Mean Absolute Deviation (MAD)
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Mean Absolute Deviation (MAD) is the absolute difference between the actual and predicted values forecasted.
The larger an error ("actual - predicted") is, the larger it becomes with MSE, since you're squaring those errors.
MAD prevents this from occurring, since we're taking the absolute value of the error ("actual - predicted") to remove negative values instead of squaring the error (like with MSE).
Scenario: Given the yearly Tinder statistics from Delta Apple Pi at Crammer Nation University, calculate the MSE.
| Year | 2019 | 2020 | 2021 | 2022 | 2023 | 2024 |
|---|---|---|---|---|---|---|
| Tinder Matches | 1204 | 1329 | 1297 | 1432 | 1406 | - |
| Estimated (y-tilde) | - | - | 1276.667 | 1352.667 | 1378.333 | - |
| Predicted (y-hat) | - | - | - | 1276.667 | 1352.667 | 1378.333 |
n is the number of periods with a predicted and actual value.
yt is the actual value for a given period "t".
y-hatt is the predicted value for a given period "t".
We're only looking for years that have predicted and actual values!
2022
Actual = 1432
Predicted = 1276.667
2023
Actual = 1406
Predicted = 1352.667
n = 2 (for 2022 & 2023)
MAD = (1 / n) x [|yt - y-hatt| + ...]
MAD = (1 / 2) x [|1432 - 1276.667| + |1406 - 1352.667|]
MAD = (0.50) x [155.333 + 53.333]
MAD = (0.50) x [208.666]
MAD = 104.333
Answer: On average, the difference between actual vs. predicted Tinder matches is 104.333 matches.