Ajuste modelo de Korsun (Kramer & Akça)

Modelo de Korsun (Kramer & Akça)

Procendencia 1

\(H=exp\left ( \alpha_{0} + \alpha_{1} * log(d) + \alpha_{2} *log(d^{2}) \right )\)

Importar datos

Pt<-read.csv("~/MCF202/data/OAXP1.CSV", header=T)
head(Pt)

##     H1 DB1   H2 DB2
## 1 0.14 0.7 0.25 0.9
## 2 0.14 0.5 0.28 0.8
## 3 0.18 0.8 0.17 0.6
## 4 0.13 0.6 0.18 0.5
## 5 0.20 0.6 0.15 0.6
## 6 0.17 0.6 0.19 0.5

Pt  <- Pt[which(!is.na(Pt$H1)),] # Eliminar NAs

Ajustar el modelo para la procedencia 1

m1 <- lm(log(Pt$H1) ~ I(log(Pt$DB1)) + I(log(Pt$DB1)^2))
print(summary(m1))

## 
## Call:
## lm(formula = log(Pt$H1) ~ I(log(Pt$DB1)) + I(log(Pt$DB1)^2))
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.64542 -0.17830 -0.02085  0.16526  0.67936 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      -1.36167    0.04373 -31.136   <2e-16 ***
## I(log(Pt$DB1))    1.04412    0.06802  15.350   <2e-16 ***
## I(log(Pt$DB1)^2)  0.05073    0.02467   2.057   0.0428 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2836 on 83 degrees of freedom
## Multiple R-squared:  0.9787, Adjusted R-squared:  0.9782 
## F-statistic:  1907 on 2 and 83 DF,  p-value: < 2.2e-16

Gráfica de datos normales y ajuste de la curva

plot(Pt$DB1, Pt$H1,  ylim=c(-3,25), xlim=c(0,40), xlab="DB (cm)", ylab="H (m)" )
curve(exp(-1.36167+1.04412*log(x)+ 0.05073*log(x)^2 ), from=0, to=30, add=TRUE, col=2, lwd=2)

Procendencia 2

Ajustar el modelo para la procedencia 2

m2 <- lm(log(Pt$H2) ~ I(log(Pt$DB2)) + I(log(Pt$DB2)^2))
print(summary(m2))

## 
## Call:
## lm(formula = log(Pt$H2) ~ I(log(Pt$DB2)) + I(log(Pt$DB2)^2))
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.69382 -0.13966 -0.01181  0.13243  0.53629 
## 
## Coefficients:
##                   Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      -1.025124   0.034930  -29.35   <2e-16 ***
## I(log(Pt$DB2))    1.149875   0.073928   15.55   <2e-16 ***
## I(log(Pt$DB2)^2) -0.009925   0.025448   -0.39    0.698    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2377 on 83 degrees of freedom
## Multiple R-squared:  0.9817, Adjusted R-squared:  0.9813 
## F-statistic:  2227 on 2 and 83 DF,  p-value: < 2.2e-16

Gráfica de datos normales y ajuste de la curva

plot(Pt$DB2, Pt$H2,  ylim=c(-3,25), xlim=c(0,40), xlab="DB (cm)", ylab="H (m)" )
curve(exp(-1.02124 + 1.149875 *log(x) - 0.009925*log(x)^2 ), from=0, to=30, add=TRUE, col=3, lwd=2)