Application of Regression Analysis to Identify the Soil and Other Factors Affecting the Wheat Yield

Hindawi Advances in Materials Science and Engineering Volume 2022, Article ID 7793187, 10 pages https://doi.org/10.1155/2022/7793187 Research Article Application of Regression Analysis to Identify the Soil and Other Factors Affecting the Wheat Yield Azhar Hayat ,1 Muhammad Amin ,2 Saima Afzal ,1 Abdisalam Hassan Muse ,3,4 Omer Mohamed Egeh ,4 and Hafiz Saqib Hayat5 1 Department Department 3 Department 4 Department 5 Department 2 of of of of of Statistics, Bahauddin Zakariya University, Multan, Pakistan Statistics, University of Sargodha, Sargodha, Pakistan Statistics, Pan African University, Institute for Basic Sciences,Technology and Innovation, Nairobi, Kenya Mathematics and Statistics, Amoud University, Borama, Somalia Agronomy, Bahauddin Zakariya University, Multan, Pakistan Correspondence should be addressed to Omer Mohamed Egeh; 1933@amoud.edu.so Received 21 February 2022; Revised 12 April 2022; Accepted 19 April 2022; Published 10 May 2022 Academic Editor: Palanivel Velmurugan Copyright © 2022 Azhar Hayat et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In farming and related fields, numerous connections exist that should be distinguished quantitatively. Several factors affect the various crop yields in different dimensions. These factors may have relation with farmer’s practices or with quality of soil. In this study, our main focus is to explore the effect of soil and other factors on the wheat yield. Regression modeling plays an important role in the identification of such factors that greatly affect the crops yield. For reliable and valid results, one has to check the data for outliers and other critical results. In this study, we have fitted the regression models with and without satisfying some regression assumptions to determine the factors affecting yield of wheat. For analysis purposes, the required data were collected from the district Multan. It was observed that when the regression assumptions were satisfied, then coefficient of determination (R2) was improved from 45% to 48%, R2 (adjusted) was improved from 40% to 46%, and the standard error of the estimates was reduced from 2.772 to 2.649. These results indicate that the soil characteristics, such as saturation, electrical conductivity, organic matter, phosphorus, potassium, calcium carbonate, and micronutrients (zinc, copper, iron, manganese, and boron), are the significant factors for wheat yield. While among all other factors, urea, chemical coating of seed, use of compost, and previously sown crops are the significant factors for wheat yield. 1. Introduction The agriculture sector plays a key role in the economy of Pakistan as it contributes 19.2% to gross domestic product (GDP) and 38.5% of the labor force is engaged in this sector [1]. It also has a major contribution to the foreign exchange earnings of the country and the development of other sectors. However, nowadays, Pakistan is facing the issues of water stress, pollution, and environmental degradation along with institutional and socio-economic problems; these issues have severely affected the agricultural productivity of the country. Consequently, there is a need for strong strategies and their implementation to improve productivity in the agriculture sector [2]. Wheat is the main food crop of Pakistan, and it dominates all crops in production. According to world population review (2022), Pakistan is ranked at seventh place among the highest wheat-producing countries in the world in terms of yield per acre, area, and production. The mean per capita consumption of wheat in Pakistan is about 125 kg per year and is about 60% of daily food for an average person [3]. The earnings of almost 80% of the farmers in Pakistan are dependent on wheat. It is grown at an area of 9 million hectares that is roughly 40% of the total cultivated land in the country. The wheat crop added about 8.7% to the total value of agriculture and contributes about 2.1% to the GDP [4]. Wheat is considered a staple crop for the countries in 2 temperate zones and is increasing in demand in the countries that are undergoing industrial and urban development. It is the main source of starch and energy, further it provides essential nutrients like vitamins, dietary fiber, and proteins, which are necessary for human growth [5]. That is why most researchers are strenuous to know factors that increase and decrease wheat production due to its high importance. Worldwide, several analysts examined the impact of various factors on the yield of wheat. Barzegar et al. [6] investigated the impact of wheat straw, composted sugarcane residue on properties, and yield of wheat in Iran. They applied the split-plot design and found that