Re-examination of the coefficient of determination (r2) using road materials engineering case studies

The analysis of scientific data is integral to materials engineering and science. The correlation between measured variables is often quantified by estimating the coefficient of determination or the r2 value. This is the recognised procedure for determining linear relationships. The authors review the derivation of the r2 value and derive an associated quantity, termed the relative deviation (RD), which is the ratio of the root mean square of the deviations about the fitted line to the root mean square of the deviations about the y bar line expressed as a percentage. The relative deviation has an advantage over the coefficient of determination in that it has greater numerical sensitivity to changes in the spread of data about the fitted line, especially when the scatter is small. In addition, the relative deviation is able to define, in percentage terms, the reduction in scatter when different independent variables are correlated with a common dependent variable. Four case studies in the materials field (aggregate crushing value, Atterberg limits, permeability and creep of asphalt) from work carried out at the Queensland Main Roads Department are presented to show the use of the new parameter RD.

A genetically mediated bias in decision making driven by failure of amygdala control.

Genetic variation at the serotonin transporter-linked polymorphic region (5-HTTLPR) is associated with altered amygdala reactivity and lack of prefrontal regulatory control. Similar regions mediate decision-making biases driven by contextual cues and ambiguity, for example the "framing effect." We hypothesized that individuals hemozygous for the short (s) allele at the 5-HTTLPR would be more susceptible to framing. Participants, selected as homozygous for either the long (la) or s allele, performed a decision-making task where they made choices between receiving an amount of money for certain and taking a gamble. A strong bias was evident toward choosing the certain option when the option was phrased in terms of gains and toward gambling when the decision was phrased in terms of losses (the frame effect). Critically, this bias was significantly greater in the ss group compared with the lala group. In simultaneously acquired functional magnetic resonance imaging data, the ss group showed greater amygdala during choices made in accord, compared with those made counter to the frame, an effect not seen in the lala group. These differences were also mirrored by differences in anterior cingulate-amygdala coupling between the genotype groups during decision making. Specifically, lala participants showed increased coupling during choices made counter to, relative to those made in accord with, the frame, with no such effect evident in ss participants. These data suggest that genetically mediated differences in prefrontal-amygdala interactions underpin interindividual differences in economic decision making.