Understanding Linear-Log Plots & Their Uses

[jimmy1]

What is meant by a linear-log plot and why is it used?

In the book I have, the author is demonstrating that some data fits an exponential distribution. So what he does is a linear-log plot of both the exponential distribution and the empirical data, and then overlaps the 2 graphs so show they follow a similar path.

So my question is, what exactly is a linear-log plot, and when/why do you use it?
For exmaple, if I was to show the data fitted an exponential distribution, I would just plot the data and exponetial distribution as they were, and overlap them and show they fit (or don't fit).

 

[HallsofIvy]

If you have data that happens to lie close to a curve of the form y= A log(x)+ B, (conversely, $x= e^{\frac{y-B}{A}$) then Plotting y against "X= log(x)" rather than x itself puts the points close to the straight line y= AX+ B. Yes, you could overlap your raw data and an exponential (if you were sure of the constants involved) and show that they matched but it is typically much easier to spot a straight line than more complex curves and there are standard formulae for the "best fit" line.

 

[tacman]

A linear-log plot is a type of graph where one axis is plotted on a linear scale and the other axis is plotted on a logarithmic scale. This means that the values on the logarithmic axis increase exponentially, while the values on the linear axis increase linearly. This type of plot is often used when there is a large range of values in the data being plotted, as it allows for a more accurate representation of the data.

In your example, the author used a linear-log plot to compare the exponential distribution and the empirical data because the exponential distribution follows an exponential growth pattern, meaning that the values increase exponentially. By plotting it on a linear-log scale, the data points will appear to be more evenly spaced, making it easier to see the overall trend and compare it to the empirical data.

Linear-log plots are also commonly used in science and engineering to plot data that follows an exponential or power law relationship. This is because these types of plots make it easier to visualize and analyze the data, as the logarithmic scale compresses the large range of values into a more manageable scale.

Overall, linear-log plots are a useful tool for representing data that varies greatly in magnitude and are particularly helpful in identifying patterns and trends in data that follow exponential or power law relationships.