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Research Paper

Integrating Multivariate and Econometric Approaches to Assess Yield-contributing Traits in Field Pea Production

S
Subhash Kumar Jawla1
N
Namami Gohain2
B
Bhartendu Yadav1,*
0000-0001-6761-1760
P
Pradeep Joliya3
S
Shubh Laxmi4
G
Gaurav Tomer5
R
Rowndel Khwairakpam6
A
Atin Kumar7
1Department of Agricultural Economics and Extension, School of Agriculture, Lovely Professional University, Phagwara-144 411, Punjab, India.
2Department of Economics and Sociology, Punjab Agriculture University, Ludhiana-141 004, Punjab, India.
3Faculty of Agricultural Sciences, GLA University, Mathura-281 406, Uttar Pradesh, India.
4Bihar Agricultural University, Sabour, Bhagalpur-813 210, Bihar, India.
5Faculty of Agriculture, Guru Kashi University, Bathinda-151 302, Punjab, India.
6School of Agriculture, Graphic Era Hill University, Dehradun-248 002, Uttarakhand, India.
7School of Agriculture, Uttaranchal University, Dehradun-248 007, Uttarakhand, India.

  • Submitted11-06-2026|

  • Accepted10-07-2026|

  • First Online 03-08-2026|

  • doi 10.18805/LR-5688

ABSTRACT

Background: It is essential to identify the important traits that affect the seed yield and maximize the productivity and guide the breeding programs. Research has shown variations in the factors that determine yield, but the issue of prioritizing traits for breeding in pea cultivation is still unresolved.

Methods: In this study, the relationship between the key morphological and yield-related traits of peas was analysed using multiple linear regression and principal component analysis (PCA). The 94 varieties of peas were evaluated on the basis of seed yield, number of legumes, number of seeds per pod, pod length, plant height and number of branches. The statistical models were reliably validated through diagnostic plots and sampling adequacy measures.

Result: Positive seed yield indicators found significant were pod length, number of pods per plant and number of seeds per pod; whereas negligible effect was found for plant height and number of branches. PCA confirmed the multivariate structure of yield and highlighted breeding traits as its main drivers. These findings provide solid and useful information for improving pea varieties and provide guidance to breeders to focus on optimizing pod and seed traits to increase yields under similar growing conditions.

INTRODUCTION

India’s economy is based on agriculture, which contributes significantly to the nation’s GDP (Bondyalu, 2015). About 17.66% of India’s GDP comes from the agriculture sector (IBEF, 2025). Among the many crops, pulses are crucial for maintaining food security, boosting agricultural output and making money from exports. The pea (Pisum sativum) is one of the main pulse crops farmed in India and contributes significantly to the nation’s agricultural landscape (Gurusamy et al., 2022). In India, it is specifically grown during the Rabi season, covering over 0.64 million hectares and produces roughly 0.88 million tonnes annually (Honglei et al., 2025). The major states of India where peas are grown Uttar Pradesh, Madhya Pradesh, Bihar, Assam and Odisha. Approximately 1.4 tonnes per acre pea productivity have increased over time (FAOSTAT, 2023). Peas play an important role in foreign exchange and domestic consumption. India foreign exchange reserve increase by exporting large quantity of peas to other countries (Divya et al., 2024). India exported more than 1.52 million kg of peas and earn about Rs 121.36 million rupees in the financial year 2023-2024. Maximum exported nations are Bangladesh, Bhutan, Nepal, France and the United Arab Emirates (Ahlawat et al., 2016). A significant global concern is ensuring food security, particularly in India, where a sizable portion of the population is malnourished. Pea is a rich source of micronutrient which reduce micronutrient deficiencies and improve food security (Sahoo et al., 2025). Additionally, it is reported to be able to fix nitrogen, which increases soil fertility and reduces the need for synthetic fertilizers. This makes peas a sustainable crop that can contribute to environmentally friendly agricultural practices (Bawa and Seidler, 2023). It is necessary to focus on research and development to further advance the cultivation and utilization of pea (Lake et al., 2021 and Amarakoon et al., 2012). For example, studies on improving phosphorus use efficiency (PUE) in pea crop can increase its productivity and nutritional value (Wu et al., 2023). Additionally, breeding strategies aimed at increasing the bioavailability of nutrients in pea cultivation may be helpful in overcoming micronutrient deficiencies in plants (Semaskiene et al., 2022). Research efforts focused on improving its productivity, nutritional value and sustainability can be helpful in ensuring safe and nutritious food supply for the growing population (Sharma et al., 2023).

