Correlation and Regressssion - Agricultural Statistical Data Analysis Using Stata - page 199

Y = 0.9462218*X - 0.0019585*X 2 + 38.53506

200

150

100

Yield
Y

50

0

0 100 200 300

Figure 10.13 Graph of onion yield with the corresponding quadratic equation.

he R 2 value is very good at 0.8576 and all three coefficients have
a significant t-value. To see these results graphically, enter the follow-
ing command and see the resulting graph:

twoway (scatter yield nrate ) (function y =.9462218*x
-.0019585*x^2 + 38.53506 , range( nrate ))

Using the fit plots category for a quadratic equation with a confidence
interval ( qfitci ) will result in the same curve with a confidence
interval (Figure 10.13). The command to enter is

twoway (qfitci yield nrate ) (scatter yield nrate )

For presentation purposes, you may wish to collapse the dataset aver-
aging the yield data by nitrogen rate and then construct the graph.
This makes for a cleaner presentation and does not detract from the
results. The order in the command also is important; entering the
(qfitci yield nrate ) first ensures the quadratic curve and
confidence interval appears behind the data points (Figure 10.14).
Reversing the order, putting (scatter yield nrate ) first hides
some of the data points behind the confidence interval.
Additional power terms can be added, such as the third, fourth
power, etc., and although the equation it may improve it really
doesn't add any more to the understanding of the underlying data. A
yield curve such as this with increasing amounts of nitrogen fertilizer