Study of growth–yield associations in soybean (Glycine Max L.) using correlation, correlogram and regression analysis

Introduction

Soybean, also known as the "Wonder crop" or "Golden bean" is one of the world's most versatile leguminous crops. It has tremendous importance in agriculture because of its higher oil (16-21%) and protein (36-42%) content (Imas and Magen, 2007) [7] . As per FAO, based on its productivity, soybean was classified as world's fifth largest crop in terms of agricultural productivity (Yusefi-Tanha et al., 2020) [20] . Being originated in China, soybean is cultivated across the world on more than 136.19 million hectare area, with Brazil followed by USA being its topmost producers. Around the globe, India ranks fourth and fifth in terms of area and production of soybean, respectively (Soybean outlook, 2024) [18] . According to the reports by Directorate of Agriculture and Farmers Welfare, during 2024-25, leading states across India in soybean production were Maharashtra (74.03 lakh tonne) followed by Madhya Pradesh (52.85 lakh tonne), Rajasthan (11.74 lakh tonne) and Karnataka (4.82 lakh tonne). Based on its myriad form of uses and remarkable economic impact, soybean has emerged as a promising crop for India's agricultural sector. Among the essential nutrients, Nitrogen (N) plays a vital part in soybean crop's growth and yield. Apart from being a part of chlorophyll, a photosynthetic pigment, it governs vegetative growth and imparts green color to soybean (Begum et al., 2015) [3] . On the other hand, Phosphorous (P) has crucial role in soybean growth, especially in initial stages as well as nodule and pod development. Whereas Potassium (K) plays central role in maintaining plant cell's water balance, activation of enzymes involved in various physiological processes and reducing the risks of insect and pest attacks, etc. Among these essential nutrients, soybean has ability to fix atmospheric nitrogen with the help of its root nodules and regulates half of its nitrogen demand for vegetative and reproductive growth (Alam et al., 2009). However, remaining requirement of N along with P and K is fulfilled from soil. Hence, to produce sufficient biomass which will further lead to higher yields, it is essential to judiciously manage and satisfy nutrient requirements by soybean crop. In the view of above situation, understanding the relationships between crop growth characters and yield based on application of fertilizers is essential for optimizing soybean productivity. Several previous studies conducted in various crops have shown that yield and performance of these crops is directly as well as indirectly affected by various growth parameters and environmental factors (Mahmood et [12,16,19,14,17] . For this, studies based on correlation and regression analyses help by providing crucial insights into how individual morphological and characteristics interact and influence yield. As per the findings of Dixit and Dubey(1984), correlation studies provide thorough information about the influence of various genetic factors and environmental conditions on grain yield. Correlation analysis offers delineation of nature and strength of relationship between growth and yield traits whereas regression analysis helps in further predicting influence of multiple growth variables on yield outcomes. For instance, study conducted by Nachiketa et al. (2025) [13] revealed significant associations between various growth factors and yield traits influencing productivity in Pigeon pea (Cajanus cajan L.). Sangothari and Radhamani (2025) [16] observed that most of growth parameters including plant height, dry matter production, pods plant -1 , seeds pod -1 of blackgram had stronger and positive correlation with grain yield. Despite the numerous studies on crop yield association with growth characters, there is continuing need to evaluate these dynamics specifically across various growth stages. With this in view, present study has been conducted to analyse the relationship between various growth parameters and grain yield soybean.

Materials and Methods

Location and treatment details

The present field experiment was conducted during kharif season of 2023 and 2024 at the STCR farm, Department of Soil Science, Mahatma Phule Krishi Vidyapeeth, Rahuri, Maharashtra (India). Geographically, the experimental site is located at 19 0 34' N latitude and 74 0 64' E longitude.

Climate

The data on important climatic parameters was recorded during the crop growth period (kharif season of 2023 and 2024) and acquired from Meteorological Observatory of Mahatma Phule Krishi Vidyapeeth, Rahuri (M.S.). From the data, it was observed that during the crop growing period of kharif 2023 and 2024, average values of maximum and minimum temperatures were 32.0 C and 23.8 C in 2023 and 31.0 C and 22.6 C in 2024. Whereas total daily rain observed was 22.0 mm and 36.3 mm in kharif season of 2023 and 2024, respectively. In general, the climatic conditions observed during the experimental period were found favorable for crop growth.

