Regression Analysis
Regression analysis. No. It’s not a therapy session in which your psychiatrist tries to figure out why you’ve gone back to using pacifiers. It’s simply this: the process by which a series of different independent variables are compared to a dependent variable to see which might have the greatest effect on the value of the dependent variable.
Well okay. That’s the theory of it. But...what about a practical example?
All right…let’s take Pete, the pizza joint guy. How does he know what’s bringing in customers? Is it his new “burrito pizza”? Or the virtual skee-ball machines?
Well, we can use some math to find an equation (usually a linear one) that best matches the pattern in the data. Then we can see how close the points are to that line. And that will solve our burrito pizza/skee-ball conundrum.
The closer the data points are to the line, the more likely there's some kind of link between the independent and dependent variables. It doesn’t mean one variable causes another. It just means that they're linked somehow.
Like, what about the link between ice cream sales and drowning deaths? A morbid connection, but see how close the data points are to that special line? So yeah. There's absolutely a link between ice cream sales and drowning deaths. Greater ice cream sales on a given day is always linked to more drowning deaths on that day.
Why? What’s the linking factor? Flavor of ice cream? Accessibility of public swimming pools?
Clearly ice cream isn’t some insidious killer drowning people who get in the water without waiting the requisite hour. But there is a link between these two variables. As it turns out, higher ice cream sales happen on hotter days. So heat is the linking factor.
More people go swimming on hotter days. When more people swim, there are going to be more drowning possibilities. So ice cream sales and drowning deaths are linked, but ice cream sales don’t cause drowning deaths. Similarly, there's no link between your shoe size and your GPA. Unless you buy huge shoes, build a mini-computer that fits in the extra space in your shoes, and use that to help you, um...cheat. Don’t do that, by the way. Always cite Shmoop.
Anyway, back to Pete, the owner of Zah's Pizza. Pete almost has more customers lately than he can handle. While the lightning is striking, Pete wants to find a way to...bottle it.
The thing is, he's made two significant changes to his restaurant, and he's not sure which one is most responsible for the influx of people tossing money at him. Is it the Virtual Skee-Ball machines...or his new Burrito Pizza? Is there, in fact, a link at all?
It could be both that are responsible, but that's beyond Pete's skill to determine. He can only compare one at a time to the increased revenue. Pete picks different days and plots the number of Burrito Pizza orders against the total money made that same day.
He can see that low Burrito Pizza order numbers are paired with lower daily revenues. Also, high Burrito Pizza orders are paired with higher daily revenues. The closer the points on Pete's graph are to that imaginary line, the more likely it is that the independent variable (Burrito Pizza sales) is at least related in some meaningful way to the dependent variable (total daily revenue).
From here...Pete starts getting into some pretty complicated math. Hope you've got your TI-84 handy.
All right, all right. We won't do it to you. We'll skip the numbers and formulas. For now.
Long story short, Pete used a regression analysis on the two different variables he thought might influence his bank account the most. His conclusion: any decisions he makes going forward should probably be menu-focused, as opposed to attraction-focused.
His secondary conclusion: people get mad when you roll up a pizza and call it a burrito.