Residual Sum of Squares (RSS) Calculator

This calculator finds the residual sum of squares (RSS) for a linear regression model using values for the predictor and response variables.

To use the calculator, provide a list of values for the predictor and the response, ensuring they are the same length, and then click the “Calculate RSS” button.

Predictor Values:

Response Values:

Residual Sum of Squares (RSS):

Residual Sum of Squares (RSS) Explanation

The Residual Sum of Squares (RSS) is a measure of the discrepancy between the observed data and the data predicted by a linear regression model. It is used to evaluate the goodness of fit of the model, with lower values indicating a better fit.

Key Components

Predictor Variable (X): The independent variable used to predict the response.
Response Variable (Y): The dependent variable that is being predicted.
Fitted Value (Ŷ): The predicted value of Y for a given X, based on the linear regression model.
Residual (e): The difference between the observed and the fitted value, \( e = Y – Ŷ \).

Residual Sum of Squares Formula

The RSS is calculated as the sum of the squares of the residuals:

\[ RSS = \sum_{i=1}^{n} (Y_i – \hat{Y}_i)^2 \]

where \( Y_i \) is the actual value, \( \hat{Y}_i \) is the predicted value, and \( n \) is the number of observations.

Steps to Calculate RSS

Fit a linear regression model to the data.
Calculate the predicted (fitted) values for the response variable based on the model.
Find the residuals by subtracting the predicted values from the observed values.
Square each residual and sum them up to find the RSS.

Importance of RSS

RSS is used to measure the accuracy of a regression model. A lower RSS value indicates that the model better fits the data.
It plays a key role in determining the R-squared value, which is another measure of the model’s goodness of fit.
It helps to compare different models— the one with the lower RSS generally provides a better fit to the data.

Suf is a senior advisor in data science with deep expertise in Natural Language Processing, Complex Networks, and Anomaly Detection. Formerly a postdoctoral research fellow, he applied advanced physics techniques to tackle real-world, data-heavy industry challenges. Before that, he was a particle physicist at the ATLAS Experiment of the Large Hadron Collider. Now, he’s focused on bringing more fun and curiosity to the world of science and research online.