# Example 12 (b) - 2nd degree polynomial fit to BOD data
# BOD = a0 + a1*Time + a2*Time^2
# Verified Solution: a0 = 0.224387, a1 = 0.310403, a2 = -0.006439
[
Time BOD
1 0.6
2 0.7
4 1.5
6 1.9
8 2.1
10 2.6
12 2.9
14 3.7
16 3.5
18 3.7
20 3.8
]
polyfit Time BOD 2
BOD = a0 + a1Time + a2Time2
| Variable |
Value |
95% confidence |
| a0 |
0.22438671 |
0.35305402 |
| a1 |
0.31040324 |
0.08169155 |
| a2 |
-0.00643933 |
0.00385057 |
| R^2 |
R^2adj |
Rmsd |
Variance |
| 0.9815572 |
0.9769465 |
0.0463377 |
0.0324762 |
Polynomial Regression Plot for order 2

Residuals Plot for Polynomial of order 2

Source data points and calculated data points
| |
Time |
BOD |
BOD calc |
Delta BOD |
| 1 |
1 |
0.6 |
0.52835061 |
0.07164939 |
| 2 |
2 |
0.7 |
0.81943585 |
-0.11943585 |
| 3 |
4 |
1.5 |
1.3629703 |
0.13702968 |
| 4 |
6 |
1.9 |
1.8549901 |
0.04500988 |
| 5 |
8 |
2.1 |
2.2954953 |
-0.19549526 |
| 6 |
10 |
2.6 |
2.6844857 |
-0.08448572 |
| 7 |
12 |
2.9 |
3.0219615 |
-0.12196151 |
| 8 |
14 |
3.7 |
3.3079226 |
0.39207736 |
| 9 |
16 |
3.5 |
3.5423691 |
-0.04236909 |
| 10 |
18 |
3.7 |
3.7253009 |
-0.02530088 |
| 11 |
20 |
3.8 |
3.856718 |
-0.056718 |
General
Degree of polynomial = 2
Regression including a free parameter
Number of observations = 11