Uncertainties in Fitted Parameters

However, if the fitting of the model to the experimental points is done manually by, for example, using a spreadsheet program, the method is rather convenient. In this method, for each experimental point, the entity Ai is calculated according to Eq. (3.28). The sum of these AI is then taken as the minimisation parameter with the desired constants as minimisation variables. Once the minimum sum of A/,- is obtained, the optimal values of the fitted constants can be noted  

Each parameter value in the model has to be changed step by step from its best-fit value, and the respective increase in has to be followed until is twice its minimum value. The difference between a parameter s best-fit value and its value corresponding to two times the minimum value is an estimate for the parameter variance. The square root of that difference is assigned to the parameter as its standard deviation. 

The weighting parameter /t in Eq. (3.28) is, as pointed out earlier, difficult to obtain. Different approaches exist for its selection. The most common is to simply use the actual value of the experimental point. This will ensure that each point on the curve will be important in the fit. This is especially important if the value range is large. For small value ranges, the use of k as unity is not uncommon. 

---