x_{i}\right)^{2}.} The predicted response distribution is the predicted distribution of the residuals at the given point xd. So the variance is given by Var...

error of the weighted mean Sample mean and sample covariance Standard error of the median Variance Variance of the mean and predicted responses Altman...

method and is used in the sequel. A prediction interval [ℓ,u] for a future observation X in a normal distribution N(μ,σ2) with known mean and variance may...

Analysis of variance (ANOVA) is a collection of statistical models and their associated estimation procedures (such as the "variation" among and between...

variance. No correction is necessary if the population mean is known. It is remarkable that the sum of squares of the residuals and the sample mean can...

regression and least squares fitting to variance stabilized responses, have been developed. Ordinary linear regression predicts the expected value of a given...

variable whose mean is large will typically have a greater variance than one whose mean is small. For example, a person whose income is predicted to be $100...

the variances of two samples or the ratio of variances between multiple samples. The test statistic, random variable F, is used to determine if the tested...

efficiency of the sample median, measured as the ratio of the variance of the mean to the variance of the median, depends on the sample size and on the underlying...

time from the sample set. From this new set of replicates of the statistic, an estimate for the bias and an estimate for the variance of the statistic...

In statistics, the variance inflation factor (VIF) is the ratio (quotient) of the variance of a parameter estimate when fitting a full model that includes...

The Allan variance (AVAR), also known as two-sample variance, is a measure of frequency stability in clocks, oscillators and amplifiers. It is named after...

statistics, the variance function is a smooth function that depicts the variance of a random quantity as a function of its mean. The variance function is...

estimate of the population variance around the mean. dfres is given in terms of the sample size n and the number of variables p in the model, dfres = n − p...

homoscedastic and serially uncorrelated. Under these conditions, the method of OLS provides minimum-variance mean-unbiased estimation when the errors have...

Genetic variance is a concept outlined by the English biologist and statistician Ronald Fisher in his fundamental theorem of natural selection. In his...

different expectation value. Each Ui has an expectation value of 0 and a variance of σ2. Expectation of Yi Proof: E [ Y i ] = E [ α + β x i + U i ] = α + β x...

d.) random variables with expectation μ and variance σ2. If the sample mean and uncorrected sample variance are defined as X ¯ = 1 n ∑ i = 1 n X i S...

generalization of Poisson regression because it loosens the highly restrictive assumption that the variance is equal to the mean made by the Poisson model. The traditional...

the unobserved latent variable. That is, y[i] is the vector of observed responses predicted by the unobserved latent variable ξ {\displaystyle \xi }...

controlling for other predictors, making it analogous to the r2. Eta-squared is a biased estimator of the variance explained by the model in the population (it...

regression slopes Square root of the ratio of two variances Mean cross-product of standardized variables Function of the angle between two standardized...

function and allow the magnitude of the variance of each measurement to be a function of its predicted value. The logarithm transformation and square root...

model, also called a variance components model, is a statistical model where the model parameters are random variables. It is a kind of hierarchical linear...

matrix could also be used. When the value being predicted is continuously distributed, the mean squared error, root mean squared error or median absolute...

task-relevant mental operations. Behavioral responses are typically button presses, but eye movements, vocal responses, and other observable behaviors are often...

} If the data points X i {\displaystyle X_{i}} are normally distributed with mean 0 and variance σ 2 {\displaystyle \sigma ^{2}} , then the residual...

optimal in the sense that in a linear model where the errors have a mean of zero, are uncorrelated, normally distributed, and have equal variances, the best...

{\displaystyle (i,m)} th unobserved stochastic error term with mean zero and finite variance. In matrix notation X − M = L F + ε {\displaystyle X-\mathrm...

sampling variance within the class of linear unbiased estimators, if the errors in the linear regression model are uncorrelated, have equal variances and expectation...