THE BEST FIT LINEa study of how that one group was wrong, and how modeling is impossible

By Maneesha Palakurthi

PART 1

Let’s talk about why that one group was wrong.

THIS IS THE GRAPH THAT GROUP E3 USED TO REPRESENT PEOPLE’S ECONOMIC PATHS.

As you can see, their concept was that in the cycle of loss and gain, the rich gain more than they lose (and so get continually richer), the middle class breaks even (and so remain stagnant wealth-wise), and the poor's gains don't make up for their losses (and so get progressively poorer). This graphs refers to wealth in amounts. There are two glaring mistakes in this representation.

THE FIRST PROBLEM

The first is that the three lines begin so close together. The wealth gap does widen over time, true, but that doesn't mean that it starts so small. In this case it would be more accurate to have the following:

For reference:

THE SECOND PROBLEM

The other large issue with their graph is that there are far too many "outliers". Considering that their wealth axis is set on a basis of specific economic values, only people who begin with the exact amount of the three y-intercepts are shown on this graph. So if you were to give the axes the following values: (see below graph)

For reference:

…only people who begin with 4, 8, or 12 units of wealth are represented. Those who begin with any other amount are unaccounted for.

SOLUTION FOR THE SECOND PROBLEM

The graph should really look more like the following one.

For reference:

However, it would need infinitely more lines, but creating this same basic shape. The pink line would be stationed at whatever y-value is considered at the time to be median wealth/wage.

ANOTHER APPROACH

Now there's another entirely different approach that yields the same meaning, using relativity and percentiles. It is drawn as one of the most basic graphs of all, the y=x graph. Here, the x and y axes both represent a wealth percentile. The x axis represents your financial standing when you start, and your y axis represents your financial standing when you finish.

A SIMPLIFIED EXPLANATION

Say there's 100 people in a city. You happen to be the second richest person in the city, so you are the 99th percentile. Similarly to the fashion that group E3 had been trying to demonstrate with their graph, you as one of the rich, are getting richer. However, your wealth doesn't increase faster than the one richest person, or slower than the people who started poorer than you, so you continue to rank as the second richest person in town. Thus, your final percentile value is 99, and you fall on the y=x line.

For reference:

SCATTER PLOTTED

Now that graph also has outliers not taken into account, though in this case they are actually a minority. If you were to scatter plot the percentile graph, it would look something like this:

For reference:

The red dots are outliers. However, as you can see the line is what is commonly known as a best fit line, and is therefore acceptable.

BUT.(Here starts part two in which I contradict some of

what I just said mostly because I'm switching topics to the best fit line discussion.)

Best fit lines should never be considered acceptable! The are

one of the most prevalent examples of humans and our dependency on taxonomy!

HERE’S WHY…

When given the below scatterplot…

People attempt to draw what they call a best fit line. Which ends up looking like the following.

From four unconnected points on the graph, we conjure up a best fit line, and say that it represents them. But it doesn't! Only one of the points is actually on the line, yet we deem this the line that represents the data. Unless your best fit line goes through at least 90% of the points on the graph, it should be considered invalid.

SO WHY DO WE DRAW BEST FIT LINES?

It's a form of taxonomy. A way to say that things (or points) are a part of a category (or line) that they really aren't.

It helps us to associate things with whatever is similar, and ignore outliers.

WHICH BRINGS ME TO MY NEXT POINT. (HAHA, POINT, GET IT?)

The gravest form of the best fit line and taxonomy is...

THE MODEL.

Modeling is the worst kind of best fit line.

WHY MODELS ARE UNACCEPTABLE

So we study three different revolutions, and then create a model/system based off of those three that should be applicable to every other situation. Not only are outliers disregarded, but nearly all other events are too!

Let me explain visually.

The red dots represent the events that we studied. This graph shows only the data that we studied.

Key:Red dots = Events Studied

Here the gray line is the best fit line or the model, made based on the data.

Key:Red Dots = Events StudiedGray Line = Best Fit Line for Red Dots

The green dots are all the events that took place that we didn't study. So it's obvious that the events fell in a very wide range.

Key:Red Dots = Events StudiedGray Line = Best Fit Line for Red DotsGreen Dots = Unstudied Events in History

So here are all the events throughout history, and the one model that was made to represent all of them. I don't think it quite works, do you?

Key:Red Dots = Events StudiedGray Line = Best Fit Line/Model for Red DotsGreen Dots = Unstudied Events in History

IN CONCLUSION…

We draw best fit lines and create models in order to fool ourselves into thinking that:

a) It's actually possible to categorize the worldb) There is actually one line or model that

applies to every point of datac) We understand the world

EL FIN