The scatter data below seems to have a linear relationship, so we will perform a linear regression.
| x | 1.5 |
1.5 |
2.0 |
2.5 |
2.5 |
3.0 |
3.5 |
3.5 |
4.0 |
| y | 23 |
24.5 |
25.0 |
30.0 |
33.5 |
40.0 |
40.5 |
47.0 |
49.0 |
Observation |
x |
y |
x2 |
xy |
y2 |
1 |
1.5 |
23.0 |
2.25 |
34.50 |
529.00 |
2 |
1.5 |
24.5 |
2.25 |
36.75 |
600.25 |
3 |
2.0 |
25.0 |
4.00 |
50.00 |
625.00 |
4 |
2.5 |
30.0 |
6.25 |
75.00 |
900.00 |
5 |
2.5 |
33.5 |
6.25 |
83.75 |
1122.25 |
6 |
3.0 |
40.0 |
9.00 |
120.00 |
1600.00 |
7 |
3.5 |
40.5 |
12.25 |
141.75 |
1640.25 |
8 |
3.5 |
47.0 |
12.25 |
164.50 |
2209.00 |
9 |
4.0 |
49.0 |
16.00 |
196.00 |
2401.00 |
Sum ofthe Column |
24.0 |
312.5 |
70.50 |
902.25 |
11626.75 |
Now solving the two equations below simultaneously for m and b, we obtain the least squares estimates.
The equation of the estimated regression line is y = 10.603x + 6.449