MATERIALS AND METHODS

The present study was conducted using augmented block design involving 94 diverse germplasm samples of pea (Pisum sativum), (Appendix 1: List of genotypes); obtained from the Department of Genetics and Plant Breeding of NDUAandT Kumarganj, Faizabad and Crop Improvement Division of IIPR, Kanpur. The objective of this experiment was to identify key components contributing to optimal crop production and inform selection strategies. The augmented block design was chosen due to its suitability for evaluating large numbers of genotypes with limited seed availability and resources. This design allows for evaluation of unreplicated test entries along with standard probes repeated within blocks, thereby improving experimental efficiency while controlling for environmental heterogeneity (Federer, 1956). Each test genotype and check was independently randomly allocated to plots within the respective blocks. All germplasm, including checks, was randomly allocated to each block. Observations were recorded on five competing plants per plot for most traits, except days to 50% flowering and days to maturity, which were measured on a plot basis. The recorded traits included primary branches per plant, plant height (cm), days to maturity, number of seeds per pod, pod length (cm), number of pods per plant, days to 50% flowering, 100-seed weight (grams), biological yield per plant (grams), harvest index (%) and seed yield per plant (grams). To reduce dimensionality and extract meaningful trait patterns, Principal Component Analysis (PCA) was used. PCA transforms a set of correlated variables X1, X2, …, Xp into a smaller number of uncorrelated components, TK1, TK2, …, TKp which are defined as linear combinations:
 
TK1 = a11 X1 + a12 X2 + ... + a1p Xp 

Where,
aij= Coefficients (loadings) chosen such that the first principal component.
TK1= The maximum variance in the data.

Appendix 1: List of genotypes.


       
Subsequent components are orthogonal and show progressively less variance (Jolliffe, 1986). This method is helpful in reducing the number of variables by highlighting the major characteristics that influence variability. Prior to PCA, assumptions were verified through the Kaiser-Meyer-Olkin (KMO) measure, which assesses sampling adequacy, with values   close to 1 indicating that the dataset is suitable for PCA and Bartlett’s test of sphericity to test the hypothesis that the correlation matrix is   an identity matrix. A significance test (p < 0.05) confirms the correlations between variables sufficient for PCA. Statistical calculations including KMO, Bartlett test and PCA were performed using JASP software. The combination of robust experimental design and rigorous multivariate analysis provided a solid framework for identifying important agronomic traits affecting field pea productivity.

RESULTS AND DISCUSSION

Multiple linear regression (Model fitness and prediction viability)
 
The full regression model (M1) exhibited a high R2 value of 0.648, indicating that approximately 65% of the variability in seed yield could be explained by the combination of selected traits in Table 1. This shows a strong predictive capacity of the model, especially in the context of biological and agricultural research where multiple factors interact. The Durbin-Watson statistic of 1.895 suggests that residuals are not autocorrelated, confirming the independence of errors: an essential assumption for reliable regression modelling. In contrast, the null model (M0), which included no predictors, had an R2 of 0.000, clearly demonstrating the improvement brought by the inclusion of agronomic variables. This model provides a strong foundation for predicting seed yield based on key morphological traits, essential for yield forecasting and varietal improvement.

Table 1: Model summary for linear regression.


 
Model significance
 
Table 2 of ANOVA (F = 32.441, p<.001) confirms that the model is statistically significant. This means that the set of predictor variables collectively has a strong effect on seed yield and the observed result is unlikely to be due to chance. This is a crucial validation step showing that the model is not only fitting well but is also meaningful in terms of its statistical inference.

Table 2: ANOVA for model M1.


 
Contribution of individual predictors
 
From the regression coefficients in Table 3, it was found that the Number of pods per plant emerged as the most influential predictor (β = 0.698, p<0.001). This suggests that increasing the number of pods has a substantial positive impact on seed yield. This is intuitive and aligns with earlier agronomic studies, which identify pod number as a direct determinant of reproductive success in legumes. Number of seeds per pod also had a strong, statistically significant influence (β = 0.314, p<.001), reinforcing the role of reproductive efficiency.

Table 3: Regression coefficients in model M1.


       
Similarly, a significant but moderate contribution was shown by pod length, which indicated that longer pods with more seeds probably (β = 0.176, p = 0.025). A negligible and non-significant effects of plant height and number of primary branches was found (p = 0.459 and 0.978, respectively). The findings states that these traits do not influence seed yield directly (Sree et al., 2025), in this context of genotype environment and can serve more in a structural role (Marzhan et al., 2022). To improve field pea productivity in breeding programs with targeted trait selection, the distinction between yield contributing and non-contributing traits is important (Tiwari, 2020). Further studies should emphasize towards pod-related traits rather than vegetative growth traits.
 
