singular models; optimal design; correlated observations
We discuss, partly on examples, several intuitively unexpected results in a standard linear regression model. We demonstrate that direct observations of the regression curve at a given point can not be substituted by observations at two very close neighboring points. On the opposite, we show that observations at two distant design points improve the variance of the estimator. In an experiment with correlated observations we show somewhat unexpected conditions under which a design point gives no or very little information about the estimated parameters, and so can be excluded from the design. For completeness we repeat briefly known conditions under which a design point is sensitive to the presence of outliers.
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