Log mode changes the strategy that the calculator uses to fit regression parameters. By default, regression parameters are chosen to minimize the sum of the squares of the differences between the data and the model predictions. When you work in log mode, the calculator applies a transformation to the data and the model before fitting the parameters so that the model becomes linear.
You can use log mode for the following forms:
- Exponential: \(y_{1}\sim ab^{x_{1}}\), \(y_{1}\sim a\exp\left(bx_{1}\right)\), \(y_{1}\sim2^{ax_{1}+b}\)
- Power Law: \(y_{1}\sim ax_{1}^{b}\)
- Logarithmic: \(y_{1}\sim a\ln\left(x_{1}\right)+b\)
When you work in log mode, the \(r\) and \(r^{2}\) statistics are calculated according to the transformed data, but the residuals are calculated according to the untransformed data.
Compatibility with Other Tools
Several other math software systems use procedures similar to those in log mode by default. For example, TI calculators use logarithmic transformations for ExpReg, PwrReg, and LnReg. GeoGebra uses them for FitExp, FitGrowth, FitLog, and FitPow. Excel uses them for Exponential and Power regression lines. Enabling log mode in Desmos makes it easier to compare answers with these systems.
Why Doesn't Desmos Use Log Mode by Default?
Many math software systems only allow regressing a handful of models and have different function names for each model.
Desmos is more flexible. You can use any relation between lists of data for a regression model. For example, after regressing a model of the form \(y_{1}\sim ax_{1}^{b}\), you can immediately check the effect of adding a constant by changing the model to \(y_{1}\sim ax_{1}^{b}+c\).
The first model can be linearized by a logarithmic transformation, but the second model cannot. Desmos defaults to using least squares regression without transforming the data so that the procedure used to fit these two models is the same.
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