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0001 NIST/ITL StRD 0002 Dataset Name: Rat42 (Rat42.dat) 0003 0004 File Format: ASCII 0005 Starting Values (lines 41 to 43) 0006 Certified Values (lines 41 to 48) 0007 Data (lines 61 to 69) 0008 0009 Procedure: Nonlinear Least Squares Regression 0010 0011 Description: This model and data are an example of fitting 0012 sigmoidal growth curves taken from Ratkowsky (1983). 0013 The response variable is pasture yield, and the 0014 predictor variable is growing time. 0015 0016 0017 Reference: Ratkowsky, D.A. (1983). 0018 Nonlinear Regression Modeling. 0019 New York, NY: Marcel Dekker, pp. 61 and 88. 0020 0021 0022 0023 0024 0025 Data: 1 Response (y = pasture yield) 0026 1 Predictor (x = growing time) 0027 9 Observations 0028 Higher Level of Difficulty 0029 Observed Data 0030 0031 Model: Exponential Class 0032 3 Parameters (b1 to b3) 0033 0034 y = b1 / (1+exp[b2-b3*x]) + e 0035 0036 0037 0038 Starting Values Certified Values 0039 0040 Start 1 Start 2 Parameter Standard Deviation 0041 b1 = 100 75 7.2462237576E+01 1.7340283401E+00 0042 b2 = 1 2.5 2.6180768402E+00 8.8295217536E-02 0043 b3 = 0.1 0.07 6.7359200066E-02 3.4465663377E-03 0044 0045 Residual Sum of Squares: 8.0565229338E+00 0046 Residual Standard Deviation: 1.1587725499E+00 0047 Degrees of Freedom: 6 0048 Number of Observations: 9 0049 0050 0051 0052 0053 0054 0055 0056 0057 0058 0059 0060 Data: y x 0061 8.930E0 9.000E0 0062 10.800E0 14.000E0 0063 18.590E0 21.000E0 0064 22.330E0 28.000E0 0065 39.350E0 42.000E0 0066 56.110E0 57.000E0 0067 61.730E0 63.000E0 0068 64.620E0 70.000E0 0069 67.080E0 79.000E0