Residuals (College Board AP® Statistics)
Study Guide
Written by: Mark Curtis
Reviewed by: Dan Finlay
Residuals
What are residuals?
A residual of a data point on a scatterplot is its vertical distance above the regression line
A positive residual means the point lies above the regression line
A negative residual means the point lies below the regression line
When a residual is positive, the regression line underestimates the
-value of that data pointwhereas when a residual is negative, the regression line overestimates it
What is the formula for calculating a residual?
The formula for calculating a residual is
residual =
value of the data point - value of regression linei.e. residual = actual
-value - predicted -value
Worked Example
A scatterplot and regression line are shown below. Calculate the residual for each of the five data points.
Answer:
The residuals are the numbers shown in brackets on the diagram below
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