Descriptive statistics
 
Basic statistics is required essentially in regression modelling to get foundational insights in the central tendency and variability of agronomical traits in field pea sample population (n=94).
 
Seed yield per plant
 
Moderate variability among genotypes was found with average seed yield per plant of 4.93 gms, with standard deviation of 0.86 gms. A precise population mean and adequate sample size was suggested by a small standard error of 0.089 gm. Therefore, it seems a potential in selection of high yielding plants through breeding.
 
Plant height
 
A variation in vertical growth habit was suggested with average plant height of 87.33 cm and 17.6 cm of standard deviation. Although, plant height only can relate to biomass as shown in results (Table 3), indicating that taller plants necessarily do not have effect on seed yield.
 
Number of primary branches per plant
 
A mean of 2.08 and low variability; 0.475 of standard deviation shows uniformity in this trait under existing environmental condition. It reveals that this trait is less crucial for yield improvement due to its low variability.
 
Pods per plant
 
A good diversified range of reproductive output was found with mean of 7.69 per plant and standard deviation of 1.76 in number of pods per plant. This provides a wide range to breeders with scope for selection and improvement of high pod bearing varieties, suggesting strongest correlation with seed yield in the regression model.
 
Number of seeds per pod
 
The mean seeds per pod was 3.54 and SD = 0.518 suggests moderate variability. Since this trait reflect a positive, strong and valuable impact on seed yield (Table 3), increasing number of seed per pod could be a direct strategy to increase yield.
 
Pod length
 
The averaged length of pod is 3.70 cm, with 1.01cm standard deviation, showing a significant degree of variability. This characteristic may be an indirect selection criterion, potentially affecting the quantity or size of seeds housed within, given its notable yet moderate impact on production. Hence, the descriptive statistics indicate that the characteristics like pods per plant, seeds per pod and pod length do not only exhibit enough variation to enable selection, but also supports the positive predictive power of this characteristic in the regression analysis. Traits like branching and plant height are more durable but influence of yield is very less. As a result, Table 4 attests to the dataset’s significant diversity in yield-contributing characteristics, which is necessary for significant regression and PCA analysis. Additionally, plant breeders aiming to optimize reproductive traits might use these statistics as baseline benchmarks.

Table 4: Descriptive statistics.


 
Diagnostic plots
 
Residual diagnostics
 
Residuals versus Predicted diagnostics shows no pattern which supports homoscedasticity [Fig 1A (a-d)]. Standard which we found the Standardized Residuals to be approximately normal and also our Q-Q Plot which reported that the data points fell along a diagonal line which in turn confirmed normality. Also, we saw Random Scatter in Residuals versus Covariate plots which in turn confirmed the linear relationship between predictors and seed yield as well as the assumption of homoscedasticity. In terms of the overall Assessment of Model Assumptions; that is residual distribution and normality we had support in our diagnostic plots which in turn validated the model assumptions (Ribeiro et al., 2025). We noted that the standardized residual histogram was normal. Also, in the Q-Q plot we had residual points which fell along the diagonal which in turn confirmed normality. That we saw no out of the ordinary patterns in Residuals versus Predictors plot which in turn supported the assumption of homoscedasticity. These results in turn gave us confidence in the regression estimates and their large-scale use. Similarly, in Residuals versus Individual Covariate diagnostics [Fig 1B (a-e)], the Scatter plots of residuals against each covariate showed random dispersion with no systematic trends, confirming the linearity and independence of predictors. This is particularly important in agricultural datasets where multicollinearity and interaction effects can distort results.

Fig 1: (A and B): Diagnostic plots.


 
Individual predictor analysis (Partial and marginal effect plots)
 
The strong, positive linear relationships with seed yield demonstrated by pod per plant and seeds per pod, even after adjusting for other variables. These are the strong indicators of potential yield and should be prioritized in breeding. Pod length showed a moderate relationship, indicating an auxiliary role. Also, plant height and branches per plant had almost flat trends, reinforcing their lack of predictive utility for yield.
 
Principal component analysis (PCA)
 
The results from PCA are in Table 5, which shows that; overall, MSA is above 0.5, acceptable for PCA. However, harvest index and biological yield have low values (<0.5). Pods per plant (0.718) and Plant height (0.804) show strong sampling adequacy. Biological yield (0.377) and Harvest index (0.330) have low MSA values (<0.5), meaning these variables may not fit well into the component structure.

Table 5: Sampling adequacy (MSA).