Soil

The experimental field was uniformly levelled, having medium deep black soil belonging to Inceptisol order and silty clay loam texture. The soil was slightly alkaline in reaction with normal EC. From the initial chemical analysis of experiment field soil (0-15 cm depth), fertility status revealed low available nitrogen and phosphorous (168 and 14.33 kg ha -1 , respectively) whereas very high available potassium content (434 kg ha -1 ).

Crop Variety and management KDS-992 (Phule durva) is a soybean variety widely cultivated in Maharashtra, particularly during the kharif season, due to its stronger adaptability and good performance under regional agroclimatic conditions. For two-year study, the soybean was sown on 10 July and 28 June 2023 and 2024, respectively with the spacing of 45 cm × 5 cm.

Experimental details

The experiment was conducted in randomised block design (RBD), with twelve treatments replicated thrice. The treatments included, T 1 -control; T 2 -25:0:0 N:P 2 O 5 :K 2 O kg ha -1 ; T 3 -50:0:0 N:P 2 O 5 :K 2 O kg ha -1 ; T 4 -0:50:0 N:P 2 O 5 :K 2 O kg ha -1 ; T 5 -0:75:0 N:P 2 O 5 :K 2 O kg ha -1 ; T 6 -0:0:30 N:P 2 O 5 :K 2 O kg ha -1 ; T 7 -0:0:45 N:P 2 O 5 :K 2 O kg ha -1 ; T 8 -25:75:0 N:P 2 O 5 :K 2 O kg ha -1 ; T 9 -50:50:0 N:P 2 O 5 :K 2 O kg ha -1 ; T 10 -50:75:0 N:P 2 O 5 :K 2 O kg ha -1 ; T 11 -25:75:45 N:P 2 O 5 :K 2 O kg ha -1 and T 12 -50:75:45 N:P 2 O 5 :K 2 O kg ha -1 + 10 t ha -1 farmyard manure (GRDF).

Growth and yield analysis

The growth parameters which were recorded during the crop growth interval were initial plant population, final plant population, plant spread, plant height, number of functional leaves, number of branches at 30, 45, 60 and 90 days after sowing (DAS). Plant population within each net plot area was initially counted at 14 DAS and again just before the time of harvest; this count was converted on hectare basis and plant population was worked out in percentage values as well. Plant height of crops was measured from ground surface to topmost fully opened leaf of the main stem. Plant spread was recorded by measuring horizontal spread of plant in two perpendicular directions (east-west and north-south) followed by computation of average of these values. Number of functional leaves and number of branches were counted manually by randomly selecting five healthy plants from each plot and tagging them for observations. At harvest, seed yield and straw yield of five randomly selected plants, from each net plot was recorded and converted into perhectare basis. Similarly, the biological yield of soybean was calculated by harvesting, drying and weighing of above-ground biomass of these crop plants.

Statistical analysis

The recorded data from the present study was tabulated by using MS EXCEL software followed by performing correlation and regression analysis to determine relationship between growth and yield of soybean, with the significance level set at 95% confidence level (P < 0.05). Further, correlogram analysis, a graphical tool was used in this study. Correlograms are visual illustrations which make it easier to interpret the relationship between growth and yield attributes of crops (Graffelman et al., 2023) [6] . In the present study, correlogram analysis was performed in GRAPES (General R-based analysis platform empowered by statistics) software platform which is widely used in agricultural research for different statistical analyses.

Results and Discussion

The correlation coefficient regression and correlogram analysis of pooled data from two-year study on growth parameters including initial and final plant population, plant spread, plant height, number of functional leaves, number of branches with seed yield, straw yield and biological yield of soybean is presented in Table 1, 2 and Figure 1, respectively.

