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#' @title Henry Isotherm Linear Analysis
#' @name henryanalysis
#' @description It describes the appropriate fit to the adsorption of adsorbate
#' at relatively low concentrations such that all adsorbate molecules are
#' secluded from their nearest neighbours.
#' @param Ce the numerical value for the equilibrium capacity
#' @param Qe the numerical value for the adsorbed capacity
#' @return the linear regression, parameters for the Henry isotherm, and model
#' error analysis
#' @import Metrics
#' @import stats
#' @import ggplot2
#' @examples Ce <- c(0.01353, 0.04648, 0.13239, 0.27714, 0.41600, 0.63607, 0.80435, 1.10327, 1.58223)
#' @examples Qe <- c(0.03409, 0.06025, 0.10622, 0.12842, 0.15299, 0.15379, 0.15735, 0.15735, 0.16607)
#' @examples henryanalysis(Ce, Qe)
#' @author Paul Angelo C. Manlapaz
#' @author Chester C. Deocaris
#' @references Deocaris, C., and Osio, L. (2020). Fitting Henry's
#' Adsorption Isotherm model in R using PUPAIM package.
#' @export
# Building the Henry isotherm linear model
henryanalysis <- function (Ce, Qe){
x <- Ce
y <- Qe
data <- data.frame(x,y)
# Henry isotherm linear equation
rhs <- function(x, K){
(K*x)
}
# Fitting of Henry isotherm
fit230 <- lm(y ~ x)
print("Henry Isotherm Analysis")
print(summary(fit230))
a <- (summary(fit230))
b <- a$coefficients[2]
### Parameter values calculation
print("K")
print(b)
# ---------------------------------
print("Akaike Information Criterion")
print(AIC(fit230))
print("Bayesian Information Criterion")
print(BIC(fit230))
# Error analysis of the Henry isotherm linear model
errors <- function(y){
rmse <- Metrics::rmse(y, predict(fit230))
mae <- Metrics::mae (y, predict(fit230))
mse <- Metrics::mse(y, predict(fit230))
rae <- Metrics::rae(y, predict(fit230))
N <- nrow(na.omit(data))
SE <- sqrt((sum(y-predict(fit230))^2)/(N-2))
colnames(y)<- rownames(y) <- colnames(y)
list("Relative Mean Square Error"= rmse,
"Mean Absolute Error" = mae,
"Mean Squared Error"= mse,
"Relative Absolute Error"= rae,
"Standard Error for the Regression S" = SE)
}
a <- errors(y)
print(a)
# Graphical representation of the Henry isotherm model
#### Plot details
ggplot2::theme_set(ggplot2::theme_bw(10))
ggplot2::ggplot(data, ggplot2::aes(x = x, y = y)) + ggplot2::geom_point(color ="#3498DB" ) +
ggplot2::geom_smooth(formula = y ~ x, method = "lm", se = F, color = "#D35400" ) +
ggplot2::labs(x = "Ce",
y = "Qe",
title = "Henry Isotherm Linear Model",
caption = "PUPAIM") +
ggplot2::theme(plot.title=ggplot2::element_text(hjust = 0.5))
}
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