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Data Uncertainties and Least Squares Regression

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  • S. D. Hodges
  • P. G. Moore

Abstract

Least squares regression analysis makes the assumption that the independent variables can be measured without error. This paper examines the effect of errors in these variables and suggests some practical guidelines for the user of least squares. Related empirical and theoretical work is reviewed and simple methods are derived for assessing the sensitivity of the regression coefficients to each observation, and for calculating the approximate amount of bias in the estimated coefficients. The implications for forecasting are also examined.

Suggested Citation

  • S. D. Hodges & P. G. Moore, 1972. "Data Uncertainties and Least Squares Regression," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 21(2), pages 185-195, June.
    • Handle: RePEc:bla:jorssc:v:21:y:1972:i:2:p:185-195
    DOI: 10.2307/2346491
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    Cited by:

    1. Bekker, Paul & Kapteyn, Arie & Wansbeek, Tom, 1987. "Consistent Sets of Estimates for Regressions with Correlated or Uncorrelated Measurement Errors in Arbitrary Subsets of All Variables," Econometrica, Econometric Society, vol. 55(5), pages 1223-1230, September.
    2. Mengli Zhang & Yang Bai, 2021. "On the use of repeated measurement errors in linear regression models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(5), pages 779-803, July.
    3. Bekker, P. & Kapteyn, A.J. & Wansbeek, T.J., 1984. "Measurement error and endogeneity in regression : Bounds for ML and IV-estimates," Other publications TiSEM 80b5811e-c9b0-4e05-b5fe-0, Tilburg University, School of Economics and Management.
    4. Jay Magidson, 1977. "Toward a Causal Model Approach for Adjusting for Preexisting Differences in the Nonequivalent Control Group Situation," Evaluation Review, , vol. 1(3), pages 399-420, August.

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