Linear regression, as you might imagine, isn't a one-size-fits-all solution that we can use for any problem. A lot of the relationships that exist between variables in the real world are not linear; that is, a straight line isn't able to capture the relationship. For these problems, we use a variant of the preceding linear regression known as polynomial regression, which can capture more complexities, such as curves. This method makes use of applying different powers to the explanatory variable to discover non-linear problems. This looks as follows:
Or, we could have the following:
This is the case for 
.
As you can see from the preceding equation, a model such as this is not only able to capture a straight line (if needed) but can also generate a second-order, third-order, or nth-order equation that fits the data points.
Let's suppose we...