       
Table 6 results show that, Bartlett’s test is significant, supporting factorability of the correlation matrix. The observations in Bartlett’s test (χ2 = 859.547, p<0.001) confirms the dataset is suitable for PCA and the model χ2 = 347.024, p<0.001, supports factor model validity.

Table 6: Bartlett’s test of sphericity and chi-squared test of model.


       
Table 7 show that the Seed yield loads moderately on two components (RC1 and RC2), showing it is influenced by both yield structure and physiological maturity traits. PCA was used to explore the multivariate structure of yield-related traits and reduce dimensionality.

Table 7: Component loadings (Promax rotation).


       
The kaiser-meyer-olkin (KMO) measure of 0.513 and significant Bartlett’s test (p<.001) confirmed that the data were suitable for PCA. However, the biological yield (0.377) and harvest index (0.330) exhibited inadequate sample adequacy and should be taken cautiously.
 
Component loadings and trait clustering
 
Promax-rotated loadings in Table 8, revealed the following: Vegetative growth dimension showed by RC1 by loading strongly on biological yield and plant height. The traits like pods per plant, seed yield and harvest index, aligning with yield structure is showed by RC2. In RC3 and RC4 includes reproductive precision traits like seeds per pod and pod length. Interestingly in both RC1 and RC2 we see seed yield which tells us of a complex relationship between growth and reproductive elements. This puts forth that it is a function of both size of the biomass and also separate yield related traits.

Table 8: Component characteristics.


       
Many different factors play into the determination of seed yield which in turn indicates that it isn’t a product of a single group of variables. What we see in the diverse grouping of traits like biological yield, plant height and pods per plant is a reflection of the very many aspects that go into the formation of yield (Patel et al., 2023).
       
The first three components explain over 56% of total variance, supporting dimensional reduction and helping focus on dominant traits. In the figure, i.e., the Scree Plot shows a sharp drop after 3 components. It justifies retaining 3-4 principal components (above Kaiser’s rule of eigenvalue >1), which confirms retention of 3 components as ideal. In the figure, i.e., the path diagram shows the causal paths between the latent variable (PC) and the observed variable, confirming the multi-trait effect on seed yield, showing how yield is influenced by multiple underlying factors rather than a single dominant trait.
 
Parallel analysis
 
Components to retain (Parallel analysis and scree plot)
 
The scree plot showed a clear bend after the third component and parallel analysis confirmed the persistence of three components based on actual versus simulated eigenvalues (Fig 2). These components together explained 56.9% of the total variance, which suggests that a significant portion of trait variability can be explained through the three major axes (Table 9). This dimensionality reduction simplifies future modelling and trait-targeting efforts by highlighting the core structures underlying traits (Angel et al., 2021).

Fig 2: Scree plot.



Table 9: Parallel analysis for component retention.


 
Path diagram
 
The path diagram depicted (Fig 3) how the latent components (PCs) influence the observed traits. This diagram presents that many traits which are integrated determine seed yield which in turn presents the multi-dimensional aspect of plant productivity (Ranjani and Jayamani, 2024; Jain et al., 2023). In the development of selection indices in crop improvement programs which require at the same time the improvement of related traits this is a useful tool (Kumar et al., 2024).

Fig 3: Path diagram of traits studied.


       
In our study we identified number of pods per plant, number of seeds per pod and pod length as the main determinants of seed yield in pea crop. The model we present is very statistical in nature and we did test its assumptions in great detail. PCA, we used to bring out some meaningful trait groups which in turn simplified the complex trait relationships.

CONCLUSION

This study emphasizes the aspects of the pea plant, responsible for seed yield which is mainly a function of reproductive traits number of pods per plant, number of seeds within each pod and pod length. We noted that among the vegetative traits like plant height and primary branching do not play a large role in improving yield. We report from our studies and regression models, which we supported with principal component analysis, that the best way for breeding programs is to put focus on improving key reproductive traits. Also, we note from our multivariate analysis that, which is the very complex nature of yield determination which in turn stresses the point that for crop improvement which you have to go in and target specific traits. These results will find breeders very useful in their work which in turn will help them to increase genetic gain and develop high yielding pea varieties. Therefore, the insights gained not only elucidate the genetic determinants of yield, but also provide statistically sound guidance for strategies in pea breeding programs.

ACKNOWLEDGEMENT

This study is supported by the Department of GPB and AE andUAandT, Kumarganj, Ayodhya, Uttar Pradesh.
 
Disclaimers
 
The authors accept responsibility for the accuracy and quality of the content in the article.

CONFLICT OF INTEREST

None of the authors has any conflict of interest.