organic materials increased wheat yield, aggregate stability, water retention, and decrease soil bulk density. Martre et al. [7] proposed mechanistic hypotheses for grain nitrogen accumulation in cereal. The four cultivars were tested in France. The proposed hypotheses were tested with the help of linear regression. It was found that under normal conditions, Arche and Rectal cultivars had the highest grain per year while Tamaro cultivar had the lowest grain per year. Plaut et al. [8] conducted experiments on Suneca and Batavia wheat varieties in Australia. A mechanistic model was developed and showed that kernel number was not affected by water deficit, but high temperature caused a significant reduction in both varieties. Water deficit and the high temperature were also found to increase the relative contribution of transported dry matter to kernels. Leilah and AlKhateeb [9] explored the association between wheat yield and its components under drought conditions in Saudi Arabia. Multiple statistical techniques including correlation, linear regression, path analysis, factor analysis, cluster analysis, and principal components analysis were used and it was revealed that weight of grain, number of spikes per square meter, and biological yield had the most influence on wheat grain yield indicating that breeding material with these qualities can produce a high yield in drought conditions. Moriondo et al. [10] adapted the use of Normalized Difference Vegetation Index (NDVI) data obtained from the simulation model and satellite platforms for the estimation of wheat yield. This methodology was applied in two high wheat-yielding provinces of Italy. They found that the proposed methodology produced a better accuracy in the estimation of wheat yield. Khan et al. [11] studied the effect of zinc fertilizer at different levels on the yield of wheat in Multan, Pakistan. The difference among these treatments was compared using the least significant differences (LSD), polynomial curve fitting, and coefficient of determination, and it was found that application of 5 kg ha−2 of zinc sulphate gave the highest marginal rate of return as compared to other amounts of application of zinc sulphate. Whalley et al. [12] discussed the relation between soil strength and yield of wheat for two different soil types in England. They applied the factorial design and found that soil strength is a good predictor of crop yield irrespective of soil type, water status, and concluded that soil strength seemed to limit crop productivity. Abbas et al. [13] evaluated the influence of trace elements in nitrogen, phosphorus, and potassium absorption on wheat yield. With the help of randomized Advances in Materials Science and Engineering complete block design (RCBD) and Duncan’s multiple range test, they showed that limited use of iron increased wheat yield. If the application of iron was increased, the effect on the yield was insignificant or undesirable. Hassan et al. [14] conducted a study to find significant factors that were influencing the wheat yield in mixed cropping zones of Punjab. The data were collected from four different districts of Punjab. They applied the linear regression and found that seed rate, cost weedicide that was used, education of farmer, use of nitrogenous fertilizer, rotavator use, and sowing time are the significant factors for wheat yield. Gul et al. [15] explored the effect of foliar application of micronutrients on Ghazanive-98 variety of wheat in Peshawar, Pakistan. They applied the RCBD and found that foliar treatment of micronutrients affected the growth of the wheat variety without causing any effect on the time of growth. Nadim et al. [16] evaluated the yield characteristics and physiology of the Gomal-8 variety of wheat for different levels of micronutrients in Dera Ismail Khan. With the help of RCBD, they found that the application of Boron produced a higher leaf area index while the application of copper produced a maximum number of tillers causing an increase in wheat yield. Rezaei and Hemati [17] studied the effect of soil properties on wheat yield in Iran. They applied the RCBD, and the results showed that a balanced percentage of sand, clay, and silt provide favorable conditions for the improvement of wheat yield. El-Lethy et al. [18] discussed the potassium impacts on wheat plants under saline conditions in Giza, Egypt. With the help of analysis of variance (ANOVA) and LSD, they concluded that the yield of wheat is decreased significantly in saline conditions, and potassium fertilizer reduces the undesirable effects of salinity. Alam and Salahin [19] conducted a series of experiments to study the effect of soil density and moisture retention on wheat yield in Bangladesh. They applied the multiple regression models and found