1.The "Anscombe" dataset has four different sets of (X, Y) data that can be used to illustrate the critical importance of creating scatterplots before determining the best fitting line.

(a)Create four fitted line plots - one each for (X₁, Y₁), (X₂, Y₂), (X₃, Y₃), and (X₄, Y₄). Comparing the four scatter plots and four best fitting lines, write a brief summary of what you found.

(b)What do these four data sets therefore suggest that you should always do before just automatically finding a best fitting line?

(c)Do the (X₁, Y₁) data appear to vary a lot or a little around the best fitting line? Do you think the best fitting line would lead to precise predictions of Y₁? Why or why not?

(d)Does a straight line appear to fit the (X₂, Y₂) data well? If not, what might be a better fitting relation?

(e)As a researcher, what might be a reasonable thing to check out further before relying too heavily on the best fitting line for the (X₃, Y₃) data?

(f)Describe roughly how the best fitting line for the (X₄, Y₄) data would change if the (19, 12.5) point were changed to (19, 5)? What does this suggest about such a point? You need not produce the fitted line here.

The Anscombe data is below:

x1 y1 x2 y2 x3y3 x4y4

10 8.04 10 9.14 107.46 86.58

8 6.95 8 8.14 86.77 85.76

13 7.58 13 8.74 1312.74 87.71

9 8.81 9 8.77 97.11 88.84

11 8.33 11 9.26 117.81 88.47

14 9.96 14 8.1 148.84 87.04

6 7.24 6 6.13 66.08 85.25

4 4.26 4 3.1 45.39 1912.5

12 10.84 12 9.13 128.15 85.56

7 4.82 7 7.26 76.42 87.91

5 5.68 5 4.74 55.73 86.89