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# Regression Residuals Calculator

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

$$r_{i}= y_{i} ~-~ \hat{y_{i}}$$

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.

Please enter a list of values for the predictor and response variables in the boxes below then click the Do Linear Regression button.

Regression Line:
y = a + bx

Goodness of fit:
Correlation coefficient r =
Residuals =