Plant population

Initial and final plant population of soybean was found positively correlated with growth characters such as plant spread (p < 0.01, r = 0.899), plant height (p < 0.01, r = 0.943), number of functional leaves (p < 0.01, r = 0.836) and number of branches (p < 0.01, r = 0.759). Among these growth parameters, highest correlation of plant population was found with plant height while lowest correlation was found with number of branches of soybean. Results revealed that, plant population also positively correlated with seed yield (p < 0.01, r = 0.866), straw yield (p < 0.01, r = 0.848) and biological yield (p < 0.01, r = 0.856). The regression analysis revealed that both initial and final plant population had positive R 2 with seed yield (R 2 = 0.75). These associations of plant population with growth and yield determining characters of soybean indicated that higher plant populations densities helped in improving overall growth and yield of crops. These results were supported by Nachiketa et al. (2025) [13] and Kumakech et al., (2024) [10] .

Plant spread

Table 1 showed positive and strong correlation between plant spread of soybean with growth and yield parameters which included plant population (p < 0.01, r = 0.899), plant height (p < 0.01, r = 0.982), number of functional leaves (p < 0.01, r = 0.961), number of branches (p < 0.01, r = 0.951), seed yield (p < 0.01, r = 0.981), straw yield (p < 0.01, r = 0.977) and biological yield (p < 0.01, r = 0.979). This suggested that plants with wider canopy spread captured more sunlight causing increase in area available for photosynthetic activity, resulting in more productivity. Similar results are consistently reported in findings by Mahendraraj et al. (2024) [11] and Dash et al. (2024) [4] . Findings from regression study showed highest R 2 between plant spread and seed yield (R 2 = 0.96) at 60 DAS, which is peak maturity stage in soybean. These findings are supported by Amarullah et al. (2016) [1] and Apea-Bah et al. (2011) [2] .

Plant height

Plant height had a positive correlation with growth and yield parameters which included plant population (p < 0.01, r = 0.943), plant spread (p < 0.01, r = 0.982), number of functional leaves (p < 0.01, r = 0.916), number of branches (p < 0.01, r = 0.897), seed yield (p < 0.01, r = 0.971), straw yield (p < 0.01, r = 0.962) and biological yield (p < 0.01, r = 0.967). Table 2 revealed positive R 2 between plant height and seed yield at all growth stages. However highest R 2 was observed at 60 DAS (R 2 = 0.95) of soybean crop. According to Jakhad et al. (2025) [8] , tall plants have more vegetative vigour which subsequently leads to more productivity and grain yield by plants. Results from present study suggested that taller plants had positive associations with yield of soybean which was found highest at peak maturity stage of plant growth. Similar results are consistently reported in findings by Zhange et al. (2021) in maize.

Number of functional leaves per plant

Strong correlation between number of functional leaves per plant and growth-yield characters of soybean including plant population (p < 0.01, r = 0.836), plant spread (p < 0.01, r = 0.961), plant height (p < 0.01, r = 0.916), number of branches (p < 0.01, r = 0.973), seed yield (p < 0.01, r = 0.916), straw yield (p < 0.01, r = 0.915) and biological yield (p < 0.01, r = 0.916) were observed in Table 1. Among the growth parameters, highest correlation coefficient of number of functional leaves per plant was found with number of branches while lowest correlation was found with plant population of soybean. The regression analysis revealed that number of functional leaves per plant had positive R 2 with seed yield across the growth stages, which was highest at 60 DAS (R 2 = 0.85). These association between number of functional leaves per plant and growth-yield characters of soybean revealed that leaf development in plants is closely linked to growth and yield (Zhange et al. (2021).

