Fig. 3

The automated linear modeling diagram of influential attributes (e.g., LFW: leaf fresh weight, leaf N/P/K+: leaf nitrogen/phosphorus/potassium, Na+: sodium, and α-AN: alpha-amino-N) in sugar beet’s pure sugar yield (PSY) by data of indole‒3‒acetic acid (IAA) × nitrogen (N) interaction (data pooled across 2022/23 and 2023/24 cropping seasons) under saline soil (saturated electrical conductivity = 6.98 dS m− 1) conditions. AdjR2, Coeff, and sig. stand for adjusted determination coefficient, estimate coefficient, and significance, respectively. * and ** indicate significance levels at p ˂ 0.05 and p ˂ 0.01, respectively; ns denotes no significance