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    Research Paper

    Integrating Multivariate and Econometric Approaches to Assess Yield-contributing Traits in Field Pea Production

    S
    Subhash Kumar Jawla1
    N
    Namami Gohain2
    B
    Bhartendu Yadav1,*
    0000-0001-6761-1760
    P
    Pradeep Joliya3
    S
    Shubh Laxmi4
    G
    Gaurav Tomer5
    R
    Rowndel Khwairakpam6
    A
    Atin Kumar7
    1Department of Agricultural Economics and Extension, School of Agriculture, Lovely Professional University, Phagwara-144 411, Punjab, India.
    2Department of Economics and Sociology, Punjab Agriculture University, Ludhiana-141 004, Punjab, India.
    3Faculty of Agricultural Sciences, GLA University, Mathura-281 406, Uttar Pradesh, India.
    4Bihar Agricultural University, Sabour, Bhagalpur-813 210, Bihar, India.
    5Faculty of Agriculture, Guru Kashi University, Bathinda-151 302, Punjab, India.
    6School of Agriculture, Graphic Era Hill University, Dehradun-248 002, Uttarakhand, India.
    7School of Agriculture, Uttaranchal University, Dehradun-248 007, Uttarakhand, India.

    • Submitted11-06-2026|

    • Accepted10-07-2026|

    • First Online 03-08-2026|

    • doi 10.18805/LR-5688

    ABSTRACT

    Background: It is essential to identify the important traits that affect the seed yield and maximize the productivity and guide the breeding programs. Research has shown variations in the factors that determine yield, but the issue of prioritizing traits for breeding in pea cultivation is still unresolved.

    Methods: In this study, the relationship between the key morphological and yield-related traits of peas was analysed using multiple linear regression and principal component analysis (PCA). The 94 varieties of peas were evaluated on the basis of seed yield, number of legumes, number of seeds per pod, pod length, plant height and number of branches. The statistical models were reliably validated through diagnostic plots and sampling adequacy measures.

    Result: Positive seed yield indicators found significant were pod length, number of pods per plant and number of seeds per pod; whereas negligible effect was found for plant height and number of branches. PCA confirmed the multivariate structure of yield and highlighted breeding traits as its main drivers. These findings provide solid and useful information for improving pea varieties and provide guidance to breeders to focus on optimizing pod and seed traits to increase yields under similar growing conditions.

    INTRODUCTION

    India’s economy is based on agriculture, which contributes significantly to the nation’s GDP (Bondyalu, 2015). About 17.66% of India’s GDP comes from the agriculture sector (IBEF, 2025). Among the many crops, pulses are crucial for maintaining food security, boosting agricultural output and making money from exports. The pea (Pisum sativum) is one of the main pulse crops farmed in India and contributes significantly to the nation’s agricultural landscape (Gurusamy et al., 2022). In India, it is specifically grown during the Rabi season, covering over 0.64 million hectares and produces roughly 0.88 million tonnes annually (Honglei et al., 2025). The major states of India where peas are grown Uttar Pradesh, Madhya Pradesh, Bihar, Assam and Odisha. Approximately 1.4 tonnes per acre pea productivity have increased over time (FAOSTAT, 2023). Peas play an important role in foreign exchange and domestic consumption. India foreign exchange reserve increase by exporting large quantity of peas to other countries (Divya et al., 2024). India exported more than 1.52 million kg of peas and earn about Rs 121.36 million rupees in the financial year 2023-2024. Maximum exported nations are Bangladesh, Bhutan, Nepal, France and the United Arab Emirates (Ahlawat et al., 2016). A significant global concern is ensuring food security, particularly in India, where a sizable portion of the population is malnourished. Pea is a rich source of micronutrient which reduce micronutrient deficiencies and improve food security (Sahoo et al., 2025). Additionally, it is reported to be able to fix nitrogen, which increases soil fertility and reduces the need for synthetic fertilizers. This makes peas a sustainable crop that can contribute to environmentally friendly agricultural practices (Bawa and Seidler, 2023). It is necessary to focus on research and development to further advance the cultivation and utilization of pea (Lake et al., 2021 and Amarakoon et al., 2012). For example, studies on improving phosphorus use efficiency (PUE) in pea crop can increase its productivity and nutritional value (Wu et al., 2023). Additionally, breeding strategies aimed at increasing the bioavailability of nutrients in pea cultivation may be helpful in overcoming micronutrient deficiencies in plants (Semaskiene et al., 2022). Research efforts focused on improving its productivity, nutritional value and sustainability can be helpful in ensuring safe and nutritious food supply for the growing population (Sharma et al., 2023).

