Table 3.

Estimated effects of factors and associated P-values for dependent variables (Y₁, Y₂, and Y₃)

Factors	Response
	Y1		Y2		Y3
	Estimated effect	P-value	Estimated effect	P-value	Estimated effect	P-value
X1	5.0	0.4391	−11.2875	0.0015*	−27.8025	0.0001*
X2	10.0	0.1537	3.3	0.1259	10.9025	0.0061*
X3	115.0	0.0000*	2.4925	0.2243	6.565	0.0405*
${\mathrm{X}}_1^2$	5.41667	0.5634	−0.700833	0.8017	−0.175833	0.9621
X1X2	−2.5	0.7784	−3.36	0.2436	−1.075	0.7634
X1X3	−7.5	0.4137	−0.325	0.9033	−1.86	0.6060
${\mathrm{X}}_2^2$	10.4167	0.2878	2.41417	0.4035	−4.35583	0.2708
X2X3	17.5	0.0921	−3.63	0.2128	5.57	0.1604
${\mathrm{X}}_3^2$	−49.5833	0.0024*	−1.01083	0.7182	−3.59083	0.3544
R2	98.8172		90.8485		97.1272
Adj. R2	96.6882		74.3758		91.9562
SEE	8.41625		2.54266		3.38154
MAE	4.11111		1.21089		1.69456

Notes:

^*Significant effect of factors on individual dependent variables. X₁: ALA in TPGS; X₂: citral concentration; X₃: PG concentration; Y₁: elongation percent; Y₂: initial permeation after 2 hours; Y₃: cumulative permeation after 24 hours. R²: coefficient of determination; Adj. R²: coefficient of determination adjusted for degrees of freedom; MAE: mean absolute error; SEE: standard error of estimate.

Abbreviations: ALA, alpha lipoic acid; PG, propylene glycol; TPGS, D-α-tocopherol polyethylene glycol 1000 succinate.