that wheat yield almost doubled from lowest soil depth to highest soil depth. Muarya et al. [20] conducted a field experiment during the Rabi season in Kanpur to study the influence of potassium levels on wheat yield and growth. Using factorial RCBD, it was observed that the application of 80 kg ha−1 of potash (K2O) produced the highest grain yield, straw yield, and biological yield compared to 0, 40, and 60 kg ha−1 application of K2O. Limon-Ortega and Martinez-Cruz [21] studied the impact of nitrogen on wheat yield in Mexico. The data were analyzed through ANOVA. It was found that nitrogen sources impacted wheat yield and the number of spikes based on soil reaction while the fungicide spray had a positive influence on the wheat yield. Ghadikolayi et al. [22] studied the influence of crop residue and nitrogen on wheat yield in Iran. They applied the RCBD and found that 135 kg/ha of nitrogen gave the highest soil organic matter (OM). It was also found that all of the residues used in the experiment reduced the yield of wheat but the reduction with the use of sunflower residue was lowest compared to other crop residue tested. Sarto et al. [23] investigated the effects of silicate application on soil chemical properties in Parana, Brazil. With the help of regression models and it was concluded that the calcium/ magnesium silicate in acid clayey soil improves the yield of Advances in Materials Science and Engineering wheat. However, the soil with pH higher than 5.3 and high silicon does not impact the grain yield of wheat. Arshad et al. [24] conducted an experiment in Peshawar, Pakistan, to study the interactive impact of zinc and phosphorus on wheat. With the help of LSD test, it was found that 5 kg ha−1 of zinc gave maximum straw yield, but 10 kg ha−1 zinc significantly increased all other indicators of yield. As for phosphorus, 90 kg ha−1 was observed to produce the best results. Mehmood et al. [25] studied the input factors that positively influence wheat production in Bahawalnagar, Punjab. The researchers used the linear regression and found that the sowing method, use of fertilizer, that is, nitrogen and phosphorus, variety of wheat, use of weedicides spray and irrigation mode have a significant effect on the wheat yield. Chairi et al. [26] conducted a study on the genetic gain in yield for durum wheat in three experiment stations in Spain. They considered the linear regression to determine variability in locations for absolute and relative genetic gain (AGG and RGG). The result of the analysis showed that the rate of genetic progress in durum wheat yield has been low in the past decade. Rajicic et al. [27] carried out tests on wheat plants in soil with low pH by applying nitrogen along with phosphorus and potassium fertilizers in Serbia. They applied correlation analysis and found that nitrogen had a significant impact on wheat yield and the treatments where the highest amount of nitrogen was applied with other combinations of phosphorus, and potassium had a high yield compared to the lower application of nitrogen. Polisetty and Paidipati [28] estimated the trends in the production of wheat using data from four states of India. The trend analysis was conducted using nonparametric methods including Pettitt’s Standard Normal Homogeneity, Buishand’s range test, and Mann Kendall test. The outcomes of the trend analysis showed that all states under consideration had an upwards trend and indicated an improvement in wheat production. Sial et al. [29] investigated the effect of waste-derived-biochars of milk tea and fruit peels on growth, yield, root traits, soil enzyme activity, and nutrient status of the wheat crop in Shaanxi, China. Eight treatments were analyzed with one-way ANOVA and it was found that plant height, dry weight of root and shoot, chlorophyll amount, grain yield significantly increased using the treatment of milk tea biochar and chemical fertilizer. Ashraf et al. [30] analyzed the input-output flow for wheat production to identify energy-efficient ways through data from Mailsi, Pakistan. It was found through multiple regression models that higher inputs, large fields, high fertilizer application, and tillage operation provided the highest energy outputs with high productivity and efficiency in energy. Zhou et al. [31] studied the relationship between the depth distribution of wheat roots and soil macroporosity in United Kingdom with six varieties of wheat. Two-way ANOVA was used, and it was determined that there was no significant difference in wheat genotypes, and the wheat root system was more affected by the soil macropore system. Recently, Hayat et al. [32] explored the effect of soil properties and other factors on the cotton yield of Pakistan. They observed that EC, pH, saturation, OM, P, Zn, Cu, Fe, and B