algebra)

In linear algebra, the trace of an n-by-n square matrix A is defined to be the sum of the elements on the main diagonal (the diagonal from the upper left to the lower right) of A, i.e., where aii denotes the entry on the ith row and ith column of A. The trace of a matrix is the sum of the (complex) eigenvalues, and it is invariant with respect to a change of basis.

## Variance

In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its mean.

## 2018

2018 has been designated as the third International Year of the Reef by the International Coral Reef Initiative.

## 2019

2019 (MMXIX) will be a common year starting on Tuesday of the Gregorian calendar, the 2019th year of the Common Era (CE) and Anno Domini (AD) designations, the 19th year of the 3rd millennium, the 19th year of the 21st century, and the 10th and last year of the 2010s decade.

## References

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