Residuals are basically left overs from the model fit. We can think of the data point as the combination of fit and residuals
Residual is the difference between the observed value of data point to the predicted value of data point.
where Yi is the observed value and ^Yi is the predicted value
If the predicted value of the response variable for a given data point is above the observed value, the residual is negative
The actual value which is above the fit line is more than the predicted value which means we are under estimating the predicted value. Similarly, the value which are below the fit line is overestimating the actual value.
The difference that we are predicting and the actual value which is occurring at that point is called the error also known as Residual.
