Abstract To investigate the relationships between some principal attributions of morphology with seed yield per soybean, the18 soybeangenotypes were examined by random complete block design (RCBD) study. These study was also carried out three replicates to gain reliable results. The results of variance analysis indicated that, there were a significance differences among all soybean genotypes. Moreover, the results of correlated analysis revealed that biological yield (0.96), harvest index (0.92), and number of branches (0.92) had the uttermost correlation with seed yield. To data factor analysis, four independent variables justified 99.92 percent of all data. The first variable, seedyield, justified 96.71 percent of entire variance. To examine soybean seed yield, Multiple-Regression Model with method Analytical Regression Model (step-by-step) was utilized. This model proved that biological yield, thousand seed weight, and harvest index entered into model respectively and justified 98.85 percent of variation of seed yield. Correlated coefficients of considered attributions were 0.96, 0.78, and 0.92 respectively. All of these indexes had significant at 1% in statistical process. Therefore, these traits can be notability used in soybean breeding programs. Also, accordance of cluster analysis. the sample was divided into three groups. Keywords: Soybean, Morphological Traits, Factor Analysis, Step-by-step Regression Introduction Soybean as strategic plant can cope with nutria demands by the production of 40% protein and 20% oil (Monthly oil industry, 2004). In Iran, approximately 100000 hectare of farmland under proper weather conditions has been planting in soybean. Moreover, in several provinces e.g., Golestan, Gilan, Mazandaran, and Ardebil around 2.2 tones soybean a hectare has been cultivated (Hymowitz and Kaizuma, 2008). Therewith, Soybean as well as five oily plants (oil palm, rapeseed, cotton seed, peanut, and sunshine seed) can produce 84% oil of the world (Top Fer et al., 1995). Hence, soybean and its attributions have substantial roles in economics. Hence, the cognition of attributions’ relations and their interactions are crucial for all repairing plans (Acquah et al., 1992). It’s also worthwhile to utter that soybean has a considerable interaction with daylight; therefor, exploring convenient genotypes, determiningappropriate period of cultivation, and varieties of soybean are essential factors to plant of this seed. Two principals has been heeded to produce high qualified soybean, namely, variety of soybean with high potential genotype and variety of soybean with high adaptability. Kumudini et al., (2002) compered the new and old variety of soybean, the results indicated that new cultivar of soybean had high quality due to the long durability of leaf at filling crustacean level and the escalation of dry materials at this level. The results of several studies alsodemonstrated that soybean with high-level of yield is reachable through high harvest index and more devotee of Photosynthesis into natal parts, whereas increasing surface of leaf until graining has contradictory relation with seed yield (Kumudini et al., 2002). In this vein, Jian Jin et al., (2010) studied 41 varieties of soybean and they found out that the duration (from sheathing to graining) was overriding to produce outstanding qualified soybean. Khan and Hatam (Khan and Hatam, 2000) illustrated that most of morphological attributions had meaningfuland positive correlation with seed yield. Masudi et al (2009), also reported that bush weight, numbers of seed and in bush had higher correlation with soybean yield. On the contrary, in study of Bangar et al (2003) it was found that soybean yield had significance relation with weight of 100 grains, numbers of days from germination to 50% flowering, and time of cultivation. Henrico et al., (2004) as well as Akhtar and Sneller (1996) studies indicated that numbers of seed per plant had meaningful correlation with seed yield, whereas, this attribution hadthe highest direct impact on yield. Rezaizad (1999) investigated the existence relations between seed yield and its components and he explored that number of seed per plant, biological yield, and numbers of pod per plant had the most correlation with seed yield. In this vein, due to the complicated relations among attributions, the exact results cannot be reported through simple correlated coefficients. For this purpose, multi-variables statistical model is utilized to recognize the relations among attributions. Thus, data factor analysis as statistical method which revealed high correlations among variables, is required to decrease data and get the fruits of data (Moqadam et al., 2004). The study on 14 attributions of 20 cultivar of soybean demonstrated four results through variables analysis method: first variable justified 38.83 percent of data and was called as natal variable; second variable justified 21.4 percent of data and was called as seed specifications variable; third variable justified 17.35 percent of data and was called as yield variable and the final variable justified 7.5 percent of data andwas called as number of seed per pod variable (Sabokdast nodemi et al., 2010). Zhao et al., (1991) employed data factor analysis method in 12 important agricultural attributions by 16 soybean genotype in China. These attributions were classified into four groups. The first variable was contained number of seed per plant and