Surface area of general ellipsoid shaped food materials by simplified regression equation method

Surface area of food materials resembling geometrical general ellipsoids can be evaluated theoretically using numerical techniques. The existing general ellipsoid surface area numerical model of triangular elements that was used to develop the ready reckoner table of surface area, was employed to develop individual linear regression equations for different thickness/length curves and an overall equation to cover the entire range of general ellipsoidal objects. As the thickness/length curves exhibited a linear nature, simple linear regression was carried out and the fitted individual equation produced very high correlation coefficients that were significant at the 99% level. Statistical analysis revealed that the null hypothesis on intercepts and slopes of the individual equations were rejected, showing the existence of a definite intercept and slope on every fitted thickness/length. The obtained smaller values of the confidence intervals at the 99% level of significance depicted the accuracy of the developed regression constants. Of the developed regression constants, the intercepts followed a clear linear trend whereas for the slopes a second-order polynomial was fitted, and from the obtained combined regression constants the overall regression equation was developed. In the error analysis, based on the absolute average error, the performance of the individual equations was better than the overall equation. The error produced by the developed equations reduced when the thickness/length and width/length increased. For a practical range of ellipsoidal objects having a thickness/length range greater than 0.1, the absolute average error produced would be less than 0.8652% for the individual equation and less than 1.7264% for the overall equation. The following overall equation with only five regression constants would be useful in finding the surface area and could completely replace the model and the ready reckoner table: A(s) = pi[- 1.02274828 x 10(-2)L(2) + 4.92988817 x 10(-2)LW + 3.43560219 x 10(-1)LT -5.29422959 x 10(-2)WT + 2.35999474 x 10(-1)WT(2)/L] (R = 0.999575). (C) 2000 Elsevier Science Ltd. All rights reserved.