I wanted to ask a question about manipulating the data set of x-values to give a linear plot.
I was studying a reaction as part of a chemical reaction and asked to plot conductivity over time. Some sample data is shown below.
The x-values of the data points follow an exponential relationship with $n$ i.e.
xarray1 = [1, 4, 9, 16, 25, 36, 49, 64]
yarray = [100, 200, 300, 400, 500, 600, 700, 800]
But I was asked as part of my analysis to square root each x-value and plot the graph again to give a graph as shown below:
xarray2 = asarray(xarray1) ** 0.5
As a chemistry student, I'm slightly confused as to why the linearisation of the graph takes place.
My reasoning was that the points are now equidistant as they would now observe an $n+1$ relationship but for the following data set:
xdata3 = [305.5, 607.5, 1500.5, 2401.5, 3004.5]
where the square root observation no longer represents a direct $n+1$ sequential relationship, the same effect is also seen.
Why does this linearisation happen when I plot $y$ as a function of $x^{\frac{1}{2}}$ instead of $y$ against $x$?