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NonLinear Regression: Logarithmic Curve
Data:
Suppose we would like to try that our model would be logarithmic . Using model transformation and we obtain
Its mean we need to take the natural logarithm to the value of x in our data and then plot into semi logarithm paper. If the data is fitted with logarithm curve, we will obtain a straight line with high degree of Rsquared. The computation of natural log and semi logarithm plot is given below.
Plotting ln x and y, we get linear model of with Rsquared of 0.9768.
Thus, the data also fits into logarithm curve. The parameters of the logarithm curve can be obtained from the linear model using parameter transformation and . In this case, we have or . Thus, the regression line is with the same Rsquared of 0.9768.
The plot of logarithmic curve (dash red line in figure below) produces quite good result with Rsquared 0.9768.
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See Also : Regression tutorial , Power Rules , Logarithm Rules , Kernel Regression
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