3.2.3. Mathematical Modelling and Statistical Analysis

The experimental results of the factorial designs were modelled by second-order polynomial equations as [31]:

$$Y = b\_0 + \sum\_{i=1}^{n} b\_i X\_i + \sum\_{i=1 \atop j>i}^{n-1} \sum\_{j=2}^{n} b\_{ij} X\_i X\_j + \sum\_{i=1}^{n} b\_{ii} X\_i^2 \tag{1}$$

where *Y* represents the response to be modelled; *b*<sup>0</sup> is a constant coefficient, *bi* is the coefficient of linear effect, *bij* is the coefficient of interaction effect, *bii* is the coefficient of squared effect, *n* is the number of variables and *Xi* and *Xj* define the independent variables. The statistical significance of the coefficients was verified by means of Student's *t*-test (α = 0.05), goodness-of-fit was established as the adjusted determination coefficient (R2 adj) and the model consistency was determined by the Fisher F test (α = 0.05) using the following mean squares ratios (Table 6):

**Table 6.** Fisher F tests used to check the consistency of polynomial equations.


*Fnum den* are the theoretical values to α = 0.05 with the corresponding degrees of freedom for numerator (num) and denominator (den). All fitting procedures, coefficient estimates and statistical calculations were performed on a Microsoft Excel spreadsheet.

#### *3.3. Amino Acid Characterization of Acid-Soluble Collagen*

Amino acids were determined in the freeze-dried collagen obtained in each one of the 20 experimental points. For this purpose, acid hydrolysis was conducted with 6 N hydrochloric acid containing 0.1% phenol under an inert atmosphere by heating to 110 ◦C for 24 h. Then, HCl was removed from the hydrolysate by vacuum. The hydrolysate was resuspended in 20–50 μL of 0.2 M sodium citrate buffer (pH 2.2), to which a known amount of norleucine was added as an internal standard and applied to an automated amino acid analyzer (Biochrom30 Amino Acid Analyzer, Biochrom, UK).
