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...

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...

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

{\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 =...

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

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

"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...

\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...

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

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

the residual points had some sort of a shape and were not randomly fluctuating, a linear model would not be appropriate. For example, if the residual plot...

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...

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

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

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

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

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

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...

linear 2. Normality of residuals: Residuals should follow a normal distribution 3. Homoscedasticity: Constant variance of residuals across predicted values...

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

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

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

2 {\displaystyle S=\sum _{i=1}^{m}r_{i}^{2}} is minimized, where the residuals (in-sample prediction errors) ri are given by r i = y i − f ( x i , β...

It is used when there is a non-zero amount of correlation between the residuals in the regression model. GLS is employed to improve statistical efficiency...

5 {\displaystyle \tau >0.5} ), we penalize the positive residuals more than negative residuals, and vice versa, and the loss is unsymmetric. However, for...

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