When you hear the word beautiful, what comes to mind?
Maybe it’s a golden sunset. Or a vista of snow-capped mountains. Or the elegant grace of wild horses running free.
Those are all beautiful sights, no doubt.
But when I hear the word beautiful, I think of something else entirely. I think of a regression function.
You’re probably thinking this is an odd choice. And you’re right.
Beauty is supposed to be about the majesty of nature. About the tenderness of emotion.
A regression equation seemingly has little of either of these sentiments.
It’s a string of numbers, letters and symbols. As cold and calculating as a movie villain. As dry as day-old ink on the page.
Still, there is a method to my preference.
How could there not be? After all, method is math’s bread and butter.
So, let’s break it down.
At its core, a regression function is an explanation.
It explains how one variable is impacted by others.
For instance, we could run a regression to see how interest rates impact home prices. Or how days with cold temperatures impact doctors’ visits.
We could even look at the impacts of two different variables. For example, how the local football team’s performance impacts the number of traffic accidents on the city’s streets and the amount of nightly revenues at the city’s restaurants.
With enough data, we can look at just about anything. The regression model is simply the tool we use to transform the data into something worth talking about.
Now, this data-driven explanation doesn’t necessarily show cause and effect. After all, a golden rule of statistics is that Correlation does not equal causation.
No, a regression equation simply shows how the variables are related. How two — or three, or four — elements tend to work together.
This knowledge is what allows us to make predictions. It can help meteorologists build 10 day weather forecast models. It can help political consultants handicap future election results. And it can help business managers make shrewd strategic pivots.
In all these cases, the data speak volumes. The regression equations provide evidence to guide the prognosticators in their choices. They seem to illuminate the path ahead, like runway lights at an airport.
But while a strong regression can give a forecaster confidence, the process is far from failproof.
We’ve all seen a time where the weathercaster was flat out wrong. Where the pollster missed the mark. Or where a company’s bold moves fell flat.
When this happens, we’re quick to assign blame.
We rush to shame the experts for getting it wrong. For leading us astray. For not being perfect.
This is ridiculous — for multiple reasons.
For one thing, perfection is not an attainable ideal. Mistakes are a fact of life, and we all slip up from time to time. There’s no need to call out others for being human.
But just as importantly, regression models themselves are not perfect.
If you were to write out a regression equation, it would likely look something like this.
y = ß0 + ß 1x1 + ß 2x2 + e
The y’s and x’s show the part of the equation that can be predicted. This section of the equation shows how a change in variable y tends to impact variable x1 or x2.
This is the part of the equation that prognosticators — weathercasters, pollsters, business leaders — rely on. And they’re right to do so — most of the time.
But that e at the end of the equation represents something totally different.
The e stands for the error term — the part of the model that can’t be predicted.
This is the randomness, the chaos, the side effects that can’t be explained.
Statisticians do their best to build models that reduce that e term as much as possible. To isolate the exact factors that explain a relationship between multiple variables.
Still, no matter how much they try and remove all error, it remains.
That might seem like a problem. But I believe it’s a good thing.
For the world is neither simple nor clean. It can’t be neatly organized in boxes, wrapped in paper and topped with bows.
No, the world is inherently messy. It can defy logic and be straight-up perplexing at times.
The error term captures this reality. It captures life in its purest form.
This is why I love the error term. This is why I associate a regression equation with beauty.
And this is why I believe the error term requires more attention from all of us.
Throughout our daily lives, we do our best to prepare.
We brush our teeth, shower and put on climate-appropriate clothing. We add appointments and events to our calendar. We map out our immediate and future spending needs.
We do what we can so that we’re ready to act decisively now and in the future.
I am no stranger to this behavior. Indeed, I tend to obsess over preparation and organization.
This laser-sharp focus is a net benefit. It allows us to be presentable and to make proper decisions.
But relying solely on this approach can get us off track.
For life is defined by the error term. By the instances when things take an unexpected left turn. By the moments we can’t possibly prepare for.
These changes of pace, these shocks to the system — they do more than spice things up. They test our mettle.
These are the moments that define our lives. These are the occurrences that unlock ingenuity and innovation. These are the opportunities for us to display our humanity.
We build emotional connections by navigating the error term. Those connections lead to storytelling, as we share accounts of our experience through visuals, through audio and through the written word. And those stories we tell ourselves — they help shape our culture.
It’s time we embrace the error term. It’s time we stop obsessing on all that can be explained, and that we come to terms with what confounds us.
This is what will allow us to live our lifes to the fullest. To treasure the journey with a clear and open mind.
To err is human. Let’s get back in touch with our humanity.