Polynomial Regression Preview

P = a0 + a1 \cdot TC + a2 \cdot {TC}^{2} + a3 \cdot {TC}^{3} + a4 \cdot {TC}^{4}

Data-Table

	TC	P
1	-36.7	1
2	-19.6	5
3	-11.5	10
4	-2.6	20
5	7.6	40
6	15.4	60
7	26.1	100
8	42.2	200
9	60.6	400
10	80.1	760

Program validated. Ready to Solve.

# 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

Regression Model

y = a₀ + a₁ x + a₂ x² + a₃ x³ + a₄ x⁴

where y represents P and x represents TC

Variable	Value	95% confidence
a₀	24.678757	0.787233
a₁	1.6061958	0.0544632
a₂	0.036044296	0.00100889
a₃	0.00041312159	0.0000400467
a₄	0.0000039631478	4.51405e-7

R²	R²adj	Rmsd	Variance
0.999996	0.999993	0.141053	0.397920

4th order Polynomial Regression

4th order Polynomial Regression P Residuals

Data Table

	TC (x)	P (y)	Calculated Y	Residual %
1	-36.7	1	1.0477125	-4.771%
2	-19.6	5	4.5183590	9.633%
3	-11.5	10	10.415373	-4.154%
4	-2.6	20	20.739228	-3.696%
5	7.6	40	39.162336	2.094%
6	15.4	60	59.694174	0.5097%
7	26.1	100	100.33842	-0.3384%
8	42.2	200	200.26472	-0.1324%
9	60.6	400	399.76792	0.05802%
10	80.1	760	760.05176	-0.006810%

Settings and Hints

	Name/Source	Value	Type
1	Polynomial Degree	4	Setting
2	Through Origin	false	Setting
3	Data Points	10	Setting
4	y=pol(x)	P=pol(TC)	Setting
5	Version	7.0.73	Setting
6	#@report_fix_digits = 8		Default (integer)
7	#@chart_size = 428,300		Default (array)
8	#@report_show_charts = true		Default (boolean)
9	#@report_show_data_points = true		Default (boolean)
10	#@report_show_source = true		Default (boolean)
11	#@report_show_header = false		Default (boolean)
12	#@report_show_settings = true		Default (boolean)

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