Question

which of the following is a key difference between mean square error and mean absolute deviation select the value of the mean square error depends on the measurement scale of the time - series data. mean square error is influenced much more by large forecast errors than by small errors. a market share error will always have a small mean square error while the market share error will always have a large mean absolute devia mean square error is influenced much more by small forecast errors than by large errors.

Explanation:

To determine the key difference between mean square error (MSE) and mean absolute deviation (MAD):

1. Recall the formulas: MSE is the average of the squared errors ($\frac{1}{n}\sum_{i = 1}^{n}(y_{i}-\hat{y}_{i})^{2}$), and MAD is the average of the absolute errors ($\frac{1}{n}\sum_{i = 1}^{n}|y_{i}-\hat{y}_{i}|$).
2. Analyze the effect of large errors: Squaring a large error (in MSE) makes it have a much larger impact compared to taking its absolute value (in MAD). Small errors, when squared, have a smaller relative impact compared to large errors when squared.
3. Evaluate the options:

• The first option is incorrect because both MSE and MAD depend on the measurement scale (since they are based on the errors of the data).
• The second option is correct: MSE squares the errors, so large forecast errors (when squared) contribute much more to the overall MSE than small errors (when squared) do.
• The third option is incorrect as there's no inherent relationship that a market - share error will always have a small MSE and large MAD.
• The fourth option is incorrect because, as explained, MSE is more influenced by large errors (due to squaring) rather than small ones.

Answer:

Mean square error is influenced much more by large forecast errors than by small errors.