Residuals: Anscombe’s quartet
5 10 15 20
2 4 6 8 10 12 14
x
y
5 10 15 20
2 4 6 8 10 12 14
x
y
5 10 15 20
2 4 6 8 10 12 14
x
y
5 10 15 20
2 4 6 8 10 12 14
x
y
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Anscombe's Quartet: Understanding Different Stories Told by Residuals, Study notes of Descriptive statistics
Anscombe's quartet is a famous example in statistics that demonstrates how identical fitted lines and equal residual sums of squares can hide significant differences in the distribution of residuals. an overview of Anscombe's quartet, explains how to calculate residuals, and discusses the importance of analyzing residuals to understand the underlying data.
Typology: Study notes
2021/2022
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Residuals: Anscombe’s quartet
x y 5 10 15 20
x y 5 10 15 20
x y 5 10 15 20
x y
Residuals: Anscombe’s quartet
x y 5 10 15 20
x y 5 10 15 20
x y 5 10 15 20
x y
Why are the four sets of residuals different?
obvious if you have only one explanatory variable
- res1 res2 res3 res - 1 -0.740 -1.901 0.389 0.
- 2 0.179 -0.761 0.229 -0.
- 3 1.239 0.129 0.079 -1.
- 4 -1.681 0.759 -0.081 0.
- 5 -0.051 1.139 -0.230 -1.
- 6 1.309 1.269 -0.390 1.
- 7 0.039 1.139 -0.540 -0.
- 8 -0.171 0.759 -0.689 1.
- 9 1.839 0.129 -0.849 -1.
- 10 -1.921 -0.761 3.241 0.
- 11 -0.041 -1.901 -1.159 0.