numbers of pod per plant. The second variable was consisted plant height, number of node, height of the first pod from land and day numbers needed to flower. The third variable was included number of pod per plant, hundred seed weight, and weight of seed per plant. The four variable was comprised number of branches. Motivated by previous research, it was resultedthat cultivar of soybean had the significance impact on soybean seed yield. It is also notify to utter that, various sorts released different yields accordance of environment conditions and their adaptabilities to those conditions. Thus recent studies tried to gain desired sort through modifying agricultural variables including history of planting, model of planting, etc. The current study also attempted to assess yield and yield component of prevalent soybean cultivars and employ these cultivars in future repairing plans. Materials and method This study was cried out in experimental field of martyr Beheshit Company in Dezful city (capital of Khuzestan Province in south west of Iran). Tobattle against weeds, Treflan spray was used (2.5 liters for one hectare). 200 kg/ha of potassium sulfate, 150 kg/ha Triple superphosphate and 50 kg/ha nitrogen fertilizer were used. The demanding nitrogen was amounted 150 kg/ha at fourth and fifth leaf levels and was amounted 100 kg/ha at graining level to the plant, due to the lack of activated bacteria fixed soybean nitrogen, This RCBD study employed 18 genotypes of soybean and carried out three replicates. Each Crete contained 4 rows- 4m in length and 60cm in width- and the given gap between bushes was 5cm. After complete growth, 10 bushes were chosen randomly from each Crete. The considered attributions consisting number of branches, number of pod per plant, plant height, pod length, number of node, thousand seed weight, biological yield, seed yield, and harvest index were studied. All data was obtained through three-time assessment of attributions of selected bushes. This data was grouping through SAS 9.1 software (variance analysis) as well as Duncan Model (to compere average of data). To analysis variables Step-by-step Regression and SAS 9.1 software and to analysis correlation and cluster, SPSS 18 software were utilized. Results and discussion Theresults of variance analysis (table 1) proved that the impact of block and traits was significant for all attributions at 1 percent probable level. The most coefficient of genotype variation was belonged to number of node and the least coefficient was owned to biological yield. The results of compering average of attribution in table 2 revealed that the most number of branches (13.33), number of pod per plant (101), number of node (11.33), biological yield (765 kg/ha), seed yield (337 kg/ha), harvest index (44.04 kg/ha) were existence in salend. The saman cultivar showed the most plant height (101.33) from farmland. On the other hand, the most pod length (6.73Cm) was observed in SG5cultivar. The most thousand seed weight (240.66 gr) also belonged to Gorgan 3. olser and cartter (2004) stated that some components of yield consisting seed size, number of seed per pod and numbers of pod per plant, etc. are crucial factors in progression of soybean yield; therefore, genotypes empowered with these high qualified constituents have much more potations genetically. Farahani Pad et al., (2012) demonstrated that the impact of cultivar on thousand seed weight and seed yield in four cultivar were meaningful. In most of products, yieldis defined as the mixture of huge numbers of biological processes occurred during growing. Accordance of Ghorban zade neghab et al.,(2013) study, Zane cultivar with 14.8 gr had the most weight of hundred seeds and sahar cultivar with 9.2 had the least weight of hundred seeds among studied cultivars. The results illustrated that the Zane seed had the most weight of hundred seeds due to few numbers of seed per plant and lack of competition among seeds. Correlation analysis Determination of correlation analysis was one of the indexes to assess the existence relations among attributions. The result revealed that seed yield had the most correlation with biological yield (0.96) (table 3). Correspondently, Masudi et al. (2009) Yunesi hamze khanlu et al., (2010), Namdari and Mahmudi (2013), as well as Iqbal et al., (2003)reported the meaningful correlation between seed yield and these four attributions: numbers of pod per plant, number of seed per pod, harvest index and number of branches. Similar findings were reached by Pedersen and Lauer (2004), Shibels et al., (1996) and Kumudini etal., (2001). Respecting the plant height, number of node onto cardinal branch, numbers of branches, number of pod per plant and weight of thousand seeds were effective factors on improvement of soybean yield; therefore, genotypes with these high qualified attributions had more potential. This lends evidence to previous studies which suggested that cultivar of Selend, SG5, and Gorgan 3 are superior proceed than others (Amaranthath et al., 1990; Das et al., 1989; Pendy et al., 1973; Rajput et al., 1986). Factor analysis The considerable studies were conducted to assess the impact of relations on attribution proceed via analyzing coefficients to factor analysis. The recent research concentrated on causal analysis and determination of crucial criteria for repairing soybean yield. In the current study, the results of analyzing 10 morphological attribution through cardinal