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Agronomy Journal Abstract -

Determination of Input Levels for a Selected Probability of Response on a Curvilinear Regression Function1


This article in AJ

  1. Vol. 59 No. 2, p. 161-162
    Received: July 14, 1966

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  1. W. M. Walker and
  2. S. G. Carmer2



A method was developed relating the probability of obtaining a further increase in a selected dependent variable with an increased level of input of the independent variable. For the technique presented a curvilinear regression model was assumed.

The technique principally involves equating the ratio of the square of the first derivative and its variance to an F ratio. A similar equation obtained by equating the ratio of the first derivative and its standard error to t was also suggested.

The solution of either equation for X, the input factor, results in a value above which the probability of being in error by rejecting the null hypothesis is greater than α, the selected probability level. At any input value less than X, the probability of being wrong in rejecting the null hypothesis is less than α.

An example demonstrating the applicability of this concept to a fertilizer response function was shown.

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