Accounting for bias in regression coefficients with example from feed efficiency

Estimates of regression coefficients are biased if the independent (or x) variables contain errors (for example, measurement errors). Equations are derived for the amount of bias in bivariate regression where one independent variable contains significant error, but errors in the other are negligible. Results are tabulated for differing amounts of error and a range of correlations (from 0.1 to 0.9) between the two independent variables. The process of estimating residual feed intake (RFI) is used to illustrate biases present in real-life data. RFI is defined as the amount of feed eaten by an animal less what would be expected from the animal's metabolic weight and weight gain. Measurement errors of metabolic weight, especially if calculated from the mean of several weighings, are relatively small. In contrast, errors in weight gain may be substantial. Regression coefficients from fitting the RFI equation using two different estimates of weight gain are compared with equations derived from genotypic regression and feed standards tables. The unadjusted coefficients differ substantially, but are shown to be much more consistent after adjusting for bias using equations derived in this paper.