Residual vs Residual Plot
Both terms below come up in the same part of the course, and students mix them up. Here is each one defined on its own, side by side, so you can see where they part company.
Residual
Regression and correlation
A residual is the difference between an observed y-value and the value the regression line predicts for it: observed minus predicted.
A residual measures how far off the line is for a single point, so a positive residual sits above the line and a negative one below. It equals , the observed response minus the predicted response (read y-hat). For example, if the line predicts 72 but a student actually scored 80, the residual is . Least-squares regression chooses the line that makes the sum of the squared residuals as small as possible.
Residual plot
Regression and correlation
A residual plot graphs the residuals against the explanatory variable or predicted values, used to check whether a line fits the data well.
A residual plot helps you judge whether a linear model is appropriate by spreading the leftover errors out for inspection. Random scatter with no pattern around the horizontal zero line suggests a line fits well, while a curved or fanning pattern warns that it does not. For example, a U-shaped residual plot signals the true relationship is curved, so a line understates it at the ends. You read residual plots for both curvature and changing spread before trusting a regression.