Interpretation of Regression Output: Diagnostics, Graphs and the Bottom Line

A standard approach in presenting the results of a statistical analysis of regression data in scientific journals is to focus on the question of statistical significance of regression coefficients. The reporting of p-values in conjunction with a description of the various positive and negative associations between the response and the factors in question ensues. The real question of interest beyond these initial assessments ought to be, “how well does the treatment work?” The point of view taken here will be that this standard presentation, while important, constitutes only a first order approximation to a complete analysis, and that the bottom line ought to involve the quantification of regression effects on the scale of observable quantities. This will mainly be accomplished graphically. It is also emphasized that diagnostic assessment of the compatibility of the data to the model should be based on similar considerations.