Linear Regression Calculator with Residuals
Regression Line: y = + x
Correlation coefficient (r):
Residuals:
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.