the handbook of food engineering practice crc press chapter 10 ...

criterion. The value of the R 2 , for a least square fit in general, is given by the following
equation:
R 2 = 1 -
⎛
⎜
⎜
⎝
N
∑
i=1
N
(y i - y^i) /∑
2 (y i - _ y ) 2 (15)
i=1
⎞
⎟
⎟
⎠
where y i the experimentally observed values of the measured parameter (i=1 to
N), y^ i the value predicted from the regression equation, y _
the average of the observed
values and N the number of measurements (Ott, 1984). The correct apparent order is that
for which the R 2 is closer to unity. The overwhelming majority of the food reactions that
have been studied have been characterized as pseudo-zero or pseudo-first order (Labuza,
1984). Characteristic examples are listed in Table 2.
Table 2.Important quality loss reactions that follow zero or first order kinetics.
Zero order
• Overall quality of frozen foods
• Non-enzymatic browning
First order
• Vitamin loss
• Microbial death / growth
• Oxidative color loss
• Texture loss in heat processing
Caution is advised in deciding the appropriate apparent order and quality
function, as noted by Labuza (1988). For example when the reaction is not carried far
enough (less than 50% conversion) both zero and first order might be indistinguishable
from a goodness of fit point of view as is illustrated in Figure 1. On the other hand, if the
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