So, as our target variable contains continuous values, we can say that it's a regression task.
Our next step is to select a performance measure for a regression task so we can check how well our machine learning model is performing.
We generally use RMSE (Root Mean Square Error) metric as a performance measure for regression tasks.
Its formula is as-
where
Predicted is the target value or label that our model predicts for a data point,
actual is the actual label for that data point and
N is the number of instances in the datasets.
So, by taking the difference between both, it calculates the error in prediction(as how much difference is there in predicted and actual value). As large is the difference between both, large will be the error in our model.
So for example, in the above figure, suppose we want to predict output by our model for input as 2. So, as we can see the actual value(which lies as a blue data point), for x = 2 is 2. But our model will predict it on the regression line and so the predicted value will come as 2.75. Hence there will be an error of (2.75-2), which is 0.75. This error is shown by the red dashed line. And this is the objective of our training- to reduce this error as much as we can.
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