Goodness of Fit

Description

Tests predicted and observed values for the goodness of fit with various criteria. The goodness of fit tests are used to test how well the model fits. Measures of goodness of fit typically summarize the argument between targets or observed values and the values expected or predicted under the model in question.

Usage

GoF(Observations, Predicts,
                nTermInAppr = 2,
                ndigit = 3,
                RMSE = TRUE,
                RRMSE = TRUE,
                SDR = TRUE,
                CV = TRUE,
                PC = TRUE,
                PI = TRUE,
                ME = TRUE,
                RAE = TRUE,
                MRAE = TRUE,
                MAPE = TRUE,
                MAD = TRUE,
                RSq = TRUE,
                ARSq = TRUE,
                AIC = TRUE,
                CAIC = TRUE)

Arguments

Author(s)

Prof. Dr. Ecevit Eyduran, TA. Alper Gulbe

References

Comparison of the Predictive Capabilities of Several Data Mining Algorithms and Multiple Linear Regression in the Prediction of Body Weight by Means of Body Measurements in the Indigenous Beetal Goat of Pakistan, Ecevit Eyduran, Daniel Zaborski, Abdul Waheed, Senol Celik, Koksal Karadas and Wilhelm Grzesiak, Pakistan J. Zool., vol. 49(1), pp 257-265, 2017.

Examples

# dummy inputs, independent variable
# integers from 0 to 9
inputs <- 0:9

# dummy targets/observed values, dependent variable
# a product of 2*times inputs minus 5 with some normal noise
targets <- -5 + inputs*2 + rnorm(10)

# linear regression model
model<-lm(targets~inputs)

# About the model
summary(model)

# Number of Terms
n = length(model$coefficients)

# model's predicted values against targets
predicted<-model$fitted.values

# using library ehaGoF for goodness of fit.
library(ehaGoF)

# Goodness of fit statistics
GoF(targets, predicted, nTermInAppr=n)

Coefficient of Variation.

Description

Calculates and returns goodness of fit - coefficient of variation (CV).

Usage

gofCV(Obs, Prd, dgt=3)

Arguments

Value

Author(s)

Prof. Dr. Ecevit Eyduran, TA. Alper Gulbe

References

Comparison of Different Data Mining Algorithms for Prediction of Body Weight From Several Morphological Measurements in Dogs - S Celik, O Yilmaz

Examples

# dummy inputs, independent variable
# integers from 0 to 19
inputs <- 0:19

# dummy targets/observed values, dependent variable
# a product of 2*times inputs minus 5 with some normal noise
targets <- -5 + inputs*1.2 + rnorm(20)

# linear regression model
model<-lm(targets~inputs)

# model's predicted values against targets
predicted<-model$fitted.values

# using library ehaGoF for goodness of fit.
library(ehaGoF)

# Goodness of fit - coefficient of variation (CV)
gofCV(targets, predicted)

Mean Absolute Percentage Error

Description

Calculates and returns the goodness of fit criterion: mean absolute percentage error (MAPE), a.k.a. mean absolute percentage deviation or MAPD.

Usage

gofMAPE(Obs, Prd, dgt=3)

Arguments

Details

Mean absolute percentage error (MAPE) is a measure of prediction accuracy of a forecasting method in statistics. It is commonly used as a loss function for regression problems and in model evaluation, for its very intuitive interpretation in terms of relative error. It usually expresses accuracy as a percentage.

Value

Note

For more information look at these papers:

Rob J. Hyndman, Anne B. Koehler, Another look at measures of forecast accuracy, International Journal of Forecasting, Volume 22, Issue 4, 2006, Pages 679-688, ISSN 0169-2070,

Arnaud de Myttenaere, Boris Golden, Bénédicte Le Grand, Fabrice Rossi, Mean Absolute Percentage Error for regression models, Neurocomputing, Volume 192, 2016, Pages 38-48, ISSN 0925-2312,

Author(s)

Prof. Dr. Ecevit Eyduran, TA. Alper Gulbe

References

Comparison of the Predictive Capabilities of Several Data Mining Algorithms and Multiple Linear Regression in the Prediction of Body Weight by Means of Body Measurements in the Indigenous Beetal Goat of Pakistan, Ecevit Eyduran, Daniel Zaborski, Abdul Waheed, Senol Celik, Koksal Karadas and Wilhelm Grzesiak, Pakistan J. Zool., vol. 49(1), pp 257-265, 2017.

Prediction of Selected Reproductive Traits of Indigenous Harnai Sheep under the Farm Management System via various Data Mining Algorithms - Daniel Zaborski, Muhammad Ali, Ecevit Eyduran, Wilhelm Grzesiak, Mohammad Masood Tariq, Ferhat Abbas, Abdul Waheed, Cem Tirink - Pakistan journal of zoology, 2019

Comparison of Different Data Mining Algorithms for Prediction of Body Weight From Several Morphological Measurements in Dogs - S Celik, O Yilmaz

Examples

# dummy inputs, independent variable
# integers from 0 to 9
inputs <- 0:9

# dummy targets/observed values, dependent variable
# a product of 2*times inputs minus 5 with some normal noise
targets <- -5 + inputs*2 + rnorm(10)

# linear regression model
model<-lm(targets~inputs)

# model's predicted values against targets
predicted<-model$fitted.values

# using library ehaGoF for goodness of fit.
library(ehaGoF)

# Goodness of fit - mean absolute percentage error statistics
gofMAPE(targets, predicted)

Pearson's Correlation Coefficients

Description

Calculates and returns Pearson's correlation coefficients (PC).

Usage

gofPC(Obs, Prd, dgt = 3)

Arguments

Value

Author(s)

Prof. Dr. Ecevit EYDURAN, TA. Alper GULBE

References

OBILOR Esezi Isaac, AMADI Eric Chikweru, Test for Significance of Pearson’s Correlation Coefficient, International Journal of Innovative Mathematics, Statistics & Energy Policies 6(1):11-23, Jan-Mar, 2018.

Reza Soleimani, Amir Hossein Saeedi Dehaghani, