The Residual Sum of Squares (RSS) is the sum of the squared residuals (differences between predicted and actual values) across all data points. It is defined by the formula:

$RSS = e_1^2 + e_2^2 + \\dots + e_n^2$

Alternatively, in simple linear regression, it can be written as:

$RSS = \\sum_{i=1}^n (y_i - \\hat{\\beta}_0 - \\hat{\\beta}_1 x_i)^2$

where $\\hat{\\beta}_0$ and $\\hat{\\beta}_1$ are the estimated model parameters. A smaller RSS indicates that the regression model fits the data more closely.