are the significant factors for cotton yield. They also 3 found that fertilizer (Nitrophos, nitrogen, and urea), previously sown crops (wheat and corn), type of seed, chemical coating of seed, type of water, way of cultivation, and use of compost are also a significant factors for cotton yield. As we have seen in the literature that worldwide, mostly researchers studied the effect of individual soil characteristic or two or other factors on the wheat yield separately. No one still studied the joint influence of soil characteristics and other factors on the wheat yield. So, in this study, our main focus is to explore the joint influence of these factors on the wheat yield. To explore the influence of these factors on the wheat yield, we will consider the linear regression model and will identify which factors contribute a significant role in the wheat yield. Moreover, we will also evaluate some of the regression assumptions to obtain the reliable results. These assumptions include no multicollinearity, constant error variance, no autocorrelation, no outlier, and influential observation [33, 34]. In this article, we have paid special attention to the regression model diagnostics and its impact on the wheat yield model for the identification of factors. Regression diagnostics include outliers and influential observations analysis which can affect the model estimates and predicted values. With the presence of these values, the fitted model results may indicate the significance of the factors which are playing no role in the response variables and vice versa. 2. Materials and Methods The major food producing province of Pakistan is Punjab and is titled as “bread basket” to feed more than 220 million Pakistanis. Wheat is the main cereal crop produced in Punjab. The investigation zone is in the bond that is made by five rivers of Punjab situated at 30.157 degrees North and 71.524 degrees South with an average elevation of 122 m above ocean level. The region as a zone of about 132.1 km square is partitioned into various tehsils. The normal temperature in the area fluctuates from 20°C to 45°C with normal precipitation of 175 mm a year. This demonstrates that a particular crop cannot be planned to cultivate in the soil for the entire year in the area because climate conditions change drastically. The conditions of this zone in winter are ideal for wheat production. The population size is 2620 acres of this area, where one acre is taken as a single sampling unit. The sample was taken as 655 and computed using appropriate formula. Systematic random sampling technique was used to collect the soil samples. The sample was collected from every fourth acre using 4 as sampling interval. It is necessary to maintain the specific concentrations of organic and inorganic matter in the soil for a good yield of crops. Five hundred grams soil was taken from each selected acre of land to measure the variables specified in Table 1. Then these samples were sent to laboratory of the Agriculture Department of Punjab under Agri-Smart project for the computations of the soil characteristics, where they used the several apparatus. The details of apparatus to measure variables related to soil characteristics are presented in 4 Advances in Materials Science and Engineering Table 1: Apparatus for measuring the soil characteristics Sr. No Variable 1 Saturation percentage 2 Electrical conductivity 3 Power of hydrogen 4 Organic matter 5 Phosphorus 6 Potassium 7 Calcium carbonate 8 Zinc 9 Copper 10 Iron 11 Manganese 12 Boron Apparatus 1. Polythene sheets 2. Spade 3. Soil auger 4. Moisture boxes/cans 5. Balance 6. Oven 7. Ring stand 8. Funnel (glass or plastic) 9. Tubing (to attach to bottom of funnel) 10. Clamp (to secure tubing) 11. Filter paper (to line funnel) 12. Beakers (250 mL) 13. Graduated cylinder 14. Stirring rod (long) 1. Conductivity bridge 2. Vacuum filtration system 1. pH meter with combined electrode 2. Beakers: Preferably use polyethylene or TFE beakers 3. Mechanical stirrer, with inert plastic coating 4. Wash bottle, plastic 1. Magnetic stirrer and teflon-coated magnetic stirring bar 2. Glassware and pipettes for dispensing and preparing reagents 3. Titration apparatus (burette) 1. Spectrophotometer or colorimeter 2. Standard laboratory glassware: beakers, volumetric flasks, pipettes, and funnels 1. Flame photometer with accessories 2. Beakers 3. Pipettes and volumetric flasks, as required for dilution and tests of interference effects 1. Hot plate 2. Burette 3. Erlenmeyer flask 4. Volumetric pipette 1. Atomic absorption spectrophotometer 2. Mechanical shaker, reciprocal 1. Atomic absorption spectrophotometer 2. Mechanical shaker, reciprocal 1. Atomic absorption spectrophotometer 2. Mechanical shaker, reciprocal 1. Atomic absorption spectrophotometer 