Regressão linear, regressão não linear de uma variável indicadora, regressão x-y, Victor Miguel Ponce, Isabel O. Consoli

regressão linear 12: Regressão não linear de uma variável indicadora   ⇒   y = f(x)

Fórmulas

y= ax^b         log(y)= log(a) + b[log(x)]
u= log(x)        v= log(y)         v= log(a) + bu
v= α + βu         log(a)= α        b= β        a= 10^α
β= [Σ(uv)-(ΣuΣv)/n]/{Σ(u²)-[(Σu)²/n]}
α= [Σv-(βΣu)]/n        y = 10^αx^β

Referência

Ponce, V. M. 2014. Engineering Hydrology, Principles and Practices, online text.

Exemplo

DADOS DE ENTRADA:
Digite o tamanho da matriz n:

Insira os pares de valores X e Y da matriz (separe cada valor com umavírgula; comprimento máximo da cadeia é de 300 caracteres).
y:

x:

ECO DE ENTRADA:
n =
y(1) = .
x(1) = .

RESULTADO:

a =            b =            y = x



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online calc

normal depth critical depth normal and critical depth discharge in channel critical slope

normal depth in culvert critical depth in culvert discharge in culvert discharge sluice discharge weir

M1 wsprofile M2 wsprofile M3 wsprofile S1 wsprofile S2 wsprofile S3 wsprofile

C1 wsprofile H2 wsprofile A2 wsprofile C3 wsprofile H3 wsprofile A3 wsprofile

sequent depth HJ energy loss HJ initial sequent HJ efficiency HJ critical width constriction

ogee spillway Hazen-Williams parallel pipes three reservoirs tractive force

V-notch weir V-notch partially contracted Cipolletti weir Rectangular weir Standard contracted rectangular weir Standard suppressed rectangular weir

Froude number Vedernikov number Limiting contracting ratio

Creager rational slope-area linear reservoir storage indication 1 storage indication 2

Muskingum Muskingum-Cunge time-area Clark UH Cascade of linear reservoirs

USGS Methods for magnitude of floods in California Kinematic wave applicability Diffusion wave applicability Clark's unit hydrography compared to Ponce's version Correlation coefficient of a joint probability distribution Storage volume of a detention basin

Blaney-Criddle Penman Penman-Monteith reference crop Thornthwaite Priestley-Taylor Penman-Monteith ecosystems
Gumbel Gumbel 2 Log Pearson Log Pearson 2 TR-55 graphical curve number

Overland flow using the diffusion wave method Dynamic hydraulic diffusivity convolution S-hydrograph time of concentration water balance

UH cascade dimensionless UH cascade general UH cascade series UH cascade all series UH cascade

one-predictor linear one-predictor nonlinear two-predictor linear two-predictor nonlinear hyperbolic regression

fall velocity Lane & Koelzer USLE USLE2 Dendy-Bolton Shields

Duboys Meyer-Peter Colby 1957 Colby reservoir design life Equilibrium channel top width using the Lane et al. theory

Modified Einstein Procedure bridge scour using Melville equation

DO sag DO sag analysis Oxygenation Salinity (EC to TDS)

online calc
normal depth	critical depth	normal and critical depth		discharge in channel	critical slope
normal depth in culvert	critical depth in culvert	discharge in culvert		discharge sluice	discharge weir
M1 wsprofile	M2 wsprofile	M3 wsprofile	S1 wsprofile	S2 wsprofile	S3 wsprofile
C1 wsprofile	H2 wsprofile	A2 wsprofile	C3 wsprofile	H3 wsprofile	A3 wsprofile
sequent depth HJ	energy loss HJ	initial sequent HJ	efficiency HJ	critical width constriction
ogee spillway	Hazen-Williams	parallel pipes	three reservoirs	tractive force
V-notch weir	V-notch partially contracted	Cipolletti weir	Rectangular weir	Standard contracted rectangular weir	Standard suppressed rectangular weir
Froude number		Vedernikov number		Limiting contracting ratio
Creager	rational	slope-area	linear reservoir	storage indication 1	storage indication 2
Muskingum	Muskingum-Cunge	time-area	Clark UH	Cascade of linear reservoirs
USGS Methods for magnitude of floods in California	Kinematic wave applicability	Diffusion wave applicability	Clark's unit hydrography compared to Ponce's version	Correlation coefficient of a joint probability distribution	Storage volume of a detention basin
Blaney-Criddle	Penman	Penman-Monteith reference crop	Thornthwaite	Priestley-Taylor	Penman-Monteith ecosystems
Gumbel	Gumbel 2	Log Pearson	Log Pearson 2	TR-55 graphical	curve number
Overland flow using the diffusion wave method	Dynamic hydraulic diffusivity	convolution	S-hydrograph	time of concentration	water balance
UH cascade	dimensionless UH cascade		general UH cascade	series UH cascade	all series UH cascade
one-predictor linear	one-predictor nonlinear	two-predictor linear	two-predictor nonlinear	hyperbolic regression
fall velocity	Lane & Koelzer	USLE	USLE2	Dendy-Bolton	Shields
Duboys	Meyer-Peter	Colby 1957	Colby	reservoir design life	*Equilibrium channel top width using the Lane et al.* theory**
Modified Einstein Procedure		bridge scour using Melville equation
DO sag	DO sag analysis		Oxygenation	Salinity (EC to TDS)