## Render Google Maps Tiles with Mapnik and Python

If you want to take a bunch of GIS data and rasterize it as a tiled image map for public consumption, the folks at ESRI would be happy to sell you an expensive solution. Of course, as with oh-so-many projects, you can accomplish the same thing for free with open-source software. In this case, we'll use Python and a library called Mapnik to render beautiful map layers, then display them on Google Maps, just like this demo rendering of my home county!

Ready to get started? Dust off your Python skills, and let's go!

## Project Mean Customer Lifetime by Modeling Churn

In a past post on analyzing churn in the subscription or Software as a Service business, I talked about two different ways to quantify the dollar cost of churn. You could use 1 / churn as an estimation of mean customer lifetime (though this simple method makes a lot of assumptions). Or, you could use “pseudo-observations” to calculate the dollar value of certain groups of customers during a particular time period (which doesn’t let you quantify the full lifetime value of a customer).

But what if there was another way? What if we took our Kaplan-Meier best estimate of our churn curve, fit a linear model to that model, and then projected it out?

A model within a model, if you will. Churnception.

Well, as it turns out, we’d get a reasonable estimation of our lifetime churn curve, which would let us estimate average customer lifetime, and customer lifetime value. Let’s get started.

## Identifying Trends in SQL with Linear Regression

One of the best ways to learn how a statistical model really works is to code the underlying math for it yourself. Today, we’re going to do that with simple linear regression.

In the book Data Smart, John Foreman introduces a bunch of awesome methodologies by walking you through how to build them in Excel…

Of course, doing regression in SQL also has (some) practical use as well! For example, suppose you wanted to identify which city in a database of temperature records had the biggest warming trend in the last month. This method would send you on your way without having to bring your data into an external tool. Nifty!