## Quick Reference

Artificial data created by Anscombe to illustrate the necessity for studying residuals. Each of the four data sets has the same fitted regression line, *y*=3+0.5*x*, and the same summary ANOVA table (with the same regression sum of squares, total sum of squares, and value for *R*^{2}).

**Anscombe's regression data.** Each data set has the same mean and variance for *x*, the same mean and variance for *y*, the same fitted regression line, and the same residual sum of squares—Anscombe created these data sets to emphasize the need for the statistician to look carefully at data.

*x*

*y*

*x*

*y*

*x*

*y*

*x*

*y*

10

8.04

10

9.14

10

7.46

8

6.58

8

6.95

8

8.14

8

6.77

8

5.76

13

7.58

13

8.74

13

12.74

8

7.71

9

8.81

9

8.77

9

7.11

8

8.84

11

8.33

11

9.26

11

7.81

8

8.47

14

9.96

14

8.10

14

8.84

8

7.04

6

7.24

6

6.13

6

6.08

8

5.25

4

4.26

4

3.10

4

5.39

19

12.50

12

10.84

12

9.13

12

8.15

8

5.56

7

4.82

7

7.26

7

6.42

8

7.91

5

5.68

5

4.74

5

5.73

8

6.89

*Subjects:*
Probability and Statistics.