    MATERIALS AND METHODS

    The present study was conducted using augmented block design involving 94 diverse germplasm samples of pea (Pisum sativum), (Appendix 1: List of genotypes); obtained from the Department of Genetics and Plant Breeding of NDUAandT Kumarganj, Faizabad and Crop Improvement Division of IIPR, Kanpur. The objective of this experiment was to identify key components contributing to optimal crop production and inform selection strategies. The augmented block design was chosen due to its suitability for evaluating large numbers of genotypes with limited seed availability and resources. This design allows for evaluation of unreplicated test entries along with standard probes repeated within blocks, thereby improving experimental efficiency while controlling for environmental heterogeneity (Federer, 1956). Each test genotype and check was independently randomly allocated to plots within the respective blocks. All germplasm, including checks, was randomly allocated to each block. Observations were recorded on five competing plants per plot for most traits, except days to 50% flowering and days to maturity, which were measured on a plot basis. The recorded traits included primary branches per plant, plant height (cm), days to maturity, number of seeds per pod, pod length (cm), number of pods per plant, days to 50% flowering, 100-seed weight (grams), biological yield per plant (grams), harvest index (%) and seed yield per plant (grams). To reduce dimensionality and extract meaningful trait patterns, Principal Component Analysis (PCA) was used. PCA transforms a set of correlated variables X1, X2, …, Xp into a smaller number of uncorrelated components, TK1, TK2, …, TKp which are defined as linear combinations:
     
    TK1 = a11 X1 + a12 X2 + ... + a1p Xp 

    Where,
    aij= Coefficients (loadings) chosen such that the first principal component.
    TK1= The maximum variance in the data.

    Appendix 1: List of genotypes.


           
    Subsequent components are orthogonal and show progressively less variance (Jolliffe, 1986). This method is helpful in reducing the number of variables by highlighting the major characteristics that influence variability. Prior to PCA, assumptions were verified through the Kaiser-Meyer-Olkin (KMO) measure, which assesses sampling adequacy, with values   close to 1 indicating that the dataset is suitable for PCA and Bartlett’s test of sphericity to test the hypothesis that the correlation matrix is   an identity matrix. A significance test (p < 0.05) confirms the correlations between variables sufficient for PCA. Statistical calculations including KMO, Bartlett test and PCA were performed using JASP software. The combination of robust experimental design and rigorous multivariate analysis provided a solid framework for identifying important agronomic traits affecting field pea productivity.

    RESULTS AND DISCUSSION

    Multiple linear regression (Model fitness and prediction viability)
     
    The full regression model (M1) exhibited a high R2 value of 0.648, indicating that approximately 65% of the variability in seed yield could be explained by the combination of selected traits in Table 1. This shows a strong predictive capacity of the model, especially in the context of biological and agricultural research where multiple factors interact. The Durbin-Watson statistic of 1.895 suggests that residuals are not autocorrelated, confirming the independence of errors: an essential assumption for reliable regression modelling. In contrast, the null model (M0), which included no predictors, had an R2 of 0.000, clearly demonstrating the improvement brought by the inclusion of agronomic variables. This model provides a strong foundation for predicting seed yield based on key morphological traits, essential for yield forecasting and varietal improvement.

    Table 1: Model summary for linear regression.


     
    Model significance
     
    Table 2 of ANOVA (F = 32.441, p<.001) confirms that the model is statistically significant. This means that the set of predictor variables collectively has a strong effect on seed yield and the observed result is unlikely to be due to chance. This is a crucial validation step showing that the model is not only fitting well but is also meaningful in terms of its statistical inference.

    Table 2: ANOVA for model M1.


     
    Contribution of individual predictors
     
    From the regression coefficients in Table 3, it was found that the Number of pods per plant emerged as the most influential predictor (β = 0.698, p<0.001). This suggests that increasing the number of pods has a substantial positive impact on seed yield. This is intuitive and aligns with earlier agronomic studies, which identify pod number as a direct determinant of reproductive success in legumes. Number of seeds per pod also had a strong, statistically significant influence (β = 0.314, p<.001), reinforcing the role of reproductive efficiency.

    Table 3: Regression coefficients in model M1.


           
    Similarly, a significant but moderate contribution was shown by pod length, which indicated that longer pods with more seeds probably (β = 0.176, p = 0.025). A negligible and non-significant effects of plant height and number of primary branches was found (p = 0.459 and 0.978, respectively). The findings states that these traits do not influence seed yield directly (Sree et al., 2025), in this context of genotype environment and can serve more in a structural role (Marzhan et al., 2022). To improve field pea productivity in breeding programs with targeted trait selection, the distinction between yield contributing and non-contributing traits is important (Tiwari, 2020). Further studies should emphasize towards pod-related traits rather than vegetative growth traits.
     
