1. What is Sum of Squared Residuals?

The Sum of Squared Residuals (RSS) is a measure of the discrepancy between the data and an estimation model. It represents the sum of the squares of the differences between observed and predicted values.

2. How Does the Calculator Work?

The calculator uses the RSS formula:

Where:

• \( y_i \) — Observed values
• \( \hat{y}_i \) — Predicted values from the model

Explanation: For each data point, calculate the difference between observed and predicted value, square it, and sum all these squared differences.

3. Importance of RSS Calculation

Details: RSS is fundamental in regression analysis, used to evaluate model fit, compare models, and is the basis for calculating R-squared and other statistics.

4. Using the Calculator

Tips: Enter comma-separated lists of observed and predicted values. Both lists must have the same number of values.

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, making it a normalized version of RSS.

Q2: What does a low RSS value indicate?
A: A lower RSS indicates a better fit of the model to the data, as the predictions are closer to the observed values.

Q3: Can RSS be used to compare models?
A: Yes, when comparing models with the same dependent variable, the model with lower RSS fits the data better.

Q4: What are limitations of RSS?
A: RSS is sensitive to outliers and doesn't account for model complexity. It always decreases as more predictors are added.

Q5: How is RSS related to R-squared?
A: R-squared is calculated as 1 - (RSS/TSS), where TSS is the total sum of squares.