Number of branches per plant

Number of branches per plant in soybean had a positive correlation with growth and yield characters as observed in Table 1. The correlation coefficient observed between number of branches per plant and growth-yield characters included plant population (p < 0.01, r = 0.759), plant spread (p < 0.01, r = 0.951), plant height (p < 0.01, r = 0.897), number of functional leaves (p < 0.01, r = 0.973), seed yield (p < 0.01, r = 0.937), straw yield (p < 0.01, r = 0.943) and biological yield (p < 0.01, r = 0.940). From the close perusal of these results, it was revealed that across the growth parameters, highest correlation coefficient of number of branches per plant was found with number of functional leaves per plant while lowest correlation was found with plant population of soybean. Table 2 revealed positive R 2 between Number of branches per plant in soybean and seed yield at all growth stages. However highest R 2 was observed at 60 DAS (R 2 = 0.95) of soybean crop. These substantial associations indicate that increased number of branches as growth of plant succeeds led to near-perfect correlation of number of branches with growth-yield characters. Similar results were reported by Nguyen et al. (2022) in maize. According to study conducted by Nachiketa et al. (2025) [13] , greater number of branches per plant result in improved reproductive sink, leading to increased pod and ultimately seed production in pigeon pea. Similar results were reported by Pranati et al., 2024 [15] .

Seed yield

The correlation coefficient among seed yield and other growthyield characters is presented in Table 1. A thorough examination of the data revealed that seed yield had positive correlation coefficient growth and yield characters that included plant population (p < 0.01, r = 0.866), plant spread (p < 0.01, r = 0.981), plant height (p < 0.01, r = 0.971), number of functional leaves (p < 0.01, r = 0.916), number of branches (p < 0.01, r = 0.937), straw yield (p < 0.01, r = 0.999) and biological yield (p < 0.01, r = 1.000). Among these parameters, seed yield had perfect of correlation with biological yield whereas lowest correlation coefficient of seed yield was observed with plant population. These results emphasised that seed yield in crops are closely linked with total biomass produced by plants and reported by Pashawar et al., (2024) and Nachiketa et al. (2025) [13] while working on Pigeon pea.

Straw yield

Straw yield of soybean was positively correlated with plant population (p < 0.01, r = 0.848), plant spread (p < 0.01, r = 0.977), plant height (p < 0.01, r = 0.962), number of functional leaves (p < 0.01, r = 0.915), number of branches (p < 0.01, r = 0.943), seed yield (p < 0.01, r = 0.999) and biological yield (p < 0.01, r = 1.000). Results indicated perfect correlation of straw yield with seed yield and biological yield. Similar results were reported by Pashawar et al., (2024) and Nachiketa et al. (2025) [13] , suggesting close association between yield contributing parameters in plants. However, among these parameters, lowest correlation of straw yield was observed with plant population (Table 1).

Biological yield

Biological yield of soybean was found positively correlated with every growth and yield parameter (Table 1). Results showed that the observed correlation coefficients between biological yield and other parameters included, plant population (p < 0.01, r = 0.856), plant spread (p < 0.01, r = 0.979), plant height (p < 0.01, r = 0.967), number of functional leaves (p < 0.01, r = 0.916), number of branches (p < 0.01, r = 0.940), seed yield (p < 0.01, r = 1.000) and straw yield (p < 0.01, r = 1.000). Close association of biological yield of soybean with growth parameters emphasized the positive effect of improvement in vegetative and reproductive structure of plant on overall biomass accumulation by plant, as reported by Nachiketa et al. (2025) [13] and Kandarkar et al. (2020) [9] .

population, plant spread, plant height, number of functional leaves, number of branches with seed yield, straw yield and biological yield. From the above study, it was discovered growth-yield parameters of soybean plants showed positive association with each other. This association was observed higher between plant height, plant spread, number of branches per plant and number of functional leaves per plant at maturity stages of soybean and seed yield. It was highlighted from the study that taller and plants having higher canopy spread along with larger number of functional leaves and branches positively linked with yield characters of soybean plants.

