Polynomial Regression Preview

BOD = a0 + a1 \cdot Time + a2 \cdot {Time}^{2}

Data-Table

	Time	BOD
1	1	0.6
2	2	0.7
3	4	1.5
4	6	1.9
5	8	2.1
6	10	2.6
7	12	2.9
8	14	3.7
9	16	3.5
10	18	3.7
11	20	3.8

Program validated. Ready to Solve.

# 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

Regression Model

y = a₀ + a₁ x + a₂ x²

where y represents BOD and x represents Time

Variable	Value	95% confidence
a₀	0.22438671	0.353054
a₁	0.31040324	0.0816915
a₂	-0.0064393337	0.00385057

R²	R²adj	Rmsd	Variance
0.981557	0.976946	0.0463377	0.0324762

2nd order Polynomial Regression

2nd order Polynomial Regression BOD Residuals

Data Table

	Time (x)	BOD (y)	Calculated Y	Residual %
1	1	0.6	0.52835061	11.94%
2	2	0.7	0.81943585	-17.06%
3	4	1.5	1.3629703	9.135%
4	6	1.9	1.8549901	2.369%
5	8	2.1	2.2954953	-9.309%
6	10	2.6	2.6844857	-3.249%
7	12	2.9	3.0219615	-4.206%
8	14	3.7	3.3079226	10.60%
9	16	3.5	3.5423691	-1.211%
10	18	3.7	3.7253009	-0.6838%
11	20	3.8	3.8567180	-1.493%

Settings and Hints

	Name/Source	Value	Type
1	Polynomial Degree	2	Setting
2	Through Origin	false	Setting
3	Data Points	11	Setting
4	y=pol(x)	BOD=pol(Time)	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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