Identifying mathematical and statistical models

0:00- [Tutor] We're told that "DeShawn uses the formula F equals MA to find the force on an object, where M is mass and A is acceleration. Is this a mathematical or statistical model?" Pause this video. Have a go at that before we do it together. Okay, well, a mathematical model is one that completely predicts what's going to happen to one variable or actually to several variables, sometimes, based on what other variables are doing.

0:25And so here, it's saying, "Look, you give me a mass in acceleration, I will tell you exactly what that force is going to be." So this is a very clear mathematical model, so I'll pick mathematical, because it describes, "An exact relationship with no uncertainty."

0:41If this was, let's say before Newton gave us F equals MA, he did a bunch of measurements, and I'm sure he actually probably did something like this, and he fit a line to old measurements and then tried to extrapolate that out, knowing that the future measurements might not be exactly the same, that might be a little bit more like a statistical model.

1:00And maybe if you did enough, he might eventually, "Hey, this looks a lot like F equals MA, and maybe the variation I'm seeing is just because of my measurement variability." But this is clearly a mathematical model, something nice and clean like this, that is claiming to perfectly predict, "You give me an M and an A and I can give you an F."

1:18Let's do another example. "Naira works for an energy company and creates a model to estimate the amount of electricity customers will use each hour using past consumption patterns and temperature records. She says the model shows what usually happens, but the actual demand can change from hour to hour.

1:39Why is this a statistical model?" So they're not even asking us whether it's statistical or mathematical, they're essentially telling us it's statistical. And before I even read these choices, which as always, you could pause this video and have a go at it yourself.

1:51If I were to say why this is a statistical model is, she is using past data over here to essentially come up with some type of a trend, which she's then using to predict what usually happens, but recognizing on any given day, on any given hour, it can be different than that.

2:11So that's what to me, tells me it is statistical. So let's see, "Is it statistical because any model used by an energy company must be statistical?" No, an energy company could use F equals MA, just like we just saw and that's a mathematical model. "Because the model is only an estimate."

2:27That one is not quite there. It's tempting because when she's predicting the future, she knows it can vary from it. Some would argue that she's estimating it, but that doesn't feel exactly right and we're not making it clear that she's basing it on past data, past statistical data.

2:46"Because a model uses a rule that always predicts the same demand for the same temperature." No, that would be a mathematical model. "Because the model is based on past data and allows for natural variation in electricity demand." Yes, for example, here, the model might predict something, but there might be just that day there, you know, more people that might be in the city, there might be an event that just changes it.

3:10It makes it a little bit less consistent with what the model would have predicted. So I definitely like choice D.