Explanation

You should start by explaining that RMSE is a common regression evaluation metric that quantifies the average magnitude of the prediction errors. It is defined as the square root of the mean of the squared differences between the predicted values $\hat{y}_i$ and the true values $y_i$: $$\text{RMSE}=\sqrt{\frac{1}{n}\sum_{i=1}^{n}(y_i-\hat{y}_i)^2}.$$ Because we take the square root, the metric is expressed in the same units as the target variable, making it easy to interpret – an RMSE of 5 on house prices measured in thousands of dollars means the model’s predictions are typically off by about $5,000. A lower RMSE indicates a model that fits the data more closely, while a higher RMSE signals poorer performance. RMSE penalizes larger errors more heavily than smaller ones, so it is sensitive to outliers. In practice you compare the RMSE to a baseline (e.g., predicting the mean) or to domain‑specific tolerances to decide whether the model is good enough.

Naive Response

RMSE is the square root of the average squared error. A lower RMSE means the model is better. It’s measured in the same units as the target variable.

Good Response

RMSE is computed as $\sqrt{\frac{1}{n}\sum_{i=1}^{n}(y_i-\hat{y}_i)^2}$. By squaring the errors before averaging, larger deviations contribute disproportionately, making RMSE especially sensitive to outliers. The square root brings the metric back to the original scale of the target, so you can directly say, for example, that an RMSE of 3.2 kilograms means the typical prediction error is about 3.2 kg. In an interview you would mention that you compare this value to a naive baseline—such as always predicting the mean of the training target—to gauge improvement, and you might also discuss whether the magnitude is acceptable given the business context (e.g., a 5‑minute error in a delivery‑time model might be fine, whereas a 5‑dollar error in a credit‑risk model could be costly).

Assessment

The naive answer states the definition but omits the exact formula, the reason for squaring and rooting, and any discussion of units or business relevance. The good answer provides the full mathematical expression, explains why the metric behaves the way it does (sensitivity to outliers), interprets the numeric value in the original units, and ties the metric to practical evaluation (baseline comparison and domain‑specific acceptability), demonstrating a deeper and interview‑ready understanding.

114. Root Mean Squared Error

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