A Regression Tree

Ralph Winters (@RDub2) tweeted a link the blog post “On Some Alternatives to Regression Models” on the Freakonometrics blog. The author of post explains various alternatives to linear regression as it is applied to non-linear functions. Each of the alternatives give us an approximation, or put another way, a gap between the numbers and reality.

The regression tree model gives us an approximation that provides flat planes in various places. Deciding to be on one of those flat planes gives our business something to optimize towards for an interval of time, with a manageable level of cognitive costs. Where you see a square area in the macro sense, you’re dealing with a normal distribution. Where you see long thin rectangles, you’re dealing with a Poisson distribution. The ordinary course of business is from the Poisson towards the Normal, eventually to the normal, and the wider normal. The ordinary course of business is from discovery to enforcement in the repeatable operational sense right up to the black swan where the flat surfaces stop and fall. This all is also ordinary, but usually growth thinking and not knowing where were are under our distributions make for the black swan. No excuses for those swans, since I know the extent of my plane and I cannot change that extent.

I’ve heard of scale being the trigger for a chasm. It struck me as odd, but the flat planes of the regression trees end in two ways, rather than one. They go down or they go up. Both can be disasters to our ongoing operations. Down is the swan, but what of the up? Moore’s chasm is one of reference bases. The early adopter and their business case is made for risk takers in the vertical, but what of those that take less risk. The important thing here is that Moore found the pragmatism gradient. He found a way to climb up to the regression tree’s adjacent plane, up to the next plateau.

The regression tree also shows up the global maxima within the scope of the regression along with the local maximas where your business might be stuck. I was amazed years ago when a discussion with my CEO showed me that that CEO didn’t understand how his very successful business might be stuck on a local maxima. I wasn’t all that attentive to math back then either.

If you were to decide to serve a particular plane, that plane would be ground, aka the x-axis for any analysis going forward. Get agreement on this and make it stick.

In the figure, I’ve annotated the swans and the chasms. There is still plenty of business to be had on the plane. This plane is Poisson. This plane is your world. The other planes are out of scope until you commit to going there. There are 21 units of  business to be had. Nine face the swan. They must know where the line is. These nice share an operational focus. Eight of them face the chasm. They share another operational focus. One of units faces both the swan and the chasm. Five units have it easy. From this the executive should see the outlines of what the problems are going to be, who should be managing what, and what kind of training needs to be done. From this outline, we can design an organization that can cope, experiment, learn, and forget in its particular terrain.

For a  product manager, roadmaps and conversations should be organized around these planes. These planes also organize communications within and between planes, so marketing, offers, service provision, and pricing organize around these planes.

Enjoy. Comments?

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One Response to “A Regression Tree”

  1. Statitical Independence | Product Strategist Says:

    […] Just another WordPress.com weblog « A Regression Tree […]

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