RAE = √(Σ |actual - predicted| / Σ |actual - mean|) ??????
The RAE (Root Mean Squared Error) is a widely used metric in machine learning and statistics to evaluate the performance of a model. It's calculated as follows:
RAE = √(Σ |actual - predicted| / Σ |actual - mean|)
Let's break it down:
**Actual**: This refers to the actual values or target variables that we're trying to predict.
**Predicted**: This refers to the predictions made by our machine learning model.
**Mean**: This is the average value of the actual data. It's calculated by summing up all the actual values and dividing by the total number of samples.
Now, let's dive deeper into each part of the equation:
1. **Σ |actual - predicted|**: This calculates the absolute differences between the actual and predicted values. The `Σ` symbol means "sum of". It adds up these differences for all the samples in our dataset.
2. **/ Σ |actual - mean|**: This is a normalization factor that helps us understand how well our model is performing compared to the average value.
The RAE formula can be interpreted as follows:
* The numerator (`Σ |actual - predicted|`) measures the total amount of error or discrepancy between our actual values and predicted values.
* The denominator (`Σ |actual - mean|`) normalizes this error by dividing it by the total range of possible values (i.e., the difference between the maximum and minimum actual values).
* By taking the square root of this ratio, we get a single value that represents the average magnitude of the errors.
In essence, RAE measures how well our model is able to predict the actual values, relative to the overall spread of those values. A lower RAE indicates better performance, while a higher RAE suggests larger differences between predicted and actual values.
For example, if your RAE is 0.1, it means that on average, your model is off by about 10% from the actual values. If your RAE is 0.5, it means that your model is off by about 50% on average.
I hope this explanation helps you understand the RAE formula better!
