Least squares regression report

FittingKVdm 1.13 (20230212) - Software Koen Van de moortel - www.lerenisplezant.be/fitting.htm

Data

File name: C:\FittingKVdm\Data\Examples\Driving times vs distance.dta1

Description: Driving time vs distance from home (Google Maps, 8h weekday)

x-variable: s (km)
y-variable: t (minutes)

# points: 34, # active points: 34

x	σ_x	y	σ_y	active	label
4.2	0.1	10	4	yes	Heusden
4.5	0.1	12	4	yes	Merelbeke
4.6	0.1	11	5	yes	Melle
5.2	0.1	12.5	5.5	yes	Gent
11.2	0.1	21	5	yes	Wetteren
22.9	0.1	32	8	yes	Evergem
26.1	0.1	27.5	7.5	yes	Lokeren
27.7	0.1	27.5	7.5	yes	Aalter
27.8	0.1	35.5	9.5	yes	Oudenaarde
28.6	0.1	32	8	yes	Zelzate
30.8	0.1	40.5	14.5	yes	Aalst
31.4	0.1	35.5	9.5	yes	Dendermonde
36.7	0.1	47.5	12.5	yes	Geraardsbergen
38	0.1	35.5	9.5	yes	Sint-Niklaas
48.1	0.1	52.5	12.5	yes	Hulst
53	0.1	85	35	yes	Brussel
55.9	0.1	82.5	27.5	yes	Antwerpen
63.1	0.1	80	20	yes	Mechelen
66.9	0.1	50	10	yes	Oostende
69.3	0.1	82.5	17.5	yes	Péruwelz
79.7	0.1	72.5	12.5	yes	Vlissingen
85	0.1	67.5	12.5	yes	Diksmuide
126	1	130	40	yes	Namur
135	1	130	30	yes	Hasselt
152	1	110	20	yes	Calais
162	1	145	35	yes	Rotterdam
191	1	165	35	yes	Venlo
207	1	180	40	yes	Bastogne
276	1	195	45	yes	Reims
278	1	225	55	yes	Luxembourg
280	1	220	50	yes	Bonn
365	1	290	50	yes	Groningen
460	1	315	65	yes	Caen
496	1	385	75	yes	Bremen

Elementary statistics:

x: μ = 116.138235294118, σ = 131.479909779325 (not weighted)
    μ = 38.5162748643761, σ = 30.9944022103328 (weighted)
    min = 4.2, max = 496
    Q₁ = 27.8, median = 59.5, Q₃ = 162
y: μ = 101.25, σ = 95.5213961435454 (not weighted)
    μ = 26.5549682956059, σ = 28.1438681060621 (weighted)
    min = 10, max = 385
    Q₁ = 32, median = 70, Q₃ = 145
x & y: Kendall τ = 0.89126559714795

Model & parameters

"Power"

y=ax^b

Results with traditional fitting (OLS) after 1905 iterations (x-errors were used in calculation):
a = 1.86 ± 0.78
b = 0.85 ± 0.083

S: 2918.390833, Χ² per d.f.: 0.5327465 (y), 12570.56 (x)