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The research work entitled “Application of response surface methodology for optimal yield of transplanted rice (Oryza Sativa L.)” was carried out at Cheruniyoor panchayat of Varkala in Tiruvananthapuram district and College of Agriculture, Vellayani during 2019-2021. The objective was to the development of response surface model using Central Composite Design (CCD) to optimize N, P and K of transplanted rice and to develop a web based application for Response Surface Methodology (RSM). A CCD experiment was conducted with 15 treatment combinations in 3 replications using the rice variety (Uma (MO16)) during the mundakan season as second crop. The grain yield and straw yield data were as the source of primary data which was used for analysis.
The analysis was initiated by finding the high and low levels of the central value taken for the studies which was 90:45:45 NPK kg ha-1. The levels were selected on the basis of previous studies and soil tests conducted. Since three factors were chosen for the experiment, α value of ±1.682 was considered. The experiment was conducted using these and observations were found for grain yield and straw yield. The average grain yield, straw yield and harvest index were found to be 5792 kg ha-1, 7578 kg ha-1 and 0.43 respectively with a standard deviation of 934.63 for N, 749.98 for P and 0.026 for K.
From analysis, it was found that the multiple R2 for grain yield was 0.89 which was closer to 1 indicating that there is a high correlation between the response variable and the predictor variables while the adjusted R2 was 0.80 representing that the model fitting was good. The predicted R2 was 0.69 i.e., it can predict 69% of new observations for the regression model. The predicted R² of was in reasonable agreement with the adjusted R²; i.e., the difference is less than 0.2. In the case of straw yield (Y2), it was found that there were no significant and the lack of fit value of 0.1046 implied that the model fitting was not good enough.
The response model was estimated using R for grain yield. The best model Y was selected based on the lack of fit and R2 values.
𝑌̂ = 6281.62 + 462.271N*+ 546.27P* + 636.12K* + 66.75N*P* + 98.25N*K*
+ 285.75P*K* -109.08N*2 -331.20P*2-281.88K*2
Where N*, P* and K* are the coded variables and
N*= (N-90)/18
115
P* = (P-45)/18
K* = (K-45)/18
From the model it was found that N*, P*, K*, P*², K*² were significant model terms. The model in overall is a significant one with a lack of fit of 0.59 (>0.05).
The stationary points for grain yield were determined which is the point of determination of maximum, minimum or saddle points. In this experiment, the optimum levels were found to be beyond our range of interest i.e., outside the fixed domain of -α and +α. Hence, the ridge analysis was performed where the optimal solutions are found within a particular radius of the stationary points. They were 94 N, 62 P and 65 K; 101 N, 65 P and 69 K and 109 N, 69 P and 73 K for 7295 kg ha-1, 7630 kg ha-1 and 7930 kg ha-1 respectively.
Among these the most feasible solution both physically and economically were 109 N, 63 P and 73 K i.e., in terms of maximisation of yield and cost.
In order to develop the RSM for CCD, a web application for experimental runs required for Circumscribed CCD and Inscribed CCD with 2, 3 and 4 factors were developed initially. The application was developed using the R codes and the server used was R Shiny. In addition, the method of estimating the Response surface models and optimum levels of factors were involved. The stationary points are also generated for the factors and ridge analysis when required.
The results of the RSM analysis using CCD concluded that the optimum doses of N, P and K for transplanted rice for variety Uma (MO16) was 93.690, 62.388 and 65.178 Kg ha-1 respectively. A web application for RSM with CCD for factors ranging from 2 to 4 was also developed using R.

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