NIST/ITL StRD

Dataset Name:  Rat43             (Rat43.dat)

File Format:   ASCII

               Starting Values   (lines 41 to 44)

               Certified Values  (lines 41 to 49)

               Data              (lines 61 to 75)

Procedure:     Nonlinear Least Squares Regression

Description:   This model and data are an example of fitting  

               sigmoidal growth curves taken from Ratkowsky (1983).  

               The response variable is the dry weight of onion bulbs 

               and tops, and the predictor variable is growing time. 

Reference:     Ratkowsky, D.A. (1983).  

               Nonlinear Regression Modeling.

               New York, NY:  Marcel Dekker, pp. 62 and 88.

Data:          1 Response  (y = onion bulb dry weight)

               1 Predictor (x = growing time)

               15 Observations

               Higher Level of Difficulty

               Observed Data

Model:         Exponential Class

               4 Parameters (b1 to b4)

               y = b1 / ((1+exp[b2-b3*x])**(1/b4))  +  e

          Starting Values                  Certified Values

        Start 1     Start 2           Parameter     Standard Deviation

  b1 =   100         700           6.9964151270E+02  1.6302297817E+01

  b2 =    10           5           5.2771253025E+00  2.0828735829E+00

  b3 =     1           0.75        7.5962938329E-01  1.9566123451E-01

  b4 =     1           1.3         1.2792483859E+00  6.8761936385E-01

Residual Sum of Squares:                    8.7864049080E+03

Residual Standard Deviation:                2.8262414662E+01

Degrees of Freedom:                                9

Number of Observations:                           15 

Data:   y          x

      16.08E0     1.0E0

      33.83E0     2.0E0

      65.80E0     3.0E0

      97.20E0     4.0E0

     191.55E0     5.0E0

     326.20E0     6.0E0

     386.87E0     7.0E0

     520.53E0     8.0E0

     590.03E0     9.0E0

     651.92E0    10.0E0

     724.93E0    11.0E0

     699.56E0    12.0E0

     689.96E0    13.0E0

     637.56E0    14.0E0

     717.41E0    15.0E0