1NIST/ITL StRD 2Dataset Name: Rat42 (Rat42.dat) 3 4File Format: ASCII 5 Starting Values (lines 41 to 43) 6 Certified Values (lines 41 to 48) 7 Data (lines 61 to 69) 8 9Procedure: Nonlinear Least Squares Regression 10 11Description: This model and data are an example of fitting 12 sigmoidal growth curves taken from Ratkowsky (1983). 13 The response variable is pasture yield, and the 14 predictor variable is growing time. 15 16 17Reference: Ratkowsky, D.A. (1983). 18 Nonlinear Regression Modeling. 19 New York, NY: Marcel Dekker, pp. 61 and 88. 20 21 22 23 24 25Data: 1 Response (y = pasture yield) 26 1 Predictor (x = growing time) 27 9 Observations 28 Higher Level of Difficulty 29 Observed Data 30 31Model: Exponential Class 32 3 Parameters (b1 to b3) 33 34 y = b1 / (1+exp[b2-b3*x]) + e 35 36 37 38 Starting Values Certified Values 39 40 Start 1 Start 2 Parameter Standard Deviation 41 b1 = 100 75 7.2462237576E+01 1.7340283401E+00 42 b2 = 1 2.5 2.6180768402E+00 8.8295217536E-02 43 b3 = 0.1 0.07 6.7359200066E-02 3.4465663377E-03 44 45Residual Sum of Squares: 8.0565229338E+00 46Residual Standard Deviation: 1.1587725499E+00 47Degrees of Freedom: 6 48Number of Observations: 9 49 50 51 52 53 54 55 56 57 58 59 60Data: y x 61 8.930E0 9.000E0 62 10.800E0 14.000E0 63 18.590E0 21.000E0 64 22.330E0 28.000E0 65 39.350E0 42.000E0 66 56.110E0 57.000E0 67 61.730E0 63.000E0 68 64.620E0 70.000E0 69 67.080E0 79.000E0 70