2. Mechanical shaker, reciprocal 1. Porcelain crucibles 2. Spectrophotometer 3. Polypropylene test tubes Table 1. The factors estimated for each sample of soil attributes incorporate OM, phosphorous (P), potassium (K), and calcium carbonate (CC). The significant micronutrients in the soil that were estimated from each sample include zinc (Zn), copper (Cu), iron (Fe), manganese (Mn), and boron (B). The information related to the utilization of fertilizer, such as DAP, potash, urea, Nitrophos, and nitrogen manures in the land per section of land is also collected from the farmers. The data about the recurrence of pesticides and water systems and strategy for the water system, that is, tubewell water or trench water were gathered. The information about the crop sown before wheat, seed type, that is, coated or uncoated, the technique for cultivating, that is, penetrating or drilling sewing strategy, and utilization of fertilizer in the land were also collected. Further details and descriptions about these factors are given in Table 2. 3. Results Descriptive analysis of all considered variables is given in Table 3. The descriptive statistics include average, standard deviation, coefficient of variation, maximum, minimum, range skewness, and Kurtosis. The average wheat yield in this area is found to be 41.87 mund/acre with a standard deviation of 3.66. The average saturation is 37.75% which Advances in Materials Science and Engineering 5 Table 2: Description of wheat yield and its associated factors. Name of variable Saturation (%) Electrical conductivity (dsm-1) pH Organic matter (%) Phosphorus Potassium Calcium carbonate (%) Zinc Copper Iron Manganese Boron Nitrophos Nitrogen DAP Potash Urea Last crop Water frequency Pesticide frequency Chemical coating of seed Type of water Way of cultivation Usage of compost Wheat yield per acre Notation — EC — OM P K CC Zn Cu Fe Mn B — — — — — — — — — — — — — Nature of variable Continuous Continuous Continuous Continuous Continuous Continuous Continuous Continuous Continuous Continuous Continuous Continuous Discrete (frequency) Discrete (frequency) Discrete (frequency) Discrete (frequency) Discrete (frequency) Discrete (frequency) Discrete (frequency) Discrete (frequency) Categorical Categorical Categorical Categorical Continuous Unit of variable — — — — Ppm Ppm — Ppm Ppm Ppm Ppm Ppm 50 kg per acer 50 kg per acer 50 kg per acer 50 kg per acer 50 kg per acer — — — — — — — Munds Note: Ppm � “parts per million”. Table 3: Descriptive statistics of the consider characteristics. Variables Wheat yield Saturation (%) EC (dsm-1) pH Org. M. (%) Phosphorus (ppm) Potassium (ppm) CC (%) Zinc (ppm) Copper (ppm) Iron (ppm) Manganese(ppm) Boron (ppm) Nitrophos Nitrogen DAP Potash Urea Water frequency Pesticide frequency Average 41.87 37.75 4.24 8.26 0.55 8.20 176.10 6.36 0.78 0.18 4.08 0.89 0.46 0.41 0.51 1.01 0.31 1.92 3.40 1.93 SD 3.66 3.82 3.97 0.29 0.15 3.26 74.81 1.43 0.22 0.02 0.68 0.15 0.01 0.58 0.71 0.50 0.49 0.68 0.70 0.82 CV 0.09 0.10 0.94 0.03 0.27 0.40 0.42 0.23 0.28 0.11 0.17 0.17 0.03 1.41 1.40 0.50 1.60 0.35 0.21 0.43 Minimum 29.00 21.00 0.20 7.20 0.12 1.40 78 2.80 0.10 0.05 0.42 0.07 0.39 0.00 0.00 0.00 0.00 0.00 2.00 1.00 means that the soil of this area is loam which indicated that this soil is suitable for wheat. The average value of EC is 4.24 dS/m depicting that there is slight saline soil which is a favorite for wheat. The average pH of the soil is 8.26 indicating that it is difficult for the plant to obtain phosphorus from the soil. The average amount of OM in the soil is 0.55%, which shows that there is a lack of organic components in the soil. The average amount of phosphorus in the soil is Maximum 50.00 45.00 22.00 9.00 1.09 23.50 380.00 13.20 1.00 0.32 4.93 1.87 0.49 2.00 3.00 3.00 2.00 4.00 5.00 6.00 Range 21.00 24.00 21.80 1.80 0.97 22.10 302 10.40 0.90 0.27 4.51 1.80 0.10 2.00 3.00 3.00 2.00 4.00 3.00 5.00 Skewness −1.41 −4.81 22.18 −1.13 3.73 13.90 1.081 5.37 −12.34 −10.10 −25.64 −20.26 −6.93 11.16 11.97 1.65 12.42 0.14 1.61 7.32 Kurtosis −2.00 −1.98 25.53 −2.66 1.51 14.43 −0.058 6.84 0.86 59.30 36.10 51.24 2.83 0.78 1.68 8.23 1.08 3.37 −0.81 2.54 8.20 ppm which is normal. The average amount of potassium in the soil is 176.10 ppm which is good for the soil to be called fertile. The average zinc is about 0.78 ppm in the soil indicating an intermediate amount of the nutrient. The average copper in the soil was found to be 0.18 ppm, which is a satisfactory amount for the fertility of the soil. The average iron in the soil is 4.08. This indicates the soil’s high fertility. The manganese in the soil on average is 0.89 ppm which is a 6 Advances in Materials Science and Engineering Type of Water 2.8% Previously Sown Crops 6.1% 3.4% 12.1% 39.9% 59.2% 19.3% Cotton Rice Corn 57.3% Cannal