    Descriptive statistics
     
    Basic statistics is required essentially in regression modelling to get foundational insights in the central tendency and variability of agronomical traits in field pea sample population (n=94).
     
    Seed yield per plant
     
    Moderate variability among genotypes was found with average seed yield per plant of 4.93 gms, with standard deviation of 0.86 gms. A precise population mean and adequate sample size was suggested by a small standard error of 0.089 gm. Therefore, it seems a potential in selection of high yielding plants through breeding.
     
    Plant height
     
    A variation in vertical growth habit was suggested with average plant height of 87.33 cm and 17.6 cm of standard deviation. Although, plant height only can relate to biomass as shown in results (Table 3), indicating that taller plants necessarily do not have effect on seed yield.
     
    Number of primary branches per plant
     
    A mean of 2.08 and low variability; 0.475 of standard deviation shows uniformity in this trait under existing environmental condition. It reveals that this trait is less crucial for yield improvement due to its low variability.
     
    Pods per plant
     
    A good diversified range of reproductive output was found with mean of 7.69 per plant and standard deviation of 1.76 in number of pods per plant. This provides a wide range to breeders with scope for selection and improvement of high pod bearing varieties, suggesting strongest correlation with seed yield in the regression model.
     
    Number of seeds per pod
     
    The mean seeds per pod was 3.54 and SD = 0.518 suggests moderate variability. Since this trait reflect a positive, strong and valuable impact on seed yield (Table 3), increasing number of seed per pod could be a direct strategy to increase yield.
     
    Pod length
     
    The averaged length of pod is 3.70 cm, with 1.01cm standard deviation, showing a significant degree of variability. This characteristic may be an indirect selection criterion, potentially affecting the quantity or size of seeds housed within, given its notable yet moderate impact on production. Hence, the descriptive statistics indicate that the characteristics like pods per plant, seeds per pod and pod length do not only exhibit enough variation to enable selection, but also supports the positive predictive power of this characteristic in the regression analysis. Traits like branching and plant height are more durable but influence of yield is very less. As a result, Table 4 attests to the dataset’s significant diversity in yield-contributing characteristics, which is necessary for significant regression and PCA analysis. Additionally, plant breeders aiming to optimize reproductive traits might use these statistics as baseline benchmarks.

    Table 4: Descriptive statistics.


     
    Diagnostic plots
     
    Residual diagnostics
     
    Residuals versus Predicted diagnostics shows no pattern which supports homoscedasticity [Fig 1A (a-d)]. Standard which we found the Standardized Residuals to be approximately normal and also our Q-Q Plot which reported that the data points fell along a diagonal line which in turn confirmed normality. Also, we saw Random Scatter in Residuals versus Covariate plots which in turn confirmed the linear relationship between predictors and seed yield as well as the assumption of homoscedasticity. In terms of the overall Assessment of Model Assumptions; that is residual distribution and normality we had support in our diagnostic plots which in turn validated the model assumptions (Ribeiro et al., 2025). We noted that the standardized residual histogram was normal. Also, in the Q-Q plot we had residual points which fell along the diagonal which in turn confirmed normality. That we saw no out of the ordinary patterns in Residuals versus Predictors plot which in turn supported the assumption of homoscedasticity. These results in turn gave us confidence in the regression estimates and their large-scale use. Similarly, in Residuals versus Individual Covariate diagnostics [Fig 1B (a-e)], the Scatter plots of residuals against each covariate showed random dispersion with no systematic trends, confirming the linearity and independence of predictors. This is particularly important in agricultural datasets where multicollinearity and interaction effects can distort results.

    Fig 1: (A and B): Diagnostic plots.


     
    Individual predictor analysis (Partial and marginal effect plots)
     
    The strong, positive linear relationships with seed yield demonstrated by pod per plant and seeds per pod, even after adjusting for other variables. These are the strong indicators of potential yield and should be prioritized in breeding. Pod length showed a moderate relationship, indicating an auxiliary role. Also, plant height and branches per plant had almost flat trends, reinforcing their lack of predictive utility for yield.
     
    Principal component analysis (PCA)
     
    The results from PCA are in Table 5, which shows that; overall, MSA is above 0.5, acceptable for PCA. However, harvest index and biological yield have low values (<0.5). Pods per plant (0.718) and Plant height (0.804) show strong sampling adequacy. Biological yield (0.377) and Harvest index (0.330) have low MSA values (<0.5), meaning these variables may not fit well into the component structure.

    Table 5: Sampling adequacy (MSA).


