Abstract
Let us consider a natural phenomenon that can be characterized by a two- dimensional variable Z = (X, Y) and let us assume that the empirical sample points (Z 1 , Z 2 ,…, Z N ) lie close to the line described by a linear relation Ŷ = AX. In order to estimate the variable Y from a given value of X we can apply the conditional average estimator defined in the previous chapter or we can directly start with the linear relation and by minimizing the mean square error determine the coefficient A. The resulting expression A = cov(XY)/var(X), is well-known from the literature on linear statistical estimation. It can then be utilized to estimate Y from given X by the linear regression equation Ŷ = X cov(XY)/var(X).
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Grabec, I., Sachse, W. (1997). Linear Modeling and Invariances. In: Synergetics of Measurement, Prediction and Control. Springer Series in Synergetics, vol 68. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60336-5_10
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DOI: https://doi.org/10.1007/978-3-642-60336-5_10
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