Garthwaite, P. H.
Fractile assessments for a linear regression model: an experimental study.
Organizational Behavior and Human Decision Processes, 43(2) pp. 188–206.
Subjects were questioned about four regression models in which the dependent variable (y) was linearly related to a single independent variable (x). Drawing graphs to help quantify their opinions, subjects assessed 0.25, 0.50, and 0.75 fractiles of their distributions for (a) the expected value of y at various x-values and (b) the expected change in y as x varied. Their opinions were generally underconfident with more than 60% of the interquartile ranges containing correct values. For task (a), proportions containing correct values were greater when x was toward the center of its range and for (b) they were greater when x varied over only a small part of its range. Both symmetric and asymmetric distributions were fitted to subjects' assessments and although assessments were sometimes markedly skew, a scoring rule judged the symmetric distributions to be slightly the more accurate.
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