Potassium fertilizer requirement of rain-fed cotton was evaluated in a 3-yr field study conducted at three locations using four rates (0, 25, 50 and 75 kg∙ha−1)of K. Significant response was not obtained above 25 kg∙ha−1 applied K. Quadratic polynomials, using leaf K, exch. K, exch. (Ca + Mg)/K and applied K as independent variables, were fitted to the seed-cotton yield. As a single parameter, leaf K emerged the best predictor of yield with a coefficient of multiple determination (R2) of 86% and a corresponding regression equation of: Y (yield) = 3099.2 + 6031.6%K − 1643.3 (%K)2, followed by fertilizer K with a coefficient of multiple determination of 81% and a yield equation of: Y = 1302.3 + 53.96 app. K − 0.54 (app. K)2. Soil exch. K and (Ca + Mg)/K ratio were slightly less efficient in predicting yield giving R2 values of 0.62 and 0.76, respectively, when both the linear and quadratic terms were entered into their respective yield equations. When all the 12 possible entries (linear, and second-order terms and their square root transformations) were fed into the computer and regressed over cotton yield using a step-wise regression procedure, only two variables, leaf %K and (Ca + Mg)/K, significantly fitted the yield equation giving a predictive value of 87%. But the improvement in the precision of yield predictability as measured by the R2 value was only marginal and would not justify recommending the equation considering the extra laboratory work that will be needed to obtain the relevant variables. Critical values of 1.84% in index leaf, 0.19 meq/100 g exch. K and 50 kg∙ha−1 applied K were approximated for a maximum predicted yield range of 2440–2700 kg∙ha−1.
Distribution of polynomials with cycles of a given multiplier
