Correlation and Regressssion - Agricultural Statistical Data Analysis Using Stata - page 201

15

To tal dry matter (t/ha)
Y

10

5

0

100 150 200 250 300

Days from Drilling

Figure 10.15 Barley dry matter yield for days after drilling showing the logistics function.

3-parameter logistic function, yield = b1/(1 + exp(-b2*(days
- b3)))
----------------------------------------------------------------
yield | Coef. Std. Err. t P>|t| [95% Conf. Interval]
----------+-----------------------------------------------------
/b1 | 13.54067 .2885517 46.93 0.000 12.92896 14.15237
/b2 |.0864115 .0082196 10.51 0.000 .0689866 .1038363
/b3 |227.9791 1.235012 184.60 0.000 225.361 230.5972
----------------------------------------------------------------

This logistic function fits well with an R 2 value of 0.9964 with all
three coefficients having a significant t value (Figure 10.15). The fit-
ted equation is Y = 13.54067/(1 + e -0.0864115(x-227.9791) ). Enter the follow-
ing command to see the data and the plotted function:

twoway (scatter yield days ) (function y = 13.54067/
( 1+exp ( -.0864115*(x-227.9791 ))), range ( days ))

It should be pointed out, however, that both commands nl
gom4: yield days and nl gom3: yield days give reason-
ably good results as well. This brings up an important point, that
fitting data to a specific function should make reasonable sense from
a biological perspective. The nl command can fit a wide range of
functions, but does the chosen function make sense? In this case,
any of the three functions would probably be adequate in under-
standing the underlying data.