Beaver, Lambert and Morse (1980) employ a regression of percentage change in prices on percentage change in earnings in which data are grouped by the dependent variable. Reverse regression offers a more intuitive and direct way to assess the information content of security prices, the objective of Beaver et al. While grouping is asymptotically equivalent, reverse regression is a more efficient way of examining the incremental explanatory power of lagged values of percentage change in price with respect to accounting earnings.

Surya N. Janakiraman, Richard A. Lambert, David F. Larcker, An Empirical Investigation of the Relative Performance Evaluation Hypothesis, Journal of Accounting Research, Vol. 30, No. 1 (Spring, 1992), pp. 53-69

ABSTRACT: This paper provides an analysis of the association between the accounting gain produced by an equity-for-debt swap and executive compensation, Our results suggest that the executives of firms completing a swap transaction experience an Increase in cash compensation (salary plus bonus). The increase is largest both in absolute magnitude and in statistical significance for firms whose compensation plans are more "accounting-oriented" (i.e., firms whose executives would be expected to experience the greatest Increase in compensation under the hypothesis that firm's compensation plan is not adjusted for the accounting gain produced by the swap), We also find that, on average, the value of the executives' personal equity holdings decreases in the period surrounding the announcement of the swap. The magnitude of this decrease is, on average, comparable in size to the increase in their compensation. However, there is some weak evidence that executives of firms whose compensation plans are more "accounting-oriented" experience a statistically significant increase in their total wealth (i.e., the sum of excess compensation and the value of personal equity holdings) as a result of the swap transaction.