Vergara - 1976 - Physiological and morphological adaptability of ri

406 ctnvrara AND RICE
If subsequent examination of the fitted regression equation indicated that
(1) it xvas significant, (2) it explained an acceptable proportion of total variation
about the mean Y, (3) the standard error of the estimate was reasonably
small, and (4) that there were no discernible patterns in the residuals. the
equation ‘was accepted. If these criteria were not met. the model was altered by
expanding it to a higher order (second. third, etc), introducing new variables
developed from cross products of existing independent variables. and/or transforming
the Y variable. This process was continued until an acceptable model
was developed.
The variance of Y in each case was calculated using the formula
Variance Y = V(b.,) + X,=V(b,) + . . . . . . + X,.=W(b‘,) +
2X,C()\"flf(b,,,b,) + . . . . . . + 2X,» (Xfiovar (by ,b,)
When regression analysis methods were not appropriate in developing a
model. and when plots of data indicated a logistic or sigmoidal response with
time, the Inhibited Growth Model or Logistic Equation (Stein, I968) was
utilized. This model assumes that as a population P increases, its growth rate
may be forced to decline as the population approaches a maximum M. The
equation
P:
MP,
mo]
+ (M _ pow-ta.
where t is a time interval. Po is the size of the population at time 0. P is the size
of the population at time t, M is the maximum size attainable by the population,
and k is a positive constant, provides a close approximation of this type of
population growth,
The constant k may be approximated by the equation
dt
=-
kP(M—P)
Sporulation. Adequate predictive equations for spore produetion/mml lesion
were developed for each of the three dew temperature (DT)-dew period (DP)
combination segments. In each case. a ‘Y transformation of the dependent
variable was necessary. The results for each segment are
24-hour dew period-all dew temperatures
Y = 3.383 = .228 (DT) + 00005 (DPDT)=
R1 = .94 Standard error of estimate = .2343
Variance Y = 1.322 + .013 (DT)= — .129 (ZDT)
30°C dew temperature-less than 24 hours dew
Y =
[.467 + .2625(DP)
R1 = .99 Standard error of estimate = .408
Variance Y = .014 + .00005(DP)= — .001 (ZDP)