           
    Table 6 results show that, Bartlett’s test is significant, supporting factorability of the correlation matrix. The observations in Bartlett’s test (χ2 = 859.547, p<0.001) confirms the dataset is suitable for PCA and the model χ2 = 347.024, p<0.001, supports factor model validity.

    Table 6: Bartlett’s test of sphericity and chi-squared test of model.


           
    Table 7 show that the Seed yield loads moderately on two components (RC1 and RC2), showing it is influenced by both yield structure and physiological maturity traits. PCA was used to explore the multivariate structure of yield-related traits and reduce dimensionality.

    Table 7: Component loadings (Promax rotation).


           
    The kaiser-meyer-olkin (KMO) measure of 0.513 and significant Bartlett’s test (p<.001) confirmed that the data were suitable for PCA. However, the biological yield (0.377) and harvest index (0.330) exhibited inadequate sample adequacy and should be taken cautiously.
     
    Component loadings and trait clustering
     
    Promax-rotated loadings in Table 8, revealed the following: Vegetative growth dimension showed by RC1 by loading strongly on biological yield and plant height. The traits like pods per plant, seed yield and harvest index, aligning with yield structure is showed by RC2. In RC3 and RC4 includes reproductive precision traits like seeds per pod and pod length. Interestingly in both RC1 and RC2 we see seed yield which tells us of a complex relationship between growth and reproductive elements. This puts forth that it is a function of both size of the biomass and also separate yield related traits.

    Table 8: Component characteristics.


           
    Many different factors play into the determination of seed yield which in turn indicates that it isn’t a product of a single group of variables. What we see in the diverse grouping of traits like biological yield, plant height and pods per plant is a reflection of the very many aspects that go into the formation of yield (Patel et al., 2023).
           
    The first three components explain over 56% of total variance, supporting dimensional reduction and helping focus on dominant traits. In the figure, i.e., the Scree Plot shows a sharp drop after 3 components. It justifies retaining 3-4 principal components (above Kaiser’s rule of eigenvalue >1), which confirms retention of 3 components as ideal. In the figure, i.e., the path diagram shows the causal paths between the latent variable (PC) and the observed variable, confirming the multi-trait effect on seed yield, showing how yield is influenced by multiple underlying factors rather than a single dominant trait.
     
    Parallel analysis
     
    Components to retain (Parallel analysis and scree plot)
     
    The scree plot showed a clear bend after the third component and parallel analysis confirmed the persistence of three components based on actual versus simulated eigenvalues (Fig 2). These components together explained 56.9% of the total variance, which suggests that a significant portion of trait variability can be explained through the three major axes (Table 9). This dimensionality reduction simplifies future modelling and trait-targeting efforts by highlighting the core structures underlying traits (Angel et al., 2021).

    Fig 2: Scree plot.



    Table 9: Parallel analysis for component retention.


     
    Path diagram
     
    The path diagram depicted (Fig 3) how the latent components (PCs) influence the observed traits. This diagram presents that many traits which are integrated determine seed yield which in turn presents the multi-dimensional aspect of plant productivity (Ranjani and Jayamani, 2024; Jain et al., 2023). In the development of selection indices in crop improvement programs which require at the same time the improvement of related traits this is a useful tool (Kumar et al., 2024).

    Fig 3: Path diagram of traits studied.


           
    In our study we identified number of pods per plant, number of seeds per pod and pod length as the main determinants of seed yield in pea crop. The model we present is very statistical in nature and we did test its assumptions in great detail. PCA, we used to bring out some meaningful trait groups which in turn simplified the complex trait relationships.

    CONCLUSION

    This study emphasizes the aspects of the pea plant, responsible for seed yield which is mainly a function of reproductive traits number of pods per plant, number of seeds within each pod and pod length. We noted that among the vegetative traits like plant height and primary branching do not play a large role in improving yield. We report from our studies and regression models, which we supported with principal component analysis, that the best way for breeding programs is to put focus on improving key reproductive traits. Also, we note from our multivariate analysis that, which is the very complex nature of yield determination which in turn stresses the point that for crop improvement which you have to go in and target specific traits. These results will find breeders very useful in their work which in turn will help them to increase genetic gain and develop high yielding pea varieties. Therefore, the insights gained not only elucidate the genetic determinants of yield, but also provide statistically sound guidance for strategies in pea breeding programs.

    ACKNOWLEDGEMENT

    This study is supported by the Department of GPB and AE andUAandT, Kumarganj, Ayodhya, Uttar Pradesh.
     
    Disclaimers
     
    The authors accept responsibility for the accuracy and quality of the content in the article.

    CONFLICT OF INTEREST

    None of the authors has any conflict of interest.

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