Table 2. The fitted polynomial equations for the response surfaces of the color (CIE L*, CIE a*, and CIE b*) of the patties (before and after cooking) with the optimized composition of BP and CC

Equation	r2	Adjusted r2	Lack-of-fit	AAD (%)
Before cooking
L *   value = 56.668 − 9.358 X 1 − 16.622 X 2 + 0.8057 X 1 2 + 3.74 X 2 2 + 1.347 X 1 X 2	0.989	0.982	0.060	5.11
a * value = 19.195 + 10.156 X 1 − 13.368 X 2 − 1.3606 X 1 2 + 5.075 X 2 2 − 1.579 X 1 X 2	0.984	0.972	0.059	10.88
b * value = 16.98 − 4.735 X 1 + 10.513 X 2 + 0.5755 X 1 2 − 2.802 X 2 2 − 1.07 X 1 X 2	0.973	0.953	0.089	10.46
After cooking
L *   value = 66.97 − 2.62 X 1 − 16.98 X 2 + 0.449 X 1 2 + 1.827 X 2 2 + 1.787 X 1 X 2	0.992	0.986	0.767	2.43
a * value = 4.841 + 3.087 X 1 − 3.714 X 2 − 0.0935 X 1 2 + 0.092 X 2 2 − 1.567 X 1 X 2	0.990	0.983	0.645	10.47
b * value = 18.00 − 1.487 X 1 + 6.32 X 2 + 0.151 X 1 2 − 1.884 X 2 2 − 0.638 X 1 X 2	0.819	0.690	0.092	3.96

BP, beet powder; CC, caramel color; AAD, absolute average deviation.