Looking at the Data
Looking at the data MUST be the first step in choosing a model to fit the data. Consider these four sets of paired data.
x1 |
y1 |
x2 |
y2 |
x3 |
y3 |
x4 |
y4 |
|||
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 |
8.1 |
14 |
8.84 |
8 |
7.04 |
|||
6 |
7.24 |
6 |
6.13 |
6 |
6.08 |
8 |
5.25 |
|||
4 |
4.26 |
4 |
3.1 |
4 |
5.39 |
19 |
12.5 |
|||
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 |
Each dataset has the following identical set of summary statistics:
| N | 11 |
| Mean of x’s | 9.0 |
| Mean of y’s | 7.5 |
| Equation of regression line | y = 3 + 0.5x |
| sum of squares (X - Xbar) | 110.0 |
| correlation coefficient | 0.82 |
| r2 | 0.67 |