What Regressions Reveal

Now let’s look at this chart that we have here. What I have here is number of promotions on the x axis. This could be something like a feature or a display that we saw in Kroger in the toothpaste aisle, like Colgate-Palmolive was put on feature and we saw a display out in the front of the aisle for Crest. So those are the promotions. So the number of promotions a company is doing, a brand is doing in each week. Is it one promotion, one feature ad or two or maybe six? And how much a customer spends is up here. How much does the customer spend when they buy on the checkout counter of that brand?

So if you’re looking at Crest over here, this is dollars spent by the customer in one shopping trip for Crest. So customers may buy things when the product is not on promotion also, that would be here. When there’s no promotion, what is the value up here? And as you can see, the dollars spent is somewhere around 9. And that’s what is the number here, 9.9, which is also called the intercept. Intercept is nothing but a fancy way to say what is the value of y; in this case, y is dollars spent and x is number of promotions, right? So what is the value of y when x is equal to zero? So here we have x is equal to zero.

So how much sales happens when there are no promotions? That’s about 9.9. Now the next thing we want to know is what happens when you move from two promotions to three promotions. In other words, what happens if I increase promotions by one unit, right? How much does sales change? That’s the whole point of a regression model, right? It is to know what happens to y if you do some changes in x, right? So how much does sales move if I shift promotions? And that can be gotten by this regression line over here. This is the number and that is 1.42. So the sales increases by 1.42 for every unit increase in x.

So what this line shows is what is called the regression line. And the objective of this regression line is to go in between as many red dots as possible. And the objective is reduce distance between red dot and regression line. So the whole concept of regression is to find a way to pass this line through all those red dots in a way that the distance between the black line, which is a regression line and the red dot is minimized. In that way, now you have an equation like this that will tell you how much sales to expect when you change the promotions. And I wanted to explain this coefficient very carefully.

What I call as coefficient is this term right here, 1.42, right? So let’s recap again. If promotion increases by one unit, sales increases by this 1.42 value here. So this 1.42 is also called slope of the regression line. How does the line slope for changes in x? It is also called coefficient of promotion. So these are fancy words that are invented by statisticians and mathematicians. For us, for all practical purposes, what we basically need to know is think of regression in this chart here and understand that the coefficient of the slope is basically change in sales for a single unit change in x. And if you know that, you’re a long way through in understanding regressions.

Now let’s look at a few more nuances and understand how to apply regression in practical real world sense.