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Multiple Regression and Response Surface Analyses of the Effects of Dietary Protein, Fat and Carbohydrate on the Body Protein and Fat Gains in Growing Chicks

Department of Animal Science, Faculty of Agriculture, Tohoku University, Sendai, 980, Japan

Multiple regression analysis of biological response as a function of three factors having a common denominator, on a triangular graph, was investigated for qualitative and quantitative evaluation of nutritional phenomena. As an example of its application, 33 groups of White Leghorn male chicks were isocalorically force-fed purified diets consisting of 5–47% protein, 6–86% fat and 2–89% carbohydrate on a metabolizable energy basis for 10 days, and prediction equations for the body weight gain, protein gain and fat gain were formulated by multiple regression techniques. Perspective views, contour maps and cross-sectional views of the response surfaces constructed from the equations revealed 1) that both body weight gain and protein gain increased with an increase in the metabolizable energy of dietary protein, and were not much affected by the calorie ratio of dietary carbohydrate to fat, showing a convex configuration of the response surfaces; 2) that fat gain decreased and appeared to become more dependent on the calorie ratio of dietary carbohydrate to fat with an increase in the metabolizable energy of dietary protein, giving a combined configuration of convex and concave surfaces, and 3) that dietary protein, fat and carbohydrate were replaceable with one another in the range of 40–50% protein metabolizable energy with respect to body weight gain and protein gain, while replaceability of fat and carbohydrate with each other seemed to decrease with an increase in protein metabolizable energy with respect to fat gain. These results demonstrated that the proposed method is a valuable tool in nutrition studies.

KEY WORDS: • triangular graph • dietary composition • growing chicks • multiple regression

Manuscript received 16 September 1981.