PolymathPlus Report
📊   Polynomial Regression 2022-04-01 12:48 

# Example 13 - Fitting Polynomials to Pressure Data
# Verified Solution: a0 = 24.6788, a1 = 1.6062, a2 = 0.036044, a3 = 0.000413, a4 = 3.96e-6
# Ref.: Comput. Appl. Eng. Educ. 6: 173, 1998

[
TC P
-36.7 1
-19.6 5
-11.5 10
-2.6 20
7.6 40
15.4 60
26.1 100
42.2 200
60.6 400
80.1 760
]
polyfit TC P 4


P = a0 + a1TC + a2TC2 + a3TC3 + a4TC4

Variable Value 95% confidence
a0 24.678757 0.78723339
a1 1.6061958 0.05446323
a2 0.0360443 0.00100889
a3 0.00041312 0.00004005
a4 3.9631E-06 4.5141E-07

R^2   R^2adj   Rmsd   Variance  
0.9999963    0.9999934    0.1410532    0.3979203   

Polynomial Regression Plot for order 4

 0 200 400 600 800 -100 -50 0 50 100 150 TC Polyn(TC) P(TC)



Residuals Plot for Polynomial of order 4

 -1 -0.5 0 0.5 1 1.5 -50 0 50 P Zero Line P - PCalc



Source data points and calculated data points

  TC P P calc Delta P
1 -36.7 1 1.0477125 -0.04771249
2 -19.6 5 4.518359 0.48164105
3 -11.5 10 10.415373 -0.41537276
4 -2.6 20 20.739228 -0.73922758
5 7.6 40 39.162336 0.83766357
6 15.4 60 59.694174 0.30582595
7 26.1 100 100.33842 -0.33841912
8 42.2 200 200.26472 -0.26472266
9 60.6 400 399.76792 0.23207928
10 80.1 760 760.05176 -0.05175524


General

Degree of polynomial = 4
Regression including a free parameter
Number of observations = 10