water Tube Well Mixture of Cannal and Tube Well Sugarcane Empty Figure 1: Pie chart for previously sown crops. Figure 3: Pie chart for the type of water. Chemical Coating of Seed Wheat Sowing Methods 11.0% 10.7% 45.7% 43.6% Gaup Chatt Method Watar Kashat Method Drilling Method 89.0% Figure 4: Pie chart for wheat sowing methods. Yes No Figure 2: Pie chart for chemical coating of a seed. good amount for the fertility of the soil. Finally, the average amount of boron in the soil is 0.46 ppm indicating enough nutrients in the soil. The skewness of most data distribution was positive, and the highest values of the skewness coefficients were EC and phosphorus. Visconti et al. [33] studying soil saturation extracts in Spain, also found higher positive skewness for the soil potassium and attributed this to the fact that fertilizers may have been applied at a higher concentration at some locations. Negative skewness was observed in some factors such as iron (ppm), manganese (ppm), and zinc (ppm). The summary of some qualitative factors is shown in Figures 1 to 5. Figure 1 shows that cotton was the most common previously sown crop as compared to other crops. From Figure 2, we have found that most of the seeds were chemically coated. Figure 3 displays that most farmers use Usage of Compost 24.9% 75.1% Yes No Figure 5: Pie chart for using compost. Advances in Materials Science and Engineering 7 Table 4: Regression analysis with and without outlier. Term Constant Saturation (%) EC (dsm-1) pH Org. M. (%) Phosphorus (ppm) Potassium (ppm) CC (%) Zinc (ppm) Copper (ppm) Iron (ppm) Manganese (ppm) Boron (ppm) Nitrophos Nitrogen DAP Potash Urea Water frequency Pesticide frequency Last crop Rice Corn Sugarcane Empty Seed chemical coating No Water type Tube well Both (tube well and canal water) Way of cultivation Water kashat method Drilling method Compost use No Full data SE T 6.2800 11.04 0.0335 −4.59 0.0297 2.44 0.4440 5.28 0.7920 1.83 0.0388 −6.78 0.0019 −5.18 0.0829 −5.96 0.5950 −7.97 5.7700 −1.86 0.1670 −2.02 0.7890 −2.71 9.2800 −5.95 0.2110 0.44 0.1690 0.83 0.2430 −0.48 0.2360 −0.22 0.1750 1.70 0.1680 −1.01 0.1360 1.02 P value 0.0000 0.0000 0.0150 0.0000 0.0670 0.0000 0.0000 0.0000 0.0000 0.0630 0.0440 0.0070 0.0000 0.6610 0.4070 0.6310 0.8270 0.0900 0.3110 0.3080 Beta 68.420 −0.145 0.080 2.340 1.862 −0.285 −0.008 −0.558 −4.892 −11.500 −0.357 −1.936 −52.210 0.001 0.069 −0.188 0.036 0.525 −0.277 0.279 0.785 0.299 0.840 0.591 0.2940 0.3680 0.6280 0.4760 2.67 0.81 1.34 1.24 0.0080 0.4170 0.1820 0.2150 0.713 0.493 0.791 0.542 0.2840 0.3590 0.6010 0.4560 2.51 1.37 1.32 1.19 0.0120 0.1700 0.1890 0.2350 −1.031 0.3700 −2.79 0.0050 −0.959 0.3580 −2.68 0.0080 −0.172 −0.350 0.6960 0.7000 −0.25 −0.50 0.8040 0.6170 −0.054 −0.229 0.6660 0.6690 −0.08 −0.34 0.9360 0.7320 0.009 0.369 0.2410 0.3940 0.04 0.94 0.9700 0.3490 0.003 0.308 0.2340 0.3830 0.01 0.8 0.9900 0.4230 −1.218 0.2570 −4.74 0.0000 Beta 69.350 −0.154 0.072 2.345 1.454 −0.263 −0.010 −0.494 −4.740 −10.740 −0.337 −2.137 −55.210 0.092 0.140 −0.117 −0.052 0.298 −0.171 0.139 2 2 F (P value) � 17.75 (0.0000), S � 2.772, R � 45.24%, R (adj) � 40% tube-well water in their wheat fields. Figure 4 indicates that most of the farmers use Gaup Chatt sowing method to grow wheat in this area. From Figure 5, we have found that most farmers did not use compost in their fields before sowing wheat. After the analysis of descriptive statistics, the next step was to identify the contribution of significant variables by fitting a linear regression model to the data of the soil chemical and other characteristics which influence the wheat yield. The results obtained from the linear regression model on full data showed that R2 of the fitted model explained 45.24% of the variability in wheat yield per acre due to the considered soil and other characteristics. The results of the F-test given in Table 4 show that considered variables contribute a 45.24% role in the wheat yield per acre. The adjusted R-squared statistic, which is a more suitable safeguard, used for not overfitting of the regression model with multiple factors, was 40%. The role of the individual factors After deleting SE 6.0800 0.0324 0.0288 0.4330 0.7730 0.0375 0.0019 0.0804 0.5810 5.6600 0.1610 0.7580 8.9500 0.2020 0.1640 0.2360 0.2300 0.1970 0.1630 0.1430 outliers T 11.26 −4.46 2.76 5.41 2.41 −7.6 −4.33 −6.93 −8.43 −2.03 −2.22 −2.55 −5.83 0.01 0.42 −0.8 0.16 2.66 −1.7 1.96 P value 0.0000 0.0000 0.0060 0.0000 0.0160 0.0000 0.0000 0.0000 0.0000 0.0430 0.0270 0.0110 0.0000 0.9950 0.6730 0.4250 0.8750 0.0080 0.0900 0.0510 −1.167 0.2470 −4.72 0.0000 F (P value) � 19.59 (0.0000), S � 2.649, R2 � 48.38%, R2 (adj) � 45.91% in the wheat yield was also explored. To determine the contribution of variables and identification of most significant variables, we use