This tutorial is a brief overview of multiple regressions. Multiple regressions are really in-depth topic that you can take a whole year to study particularly if you're an economist of some sort. But it's a good things to know about because we've only been looking at right now comparing two variables, one x and one y.
But you can do a regression when you have more than one explanatory variable. And in a lot of real world applications that makes the most sense. There's not one thing that causes something. There's usually multiple things that are kind of interacting together to show that cause.
So here, again, we're using it when we want to see the effects of more than one explanatory. And a key thing to remember is that the explanatory variables have to be independent of one another. Before when we looked at an equation, we only had this first part here, y equals b subzero plus b sub one for x. When we're doing a multiple regression, we're kind of adding on more variables and their slopes.
So you can have as many of these as you want, as many of these as is appropriate for your study. This one shows three, but you could have four, you could have many, many more. Typically as you're adding more in, you're starting to kind of create a longer and longer regression. But it's not always necessary. It doesn't always add more understanding.
One example of one you might want to use a multiple regression is if you're trying to examine the question, what causes high test scores? Because test scores are related to a student's perhaps intelligent, how much they read as children, what their classroom size is, who their teacher is, how long they studied for it, whether or not English was their first language, you want to kind of include all of those factors together when you're trying to do a study of students and their test scores. So this would be a good case for doing a multiple regression.
Similarly, example 2, says what causes the crop to have a high yield? When you're looking at crop yield, you could start off with a simple regression. You could look at days of sunlight and amount of corn grown. But if you wanted to kind of look beyond that, if you wanted to look at days of rain, or volume of rain, or location of nearby rivers, any of those other variables could have an effect. They could be explanatory. So doing a multiple regression will help us to see which variable has a bigger effect and which variables don't really relate to it as much.
So again, this is a really high level topic. You won't be expected to calculate multiple regression at this point. And you can spend almost a whole year studying it. This has been your tutorial on multiple regressions.