By Kardi Teknomo, PhD .


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Data: Logarithmic Curve

Suppose we would like to try that our model would be logarithmic Logarithmic Curve . Using model transformation Logarithmic Curve and Logarithmic Curve we obtain

Logarithmic Curve

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.

Logarithmic Curve Logarithmic Curve

Plotting ln x and y, we get linear model of Logarithmic Curve 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 Logarithmic Curve and Logarithmic Curve . In this case, we have Logarithmic Curve or Logarithmic Curve . Thus, the regression line is Logarithmic Curve 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.

Logarithmic Curve

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See Also : Regression tutorial , Power Rules , Logarithm Rules , Kernel Regression

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