How to calculate the residual errors, (MSE),(MAE), and (RMSE)?

Question

Given the following sample dataset with 5 samples and 2 features:

Sample	Feature 1	Feature 2	Actual Value	Predicted Value
1	2	3	4	6
2	3	4	5	6
3	4	5	6	7
4	5	6	7	8
5	6	7	8	9

Calculate the residual errors, mean squared error (MSE), mean absolute error (MAE), and root mean squared error (RMSE) using a sample model.

Answer 1

     1. First, we need to calculate the residual errors. Residual errors are the difference between the actual values and predicted values.

Sample	Feature 1	Feature 2	Actual Value	Predicted Value	Residual Error (Actual - Predicted)
1	2	3	4	6	-2
2	3	4	5	6	-1
3	4	5	6	7	-1
4	5	6	7	8	-1
5	6	7	8	9	-1

2. Next, we can calculate the MSE by taking the average of the squared residual errors.

$MSE = ((-2)^2 + (-1)^2 + (-1)^2 + (-1)^2 + (-1)^2) / 5 = 10 / 5 = 2$

3. To calculate the MAE, we take the average of the absolute residual errors.

$MAE = (|-2| + |-1| + |-1| + |-1| + |-1|) / 5 = 6 / 5 = 1.2$

4. Finally, to calculate the RMSE, we take the square root of the MSE.

$RMSE = sqrt(2) = 1.41$

Therefore, the residual errors are [-2, -1, -1, -1, -1], the MSE is 2, the MAE is 1.2, and the RMSE is 1.41.