References

1. Amarullah, Didik, Indradewa, Prapto, Yudono, Bambang, Sunarminto H. Correlation of growth parameters with yield of two cassava varieties. Agric Sci. 2016;1(3):100-104.
2. Apea-Bah FB, Oduro I, Ellis WO, Safo-Kantaka O. Factor analysis and age at harvest effect on quality of flour from four cassava varieties. World J Dairy Food Sci. 2011;6(1):43-54.
3. Begum MA, Islam MA, Ahmed QM, Islam MA, Rahman MM. Effect of nitrogen and phosphorus on the growth and yield performance of soybean. Res Agric Livest Fish. 2015;2(1):35-42.
4. Dash S, Murali K, Bai SK, Rehman HA, Sathish A. Influence of sowing window and planting geometry on pigeonpea nutrient uptake, quality and yield. Mysore J Agric Sci. 2024;58(1):387-396.
5. Dixet P, Dubey DK. Path analysis in lentil (Lens culinaris Med.). Lens Newsl. 1984;11:15-17.
6. Graffelman J, De Leeuw J. Improved approximation and visualization of the correlation matrix. Am Stat. 2023;77(4):432-442.
7. Imas P, Magen H. Role of potassium nutrition in balanced fertilization for soybean yield and quality: global perspective. In: Proceedings of Regional Seminar on Recent Advances in Potassium Nutrition Management for Soybean Based Cropping System; 2007. p. 1-20.
8. Jakhad A, Menon S, Singh G, Priyadarshini S, Nachiketa. Assessment of relationships between growth and yield traits in kharif maize (Zea mays L.) under planting patterns, nutrient regimes and organic mulching. Agric Sci Dig. 2025;45(Special Issue):26-34. doi:10.18805/ag.D-6448.
9. Kumakech A, Opio T, Turyagyenda FL. Effect of plant spacing on pigeonpea grain yield in Northern Uganda. Braz J Sci. 2024;3(4):41-47.
10. Mahendraraj S, Collins M, Chauhan Y, Mellor V, Rachaputi RCN. Dynamics of productivity in pigeonpea [Cajanus cajan (L.) Millsp.] in subtropical Australia. Agron J. 2024;116(6):2827-2840. doi:10.1002/agj2.21667.
11. Mahmood ET, Al-Mafarji TR, Al-Ethawi MB, Ahmed KK, Al-Ani SHI, Korolev KP. Correlation analysis of growth, yield, and quality traits in maize (Zea mays L.) hybrids under different plant densities. IOP Conf Ser Earth Environ Sci. 2025;1538:012041. doi:10.1088/1755-1315/1538/1/012041.
12. Nachiketa, Menon S, Singh G, Priyadarshini S, Jakhad A. Correlation matrix and correlogram analysis for growth and yield attributes of pigeon pea (Cajanus cajan L.) under organic mulching and system of intensification. Legume Res. 2025;48(Special Issue):154-162. doi:10.18805/LR5576.
13. Panda D, Sen A, Dhakre DS, Mondal S. Correlation analysis of some growth, physiological parameters, yield and yield attributes of chickpea (Cicer arietinum L.). Int J Bioresour Environ Agric Sci. 2015;1(3):90-95.
14. Pranati J, Chilakamarri V, Kalyan A, Shruthi HB, Bomma N, Yogendra K, et al. Strategizing pigeonpea for enhancing health-benefitting traits: a path to nutritional advancements. Crop Des. 2024;3(4):100068. doi:10.1016/j.cropd.2024.100068.
15. Sangothari A, Radhamani S. Assessment of correlation between growth and yield of blackgram with residual effect of organic and inorganic sources of nutrients and AM fungi applied to rice in aerobic rice-blackgram cropping system. Legume Res. 2025;48(5):819-827. doi:10.18805/LR-5336.
16. Sokoto MB, Abubakar IU, Dikko AU. Correlation analysis of some growth, yield, yield components and grain quality of wheat (Triticum aestivum L.). Niger J Basic Appl Sci. 2012;20(4):349-356.
17. Soybean outlook. 2024. https://pjtsau.edu.in/files/AgriMkt/2024/January/SoyabeanJanuary-2024.pdf
18. Vennila C. Assessment of leaf area index and its relationship with growth and yield of fodder cowpea as influenced by sources of irrigation and nutrients. Legume Res. 2024;47(12):2077-2085. doi:10.18805/LR-5265.
19. Yusefi-Tanha E, Fallah S, Rostamnejadi A, Pokhrel LR. Particle size and concentration dependent toxicity of copper oxide nanoparticles (CuONPs) on seed yield and antioxidant defense system in soil grown soybean (Glycine max cv. Kowsar). Sci Total Environ. 2020;715:136994.