. The Biological bulletin. Biology; Zoology; Biology; Marine Biology. 40 L. R. McEDWARD AND K. H. MORGAN of squares (r2 in linear regression and an analogous measure in nonlinear regression; hereafter referred to as fit). The second criteria are the confidence intervals around the esti- mated regression parameters. All regression calculations were carried out using Mathematical (version 4; Wolfram Research. Inc.) by means of the Regress (LinearRegression) or the NonlinearRegress (NonlinearFit) function in the Sta- tistics standard add-on package. Regression analyses pro- vided parameters of th
. The Biological bulletin. Biology; Zoology; Biology; Marine Biology. 40 L. R. McEDWARD AND K. H. MORGAN of squares (r2 in linear regression and an analogous measure in nonlinear regression; hereafter referred to as fit). The second criteria are the confidence intervals around the esti- mated regression parameters. All regression calculations were carried out using Mathematical (version 4; Wolfram Research. Inc.) by means of the Regress (LinearRegression) or the NonlinearRegress (NonlinearFit) function in the Sta- tistics standard add-on package. Regression analyses pro- vided parameters of the best-fit model, 95% confidence intervals around the fitted parameters, and the regression ANOVA. Identification of influential iliitu Influential data are those values that exert much greater than average influence on the estimation of the regression parameters. The existence of such data can be problematic because then the best-fit regression is based on a small, possibly atypical, subset of the data, and does not reflect any overall trend. Whether such data are outliers that reduce our ability to detect and describe pattern or are particularly information-rich data essential to the detection and descrip- tion of pattern is a biological, not a statistical, question. We used a regression diagnostic called the Hat Diagonal to identify strongly influential data (Belsley et«/., 1980). Once identified, strongly influential data were eliminated from the data set, and the regressions were recalculated to evaluate the effect of these data on the estimation of the scaling relationship and model fit. Evaluation of predictive power After quantifying the scaling relationship between egg volume and energy content, we evaluated the statistical significance of that relationship. In addition, we evaluated the predictive power of the relationship, using the approach described by McEdward and Carson (1987). If a regression is statistically significant, then some of the variance in egg energy
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