We have used the scikit-learn library to train a regression model. In addition to that, we have used the trained model to predict some data, and then we computed the accuracy. For example, examine Figure 9.5. The first entry says the actual value is 28.4 but our trained regression model predicted it to be 25.153909. Hence, we have a discrepancy of 28.4 - 25.153909 = 3.246091. Let's try to understand how these discrepancies are understood. Let xi be the actual value and 
be the value predicted by the model for any sample i.
The error is given by the following formula:
For any sample i, we can get the difference between the prediction and the actual value. We could compute the mean error by just summing the errors, but since some errors are negative and some are positive it is likely that they will cancel each other out. Then, the question remains, how can we know how accurately our trained model performed on all the datasets? This is where we use the concept of squared error. You should know that the square of positive and negative numbers is always positive. Hence, they have no chance to cancel each other out. So, we can represent the squared error with the following equation:
Once we know how to compute the squared error, we can compute the mean squared error. That would be easy, right? Of course, so to compute the mean squared error, we can use the following formula:
Now, if we take the root of the mean squared error, we get another accuracy measure called the root mean squared error (RMSE). The equation now becomes this:
Another type of accuracy measure that is widely used is called the relative mean squared error (rMSE). Don't get it confused with RMSE. The formula for computing rMSE is as follows:
In the preceding equation, E(x) is referred to as the expected value of x. In addition to rMSE, we have used the R2 method. The formula for computing R2 is as follows:
One more type of accuracy measure that is often seen in data science is the absolute error. As the name suggests, it takes the absolute value and computes the sum. The formula for measuring absolute error is as follows:
Finally, one more type of error that can be used in addition to absolute error is the mean absolute error. The formula for computing mean absolute error is as follows:
Was that too many? It was. However, if you check the equations closely, you will see that they are very closely related. Try to focus on the name, which explains what the accuracy measure does. Now, whenever you see any data science model using these accuracy measures, it will make much more sense, won't it?
Congratulations on learning about accuracy measures. In the next section, let's dig more into multiple linear regression, and we will try to use these accuracy measures.