672 HUMAN RIGHTS QUARTERLY Vol. 39 to what they owe, quantitative social science methods have much to offer. Towards the more advanced end of the methods spectrum sits multivariate regression analysis. Regression analysis of the multivariate kind can be used to establish the direction, strength, and significance of the relationship between an outcome variable and two or more explanatory variables.60 For instance, it can provide interesting insight into the extent to which national income, the availability of health professionals, geographical, and other “random”61 factors individually and/or collectively explain particular social outcomes. In other words, it can be used to measure the extent to which maximum available resources explain social welfare attainment. Of course, a measure of the degree to which social welfare attainment is determined by maximum available resources is valuable in and of itself. But, in the words of Nobel Laureate in economics, Paul Samuelson, “[a]lways look back. You may learn something from your residuals.”62 In estimating a relationship such as that described above, it is unlikely that resources will explain all of the variation in attainment, i.e. very few countries will have social welfare attainment equal to the predicted value.63 The residual that is produced by the regression provides information with respect to the degree to which the actual level of attainment deviates from the predicted value. The residual is the “unexplained effect.” Residual analysis is by no means new. Its application has a long tradition in the social sciences, from Robert Solow’s treatment of the residual in explaining economic growth through technological innovation,64 to Raymond Duvall and Michal Shamir’s propensity of repression indicator developed through regressing sanctions on domestic violence.65 Existing efforts that attempt to measure some form of performance with respect to human rights standards have not been blind to the virtues of residual analysis either. For example, David Cingranelli and David Richards use the regression residual to estimate a government’s efforts 60. Alan O. Sykes, An Introduction to Regression Analysis, (Coase-Sandor Inst. L. Econ., Working Paper No. 20, 1993), available at http://chicagounbound.uchicago.edu/ law_and_economics/51/. 61. Random in the statistical sense where values are statistically independent of other values and are therefore unpredictable, rather than implying true randomness; that is, objective unpredictability. 62. David L. Cingranelli & David L. Richards, Measuring Government Effort to Respect Economic and Social Human Rights: A Peer Benchmark, in Economic Rights: Conceptual, Measurement, and Policy Issues 214, 221 (Shareen Hertel & Lanse Minkler eds., 2007) (quoting Paul Samuelson, Nobel Laureate in Economics). 63. If the attempt is to explain something as complex as the factors that determine social outcomes, statistical error and unexplained variance is highly likely. 64. Robert M. Solow, A Contribution to the Theory of Economic Growth, 70 Q. J. Econ. 65 (1956). 65. Raymond D. Duvall & Michal Shamir, Indicators From Errors: Cross-National Time-Serial Measures of the Repressive Disposition of Government, in Indicator Systems for Political, Economic, and Social Analysis 155 (Charles Lewis Taylor ed., 1980).