1. What is Residual Sum of Squares?

The Residual Sum of Squares (RSS) is a measure of the discrepancy between observed data and predicted values in regression analysis. It represents the sum of the squares of the differences (residuals) between observed and predicted values.

2. How Does the Calculator Work?

The calculator uses the RSS formula:

Where:

• \( observed_i \) — The i-th observed value
• \( predicted_i \) — The i-th predicted value from the model
• \( n \) — Number of observations

Explanation: The calculator computes the squared difference between each pair of observed and predicted values, then sums all these squared differences.

3. Importance of RSS in Regression

Details: RSS is a key metric in regression analysis. Lower RSS values indicate better model fit. It's used to compare models and is the basis for calculating R-squared and other goodness-of-fit statistics.

4. Using the Calculator

Tips: Enter comma-separated lists of observed and predicted values. Both lists must have the same number of values. Example: "1,2,3,4" and "1.1,1.9,3.2,3.8".

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between RSS and MSE?
A: Mean Squared Error (MSE) is RSS divided by the number of observations. MSE is easier to interpret as it's on the same scale as the original data.

Q2: Can RSS be negative?
A: No, since it's a sum of squared values, RSS is always non-negative.

Q3: What's a "good" RSS value?
A: There's no absolute threshold - lower is better. Compare RSS values between models for the same dataset.

Q4: Does RSS have units?
A: RSS has squared units of the original data (if your data is in meters, RSS is in square meters).

Q5: Why use squared residuals instead of absolute values?
A: Squaring emphasizes larger errors and makes the function differentiable, which is important for optimization.