Compare and explain “random error of a regression” with “residuals of regression.”

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Compare and explain “random error of a regression” with“residuals of regression.”

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In statistics and optimization errors and residualsare 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 The error or disturbance of an observed value is the deviation of the observed value from the unobservable true value of a quantity of interest for example a population mean and the residual of an observed value is the difference between the observed value and the estimated value of the quantity of interest for example a sample mean The distinction is most important in regression analysis where the concepts are sometimes called the regression errors and regression residuals and where they lead to the concept of studentized residuals Suppose there is a series of observations from a univariate distribution and we want to estimate the mean of that distribution the socalled location model In this case the errors are the deviations of the observations from the population mean while the residuals are the deviations of the observations from the sample mean A statistical error or disturbance is the amount by which an observation differs from its expected value the latter being based on the whole population from which See Answer

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