Understanding Residuals in Linear Regression

A residual is the difference between an observed value and a predicted value from a regression model. It tells us how far the prediction is from the observed value. A residual is calculated as follows:

Residual = observed value - predicted value

Or mathematically:

\[ r_{i}= y_{i} - \hat{y_{i}} \]

Where the regression line has the equation:

\[ \hat{y_{i}} = a + bx_{i} \]

Therefore, the residual of an observation is:

\[ r_{i}= y_{i} - \hat{y_{i}} = y_{i} - (a + bx_{i}) \]

The aim of least squares linear regression is to find the regression parameters that minimize the sum of square residuals.

This calculator finds the residuals of a linear regression analysis for the predictor and response values provided.