Residuals
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A residual is the difference between an observed value and its predicted value based on the linear regression equation.
Scenario: Crammer Nation University wants to develop a regression equation to predict the "Number of Recruits" a given fraternity will receive this rush season given the "Parties Thrown" by the fraternity the previous year. They take a sample of 6 fraternities on campus, resulting in the following scatterplot with line of best fit.
Residual = Observed - Predicted
PRO TIP: You may see "Expected" instead of "Predicted", they mean the same thing!
Observed = 150
Predicted = 125
Residual = Observed - Predicted
Residual = 150 - 125
Residual = +25
The observed value (150) of our data point sits +25 above what we would've predicted for it (125), given its x-value.
PRO TIP: If our residual was negative, that'd mean that the observed sits below what we would've predicted!