Non-Linear Regression: Logarithmic Curve
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 R-squared. The computation of natural log and semi logarithm plot is given below.
Plotting ln x and y, we get linear model of with R-squared 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 R-squared of 0.9768.
The plot of logarithmic curve (dash red line in figure below) produces quite good result with R-squared 0.9768.