the t-test, and the results are reported in Table 4. It can be seen that saturation (%), EC, pH, phosphorus, potassium, CC, zinc, iron, manganese, and boron were found to be statistically significant factors at a 5% level of significance. Of these factors, zinc was found to be the most significant factor for wheat yield (see t values and its associated p values). The t value on absolute for this factor is larger than the t values of the other considered factors, and it is already indicated in the literature that zinc contributes a significant role in various crop yields [35–38]. The secondmost important factor is soil phosphorous, which contributes a significant role to increase or decrease the wheat yield per acre. The factor previously sown crops (rice), chemical coating of seed (no), and use of compost (no) are statistically significant factors that are increasing the wheat yield. The nutrients organic matter and copper respectively are not play 8 Advances in Materials Science and Engineering Table 5: Residual analysis for the regression based on full data. Observation number Wheat yield 27 38 82 36 135 38 153 35 213 47 302 47 315 37 319 36 366 35 368 38 370 38 388 36 477 50 506 37 517 35 533 38 614 38 617 36 Fit 43.32 41.308 43.36 40.494 41.73 41.454 42.057 41.725 40.427 43.278 43.521 41.558 44.39 42.438 40.519 43.473 43.517 41.291 Resid Std resid −5.32 −2.01 −5.308 −2.02 −5.36 −2.05 −5.494 −2.06 5.27 2.01 5.546 2.03 −5.057 −2.02 −5.725 −2.11 −5.427 −2.01 −5.278 −2.01 −5.521 −2.05 −5.558 −2.09 5.61 2.07 −5.438 −2.0 −5.519 −2.03 −5.473 −2.08 −5.517 −2.05 −5.291 −2.03 a significant role in the growth of wheat yield. As well as the impact of some fertilizers namely Nitrophos, nitrogen, DAP, potash, and urea are not beneficial to some extent as compared to the factors discussed earlier. The regression results are reliable if there, is no outlier in the residual. Checking the presence and identification of outliers is the next step. For this purpose, we used standardized residuals. The evaluation of these residuals is given in Table 5. Table 5 indicates that the observation number 27, 82, 135, 153, 213, 302, 315, 319, 366, 368, 370, 388, 477, 506, 517, 533, 614, 617 are identified as outlier. After identification of these outliers, the output showed the results of a linear regression model to describe the relationship between wheat yield per acre and 13 independents (qualitative and quantitative) variables. Since the p value of the F-test in Table 4 is less than 0.05, there was a statistically significant relationship between the wheat yield and associated factors with the exclusion of substantial values observations. The R2 indicated that the model as fitted explained 48.38% of the variability in wheat yield per acre. The adjusted R-squared statistic, which was more suitable for comparing models with different numbers of independent variables, was 45.91%. The standard error of the estimate showed the standard deviation of the residuals to be 2.649 which was smaller as compared to model fitted variability with full data. Now we explore the role of the individual factors in the wheat yield. It can be seen from Table 4 that saturation (%), EC, pH, organic matter, phosphorus, potassium, CC, zinc, copper, iron, manganese, boron, and urea were found to be statistically significant factors at a 5% level of significance. One more thing is noted, the role of organic matter, copper, and urea was hidden in the full data set due to the outliers, but after removing the outliers, they are statistically contributing a significant role in the wheat yield. Now we discuss the effect of farmer-related factors on wheat yield. One factor that is previously sown crop where several crops were indicated. Of these previously sown crops, rice was the most significant as compared to other previously sown crops which increases the wheat yield. Other previously sown crops also increases wheat yield but not significantly. The second-most important farmer-related factor is chemical coating of the wheat seed which also contributes a significant role in the wheat yield. From Table 4, we observed that the wheat yield of the chemical coating seed was maximum as compared to the wheat yield where the seed is not chemical coated. The use of compost also increases wheat yield. Results indicate that the wheat yield of the land was higher where compost was used than where it was not used. In the similar way, we also study the impact of some fertilizers namely urea, Nitrophos, nitrogen, DAP, and potash on the wheat yield. Table 4 results show that urea fertilizer has a direct influence on the wheat yield while other types of fertilizers are not beneficial to some extent of this land area. Furthermore, water frequency has negative impact on wheat yield, which means that