Linear Regression Preview

B = a0 + a1 \cdot t

Data-Table

	t	B
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 (a) - Straight line fit to BOD data
# BOD = a0 + a1*Time
# Verified Solution: a0 = 0.657797, a1 = 0.178056

[
t B
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 [origin]
polyfit t B 1

Regression Model

y = a₀ + a₁ x

where y represents B and x represents t

Variable	Value	95% confidence
a₀	0.65779698	0.374896
a₁	0.17805616	0.0316742

R²	R²adj	Rmsd	Variance
0.947273	0.941415	0.0783494	0.0825304

1st order Polynomial Regression

1st order Polynomial Regression B Residuals

Data Table

	t (x)	B (y)	Calculated Y	Residual %
1	1	0.6	0.83585313	-39.31%
2	2	0.7	1.0139093	-44.84%
3	4	1.5	1.3700216	8.665%
4	6	1.9	1.7261339	9.151%
5	8	2.1	2.0822462	0.8454%
6	10	2.6	2.4383585	6.217%
7	12	2.9	2.7944708	3.639%
8	14	3.7	3.1505832	14.85%
9	16	3.5	3.5066955	-0.1913%
10	18	3.7	3.8628078	-4.400%
11	20	3.8	4.2189201	-11.02%

Settings and Hints

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

Messages

	Severity	Description
1	Info	-Infor- 2 Known vectors variables (t, B)
2	Info	-Infor- 0 Explicit expressions
3	Info	-Infor- Regression command: polyfit t B 1

	t	B
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

	t	B
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