Morgenthaler, S. The bias of least squares polynomial interpolants. (English) Zbl 0743.62055 Metrika 39, No. 1, 45-55 (1992). Summary: The fitting of a straight line — or more generally of a low degree polynomial — to a point cloud in the plane is a commonly performed statistical technique. This paper discusses the bias of such a procedure and in particular generalizes the well-known remainder formula for polynomial interpolation to the regression setting. Designs minimizing the maximum bias are discussed as well. MSC: 62J02 General nonlinear regression 62K05 Optimal statistical designs 65D05 Numerical interpolation 65D10 Numerical smoothing, curve fitting Keywords:polynomial regression; biased response curves; bias of least squares interpolating polynomials; fitting of a straight line; low degree polynomial; remainder formula; polynomial interpolation; maximum bias PDFBibTeX XMLCite \textit{S. Morgenthaler}, Metrika 39, No. 1, 45--55 (1992; Zbl 0743.62055) Full Text: DOI EuDML References: [1] Box GEP, Draper NR (1959) A Basis for the Selection of a Response Surface Design. J Amer Statist Assoc 54:662–654 · Zbl 0116.36804 · doi:10.2307/2282542 [2] Dunford N, Schwartz JT (1988) Linear Operators, part I, General Theory. Wiley Interscience, New York · Zbl 0635.47001 [3] Hoel PG, Levine A (1964) Optimal Spacing and Weighting in Polynomial Prediction. Ann Math Statist 35:1553–1560 · Zbl 0127.10301 · doi:10.1214/aoms/1177700379 [4] Huber PJ (1975) Robustness and Design. In: Srivastava JN (ed) A Survey of Statistical Design and Linear Models. North-Holland, Amsterdam, pp 287–301 [5] Marcus MB, Sacks J (1977) Robust Designs for Regression Problems. In: Gupta SS, Moore DS (eds) Statistical Decision Theory and Related Topics, vol II. Academic Press, New York, pp 245–268 · Zbl 0422.62067 [6] Stigler, SM (1971) Optimal Experimental Design for Polynomial Regression. J Amer Statist Assoc 66:311–318 · Zbl 0217.51701 · doi:10.2307/2283928 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.