Correlation and Regressssion - Agricultural Statistical Data Analysis Using Stata - page 197

Y = 4.4804992*1.2200072 ^ X

20

15

10

Height (cm)
y

5

0 2 4 6 8

Figure 10.11 Cabbage plant height fitted with exponential function.

The fit is very good with an R 2 value of 0.9977 (Figure 10.11). Taking the
antilog of the linear equation results in Y = 4.4804992*1.2200072 x . he
two numbers are 10 raised to the power of the coefficients (0.6513264
and 0.0863624). This can be plotted with the following entry:

twoway (scatter height week) (function y =
4.4804992*1.2200072^x, range ( week ))

Along with linear functions, there also can be functions that are
referred to as polynomial functions that have the general expression
of (Figure 10.11):

Y = a + bX + cX 2 + dX 3 + …

These functions can have as many terms as one less than the total
number of treatments. Usually the more terms the better the fit (greater
R 2 ), but this can be misleading and difficult to interpret in a biological
sense. The first term, bX , is referred to as the first-degree term and is
nothing more than the linear function ( Y = a + bX ). he second term
( cX 2 ) is the second-degree term or the quadratic equation ( Y = a + bX
+ cX 2 ). The next is the third-degree term or the cubic equation and
the fourth-degree term is referred to as the quartic equation. Usually
the first, second, or third term equations are evaluated because there
can be some biological basis for these. Higher order equations (i.e., 4,
5, 6, etc.) although possible to calculate are difficult or impossible to
interpret in a biological or agricultural context.