Forecasting SEM ROI with Eureqa

There is a is powerful tool to detect equations and hidden relationships among the data sets.  What makes it irresistible tool is its cost - FREE!.  It is Eureqa.  In this blog I will explain how to find relationship between cost and long term revenue for a keyword campaign in Google Adwords.  This is a simplied version of identifying a relationship at macro level and then drilling down further to identify more details.

The sample I have taken is over two months summarized data at daily level for a campaign.  Since cost and revenue are affected by other factors including the keywords or ad words that comprised a campaign, competitors' bidding, landing page or page optimizations, etc., it is important to note that the following is to get a quick insight into how cost is related to revenue for a particular campaign.  This is one of important arsenal out of few to get better positive ROI.

The data set is shown below in the application's tab 1(Enter Data).  This very much looks like Excel spreadsheet!.  First column is cost and second is long term revenue.

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Numbers above (from 1 to 5) points to different tabs I refer to in the article.  Once the data is loaded into respective columns, name the cost column as x and revenue column y and then move to tab 2 (Smooth Data). You can enable smoothing and in the lower panel you will see y vs x curve.  In tab 3 (Pick Modeling Task), select typical operations like subtract, multiple, divide, power, exponential and logarithm that will be used in creating the formula.  I typically leave out sine, cosine and absolute value.

Also, it is important to note that for some reason the application default formula selection is x = f(y).  But in a typical situation the formula is written as y = f(x).  So if you select x as the independent variable and y as dependent variable, once after the application provides the final formula you can derive y from x.  Or in the above tab 1 (Enter Data) reverse x and y which is much simpler (option 2).  Here I will use option 1.

Click on tab 4 (Start Search) and then on "Start" button.  This will begin the evaluation and churns through lot for formulaes to fit the data and you can see the running performance in the five windows.  As it progresses, running for few minutes, you will see the curve fitting the data in tab 5 (Solution Statistics).  With more dispersed data, you can expect complicated formula to be generated. You can pick any formula that is of interest to you and evaluate.  See below with tab 4 and 5.

The formula here I choose for illustration purpose is
f(y) = 0.31y - 557.42, that is x = 0.31y - 557.42 and so to get y, I would do



I crossed checked the formula in Excel sheet and the summed revenue (over two months) was difference of -3.4%.  And running it again at some other time, I got slightly different formula f(y) = 0.31y - 519.16. With this the above difference reduced to -1.18%. Pretty good.

So, with this tool you have got the formula that you can use to do some forecasting or predictive analysis! And you can use the similar technique to find relationships among other dimensions that are of interest to you.

Cheers,
Shiva M.