Data science simplified: Understanding log-log regression models

In the last few articles of this series, we’ve discussed simple linear regression models, multivariate regression models, and methods for selecting the right model.

In our example, Fernando has experimented with creating a model and has optimized to find the best one.

Now, Fernando wants to know the following:

• How can I estimate the price changes using a common unit of comparison?
• How elastic is the price with respect to engine size, horsepower, and width?

In this article, I will address these questions and elaborate on log-log regression models.

The concept

To explain the concept of the log-log regression model, we need to take two steps back. First, we need to understand the concepts of derivatives, logarithms, and exponentials. Then, we need to understand the concept of elasticity.

Derivatives

Meet derivatives, one of the most fascinating concepts taught in high school math and physics.

Derivatives are a way to represent change and are the amounts by which a function is changing at any given point.

Here, a variable y is a function of x. We define y as y = f(x).

When we apply derivative on y, the equation is:

dy/dx = df(x)/dx = f(x)

This shows the change in y with respect to the change in x (i.e. how much will y change if x changes?).

Bringing it all together

Model building

Model evaluation

Conclusion

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