Piecewise regression analysis of rice yield trends in Manipur

Introduction

Rice (Oryza Sativa) is the third most significant crop in the World after sugarcane and corn [World Population Review, 2024 [1] , Saha et al., 2021] [2]] . It is a staple food of our region Manipur with the state ranking second only to Assam in rice production among the Northeastern states of India. Consequently, half of the valley's total area, which is home to 67% of the state's population, is dedicated to agricultural activities [Singh et al., 2023] [3] . Owing to the intensive cultivation of rice in Manipur, a systematic study and a proper analysis as well as a critical observation on the trend of production of rice is highly relevant. Due to lack of reliable data, the existing studies are not directly utilized to this region, and therefore, they should be modified to suit the specific socioeconomic, agro-climatic, and different topographical conditions of Manipur. In this regard, a scientific report with statistical analysis of rice crops, based on available data, will be highly valuable for the state's socio-economic development and future planning initiatives [Mog et al., 2017] [4] .

Materials and Methods

1. Time series secondary data from the year 1980 to 2022 were collected from the Department of Economic &Statistics, Govt. of Manipur [Anonymous, 2022] [5] . 2. Statistical model [Montgomery et al., 2012] [6] The piecewise linear regression model is used for this analysis and is defined as 𝑌 𝑖 = 𝑏 0 + 𝑏 1 𝑋 𝑖1 + 𝑏 2 (𝑋 𝑖1 -𝑋 (𝑘) )𝑋 𝑖2 + 𝜀 𝑖 This may also be written as

The above model simplifies to:

If 𝑖𝑓 𝑋 𝑖1 ≤ 𝑋 (𝑘) , the model can be written as

𝐼𝑓 𝑋 𝑖1 ≥ 𝑋 (𝑘) , the model can be written as

Results and Discussion

The findings indicated that the breaking point revealed a prominent change in the rate change of variation in the trend values of rice production and area. The "Knot value 2015" indicates that increased in production up to the year 2015 and decreased from there onwards. In the area of rice cultivation, the breaking point is 1994, where a decreasing trend was observed up to 1994 with an increasing trend thereafter (Table 1). It was observed that the positive regression coefficient 𝑏 1 (5.361) indicates increased in rice production until 2015. But there was a decrease in rice production from 2015 onward, as indicated by the negative coefficient 𝑏 2 (-3.616). The small p-value (< 0.05) indicates that the coefficient 𝑏 0 and the 𝑏 1 are statistically significant, revealing a meaningful impact on rice production.

However, the 𝑏 2 coefficient is not statistically significant (Table 2). The value of RSE (60.4) was acceptable as compare to the range of rice production. The R value of 0.734 reveals that 73.4% of the variation in rice production is explained by the independent variable. Independent variables effectively explain the variation in the dependent variable (𝑌 𝑖 ) as indicated by the significant F-value (Table 3). The significant value of F revealed that the amount of information supplied by the independent variable about the dependent variable is effective (Table 4). It confirmed that the independent variables collectively have a statistically significant influence on the dependent variable of rice production. The cultivated area under rice decreased until 1994 as indicated by the negative regression coefficient 𝑏 1 (-1.1966). However, from the year 1994 onwards, the positive coefficient 𝑏 2 (2.0937) shows an increased in cultivated area. The small p-value (< 0.05) revealed that the coefficients 𝑏 0 , 𝑏 1 and 𝑏 2 are statistically significant, demonstrating a meaningful impact on cultivated area (Table 5). The value of RSE (6.572) was acceptable given the range of the cultivated area. An R value of 0.735 indicates 73.5% of the variation in rice area explained by the independent variable. The significant value of F indicates that the independent variables accurately explain the dependent variable (𝑌 𝑖 ) (Table 6). The ANOVA table revealed that the significant value of F illustrates the effectiveness of the information provided by the independent variables (past value of cultivated area) in explaining the dependent variable of cultivated area. The result also confirms that the independent variables collectively have a statistically significant impact on the dependent variable [Montgomery et al., 2012] [6] (Table 7) (Fig. 1, Fig. 2). The present investigation showed that the significant value of F due to rice production and the cultivated area respectively indicates that the amount of information supplied by the independent variable is effective.

References

1. World Population Review. Rice production by country 2024. World Population Review; 2024.
2. Saha I, Durand-Morat A, Nalley LL, Alam MJ, Nayga R. Rice quality and its impacts on food security and sustainability in Bangladesh. PLoS One. 2021;16(12):e0259729.
3. Singh TM, Singh SG, Sen A, Sharma A. Status and dimension of rice production in Manipur: An analysis of the yield gap. AMA, Agricultural Mechanization in Asia, Africa and Latin America. 2023;54(06).
4. Mog K, Singh SH, Majumder A. A statistical study on pineapple in North-Eastern states of India for sustainable policy development. RASHI Journal of Society and Applied Statistics in Agriculture. 2017;2(2):46-51.
5. Anonymous. Economic Survey 2021-2022: Statistics and growth figures year-wise of Manipur. Indiastat; 2022.
6. Montgomery DC, Peck EA, Vining GG. Introduction to linear regression analysis. 5th ed. Hoboken (NJ): John Wiley & Sons; 2012.