factors, highlighted four principal variables (table 4). These four variables explained 96.71%,0.0235%, 0.0065%, and 0.0021% of data diversities respectively and as whole, they clarified 99.92% of data diversities. There is also a direct relationship between variables variance and variables value in data interpretations. In this vein, subscription rate was a part of variance variable related to common variables. In addition, there was direct relationship between subscription rate and accurate rate (Henrico et al., 2004). By observing of revolved variable coefficients, it was found that the first variable coefficients, proceed variable, covered most of data and contained the big and positive coefficients of seed proceed, biological proceed, removal index, and tie numbers (table 4). Similarly Yunesi hamze khanlu et al., (2010) examined variable analysis of 9 attributions within 33 mutated soybean lines. They illustrated that numbers pod per plant, numbers of seed per plant, harvest index and were crucial attributions to improve soybean yield. Moreover, Narjesi et al., (2008) tested 17 attributions of 30 soybean genotypes. The result proved that two variables of phenology and yield justified 28.21% and 16.56% of data diversities respectively. They also declared that harvest index and seed numbers had the biggest effect on soybean seed yield. The second variable, yield component, contained the big and positive coefficients of biological yield, harvest index, thousand seed weight as well as pod length and also covered 2.35% of data diversities. The third variable, contained the big and positive coefficients of number of node as well as plant height and covered 0.65% of data diversities. It also contradicts with Kohkan and et al., (2010) study in which 12 traits of 141 soybean line were examined. Based on their results, the first variable, phono-genetic variable, was consisted traits including yield, numbers of branches per plant, numbers of pod per plant, numbers of seed per plant, as well as seed weight per plant and covered 29.18% of data diversities. The fourth variable, crustacean variable, was contained the big and positive coefficients of attributions including numbers of pod per plant, numbers of branches as well as pod length and also covered 0.21% of data diversities. In the same vein,Yahueian et al., (2010), found four main variables via factor analysis in stress conditions. These variables justified 78.38% of data diversities. The first variable, phonologic-morphological variable covered most of obtained data. The second variable or yield and yield component, the third variable or quality of seed, and fourth variable in stress conditions seed size were identified. In this study, step- by- step regression model was utilized. In this model after entering the new variable into the model, the old one was assessed by the model too. Hence, in this model, the most meaningful variable remained in functions. Furthermore, in this model few variables but important ones were examined (Henrico et al., 2004). The results indicated that some attributions consisting biological yield, thousand seed weight, and harvest index entered into the model and covered 98.85% of seed yield diversities (table 5). The of inclination regression line also revealed that attributions of biological yield, thousand seed weight, and harvest index were 1 percent meaningful in statistical process. Some researchdeclared that removal index is the best variable to justify soybean seed yield (Shukla et al., 1980; Weilenmanm detau and Luguez, 2000; Narjesi et al., 2008). Results of Cluster analysis (hierarchical grouping) Accordance of grouping analysis, n people can form g groups (g < n). In other words, grouping analysis of genotypes must classified based on similarity rate of separated groups (Zareh, 2011). To select the cutting location and to determine optimal group numbers (g), the minimize variance method with below formula was used: Group numbers=g= = =3 Respecting to the results of Cluster analysis, cultivars of soybean were classified into three group including Salend, SG5 and Gorgan 3 had the best yield (figure 1). Alipour Yamchi et al., (2011) also examined genetic varieties and grouping of pea genotypes (Cicer arietinum). They stated that claster analysis accordance of morphological attributions formed four independent groups of genotypes. Safari and et al., (2008) formed three independent groups of peanut cultivars (Arachis hypogaea) via cluster analysis. Conclusion As result, analysis variable revealed that through combined selection of attributions, there are several possibilities to repair soybean seed yield in future plans. Author contribution statement SGH Conceived and designed research, wrote manuscript and acted as corresponding author. BAF and AN Supervised development of work, analyzed the data, helped in data interpretation and manuscript evaluation. NMN Conducted experiments, contributed new reagents and drafted the manuscript. All authors read and approved the final manuscript. Compliance with ethical standards Conflict of interest The authors declare that they have no conflict of interest. undefined undefined undefined undefinedundefined undefined undefined undefined undefined undefined undefined undefined undefined undefined undefined undefined undefinedundefined undefined undefined undefined undefined undefined undefined undefined undefined undefined undefined undefined undefinedundefined undefined