NIST/ITL StRD

Dataset Name:  Rat42             (Rat42.dat)

File Format:   ASCII

               Starting Values   (lines 41 to 43)

               Certified Values  (lines 41 to 48)

               Data              (lines 61 to 69)

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 pasture yield, and the

               predictor variable is growing time.

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

               Nonlinear Regression Modeling.

               New York, NY:  Marcel Dekker, pp. 61 and 88.

Data:          1 Response  (y = pasture yield)

               1 Predictor (x = growing time)

               9 Observations

               Higher Level of Difficulty

               Observed Data

Model:         Exponential Class

               3 Parameters (b1 to b3)

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

          Starting Values                  Certified Values

        Start 1     Start 2           Parameter     Standard Deviation

  b1 =   100         75            7.2462237576E+01  1.7340283401E+00

  b2 =     1          2.5          2.6180768402E+00  8.8295217536E-02

  b3 =     0.1        0.07         6.7359200066E-02  3.4465663377E-03

Residual Sum of Squares:                    8.0565229338E+00

Residual Standard Deviation:                1.1587725499E+00

Degrees of Freedom:                                6

Number of Observations:                            9 

Data:   y              x

       8.930E0        9.000E0

      10.800E0       14.000E0

      18.590E0       21.000E0

      22.330E0       28.000E0

      39.350E0       42.000E0

      56.110E0       57.000E0

      61.730E0       63.000E0

      64.620E0       70.000E0

      67.080E0       79.000E0