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

called the regression errors and regression residuals and where they lead to the concept of studentized residuals. In econometrics, "errors" are also called...

mortgage Residual (statistics) Studentized residual Residual time, in the theory of renewal processes Residual (numerical analysis) Minimal residual method...

studentized means that the variable's scale was adjusted by dividing by an estimate of a population standard deviation (see also studentized residual)...

population of all possible observations, the residuals should belong to a Student's t-distribution. Studentized residuals are useful in making a statistical test...

different residuals by different estimates for the error, yielding what are called studentized residuals. Mathematics portal F-test t2-statistic Student's T-Distribution...

the test in 1950), also known as the maximum normalized residual test or extreme studentized deviate test, is a test used to detect outliers in a univariate...

{\displaystyle 0\leq h_{ii}\leq 1} ) and the square of the internally Studentized residual ( 0 ≤ t i 2 {\displaystyle 0\leq t_{i}^{2}} ), as follows: D i =...

context of resampling and, in particular, bootstrapping. Studentized range Studentized residual Pivotal quantity Dodge, Y. (2003) The Oxford Dictionary...

distance Normalization (statistics) Omega ratio Standard normal deviate Studentized residual Mulders, Martijn; Zanderighi, Giulia, eds. (2017). 2015 European...

the goodness of fit of the regression, analyzing whether the regression residuals are random, and checking whether the model's predictive performance deteriorates...

Students Studentization, the process of adjusting a statistic for an estimate of its standard deviation Studentized range Studentized residual Student's t-test...

colinearity (rank condition), consistent for the variance estimate of the residuals when regressors have finite fourth moments and—by the Gauss–Markov theorem—optimal...

parameter estimation method in which the sum of the squares of the residuals (a residual being the difference between an observed value and the fitted value...

averaging of a set of data, 50 years before Tobias Mayer, but summing the residuals to zero he forced the regression line to pass through the average point...

"noise" or simply "error" (will be contrasted with "residual" later in the article; see errors and residuals in statistics). Note that to include a constant...

types of normalizations in statistics – nondimensional ratios of errors, residuals, means and standard deviations, which are hence scale invariant – some...

Regression validation Mean and predicted response Errors and residuals Goodness of fit Studentized residual Gauss–Markov theorem Mathematics portal v t e...

\mathbf {x} } . Ordinary least squares seeks to minimize the sum of squared residuals, which can be compactly written as ‖ A x − b ‖ 2 2 , {\displaystyle \left\|A\mathbf...

Regression validation Mean and predicted response Errors and residuals Goodness of fit Studentized residual Gauss–Markov theorem Mathematics portal v t e...

mixed models may not, however, be the only solution. LMM's have a constant-residual variance assumption that is sometimes violated when accounting for deeply...

used in statistical hypothesis testing, e.g. to test for normality of residuals, to test whether two samples are drawn from identical distributions (see...

for standardizing or the sample standard deviation for studentizing (e.g., Studentized residual). Another approach to nondimensionalization focuses on...

Regression validation Mean and predicted response Errors and residuals Goodness of fit Studentized residual Gauss–Markov theorem Mathematics portal v t e...

for the point. DFFITS also equals the products of the externally Studentized residual ( t i ( i ) {\displaystyle t_{i(i)}} ) and the leverage factor (...

Multivariate Student distribution Standard normal table (Z-distribution table) t statistic Tau distribution, for internally studentized residuals Wilks' lambda...

Gentle, James (2007). "6.8.1 Solutions that Minimize Other Norms of the Residuals". Matrix algebra. Springer Texts in Statistics. New York: Springer. doi:10...

Regression validation Mean and predicted response Errors and residuals Goodness of fit Studentized residual Gauss–Markov theorem Mathematics portal v t e...

Influential observation Random sample consensus Robust regression Studentized residual Winsorizing Grubbs, F. E. (February 1969). "Procedures for detecting...

Regression validation Mean and predicted response Errors and residuals Goodness of fit Studentized residual Gauss–Markov theorem Mathematics portal v t e...