this crop need small water frequency. If we increase the water frequency, then wheat yield may be decreased. Pesticide frequency also has a direct impact on wheat yield. This indicated that several times use of pesticides increases the wheat yield. After removing all outliers, the results of the fitted model as shown in Table 4 were entirely different as compared to the results of the model fitted to the full data model. On comparing the fitted models as given in Table 4, significant results satisfying the regression assumption outliers were found. It was found that the R2 and adj R2 (Adjusted) are increased from (45.24% to 48.38%) and (40% to 45.91%), respectively (Table 4). The standard error of the estimates decreased from (2.772 to 2.649) and indicated better results with satisfying regression assumptions. 4. Discussion All previous studies for the wheat yield model did not give any attention to regression assumptions and all these factors simultaneously. This study focused on the effect of outliers on the regression analysis to identify the factors which affects the wheat yield. Here, we also studied the effect of outliers on the regression assumptions. We have seen that outliers have strongly affected the model estimates. Also, it can be observed that insignificant factors have turned out to be significant after deleting all these outlying values. After considering the regression assumptions, the significant role of organic matter, copper, and urea from fertilizers can be observed. These variables were insignificant when regression assumptions were not satisfied. These results coincide with previous studies [35–42]. The outliers may also be the cause of multicollinearity, heteroscedasticity, and autocorrelation. It is also observed that after deleting outlying observations, the multicollinearity, heteroscedasticity, autocorrelation, and error variance were reduced substantially. Based on our results, it is found that saturation (%), EC, pH, phosphorus, potassium, CC, zinc, iron, manganese, boron, chemical coating of seed, previously sown crops are the significant factors to change the wheat yield. Based on these results, it may be suggested that in all agriculture-related fields, the Advances in Materials Science and Engineering identification and exclusion of outliers is a crucial step for obtaining better results of regression analysis. 5. Conclusion, Limitations, and Future Research There are various factors which affect the crops yields. These factors include soil characteristics and farmer-related characteristics. As our interest is to identify the soil and other factors which influence the wheat yield. Also identify which one factor(s) are most critical to increase wheat yield which can be helpful for farmer. For the identification of such factors, we considered the regression analysis with the evaluation of outliers. When we ignore the presence of outlier, then the role of some important factors is found to be statistically insignificant. When we consider the outlier and exclude from the data, then these insignificant factors now indicate the significant role in the wheat yield. From the results, we found that saturation (%), EC, pH, phosphorus, potassium, CC, zinc, iron, manganese, boron, chemical coating of seed, and previously sown crops are the significant factors to change the wheat yields. Of these significant factors, more important six factors with order of importance are zinc, phosphorous, CC, pH, boron, and saturation. This study considered some factors related to wheat yield, there may be other factors which may be related to wheat yield. These factors may be seed variety, land type, bushels, and so on. As our interest was mainly on soil characteristics and some other additional factors, we are unable to collect the information about these factors. This study can also be extended for other crops, such as maize, rice, and others to identify soil related factors and influence on yield. Moreover, such analysis can also be consider by considering some other regression models such as generalized linear models, nonlinear models, and nonparametric regression model. Data Availability The data used to support the findings of this study are included within the article. Conflicts of Interest The authors declare that they have no conflicts of interest. References [1] Government of Pakistan, “Pakistan Economic Survey 202021. Finance Division,” 2021, https://www.finance.gov.pk/ survey/chapters_21/PES_2020_21.pdf. [2] M. Aslam, “Agricultural productivity current scenario, constraints and future prospects in Pakistan,” Sarhad Journal of Agriculture, vol. 32, no. 4, pp. 289–303, 2016. [3] A. Azam and M. Shafique, “Agriculture in Pakistan and its impact on economy. 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