Yesterday, we did some work on Peter Street. We related foot traffic to patio use, all to predict pub revenue.
A Concrete Example
- X1 is the number of people walking past a patio on Peter Street.
- X2 is the number of people who are sitting on the patio, drinking a beer, on Peter Street.
- Y is beer sales for that pub operating the patio on Peter Street.
Assume a dataset and a traditional linear regression – and get the equation (it’s for illustrative purposes only – it’s not real):
Y = 1250 + 0.05 * X1 + 18.22 * X2
To which a good friend remarked:
“Ha! I got you! I finally got you! What about weather?! You can’t say anything because you haven’t taken into account weather!”
Assume, then, that W1 is the Toronto Walkability Weather Index. It’s like clout…FOR WALKING
Let’s take temperature (celcius), degree of cloud cover (as reported by environment canada), and precipitation, and create an index from 0 to 100. Zero would represent least desirable walking weather – say, -35 c and below, whiteout conditions, and 10cm of snow. It may also represent 39 c, clear skies, and a humidex of 54 c. And a W1 of 100 would represent optimal walking conditions: 22.4 c, scattered clouds, low humidex, and zero precipitation.
We got this index, and we’ll call it W1.
W1 is judged useful if we observe changes in X1. And, let’s say we gathered the data and did the regression and it yielded, for Peter Street:
X1 = 95 + 127*W1
For every incremental point in the W1 index, we get an extra 127 people.
You could run a straight regression between W1 and Y and call it a day:
Y = 1115 + 7.22*W1 – 0.14*W1^2
And we’re done!
You can tell the bar marketer that they can’t control the lever, and, that’s just it. Their revenue is totally attributed to weather.
If you take attribution all the way back to the roots, that’s what you start to get.
The weather’s gonna be what the weather’s gonna be.
That’s ridiculous, isn’t?
And yet – how often have you heard that explanation? How often have you heard that because of weather, or some other spurious variable, we can’t make assertions about our world, let alone optimize it.
And this objection is raised time and time and time and time again.
Assume that you’re that bar marketer. What would you do?
Is weather predictable? Do any agencies make forecasts?
What about marketing? Should we just give up because an uncontrollable factor enters into the mix?
Tomorrow, I’ll expand on the role of control and levers in understanding attribution in complex systems.
I’m Christopher Berry.
I tweet about analytics @cjpberry
I write at christopherberry.ca