PolymathPlus Report
📊   Polynomial Regression 2022-04-01 12:47 

# Example 12 (c) - 2nd degree polynomial passing through the origin fit to BOD data
# BOD = a1*Time + a2*Time^2
# Verified Solution: a1 = 0.354779, a2 = -0.008236

[
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 origin


BOD = a1Time + a2Time2

Variable Value 95% confidence
a1 0.35477939 0.04417138
a2 -0.00823582 0.00272357

R^2   R^2adj   Rmsd   Variance  
0.9766053    0.9740059    0.0521891    0.0366186   

 0 1 2 3 4 5 0 5 10 15 20 Time P(Time) BOD(Time)


Residuals Plot for Polynomial of order 2 via origin

 -0.4 -0.2 0 0.2 0.4 0.6 0 5 10 15 20 BOD Zero Line BOD - BODCalc



Source data points and calculated data points

  Time BOD BOD calc Delta BOD
1 1 0.6 0.34654357 0.25345643
2 2 0.7 0.67661551 0.02338449
3 4 1.5 1.2873445 0.21265553
4 6 1.9 1.8321869 0.06781312
5 8 2.1 2.3111427 -0.21114274
6 10 2.6 2.7242121 -0.12421206
7 12 2.9 3.0713948 -0.17139484
8 14 3.7 3.3526911 0.34730894
9 16 3.5 3.5681007 -0.06810074
10 18 3.7 3.7176239 -0.01762387
11 20 3.8 3.8012605 -0.00126046


General

Degree of polynomial = 2
Regression not including a free parameter
Number of observations = 11