Data Uncertainties and Least Squares Regression

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.