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.

**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:

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.

### Further Reading

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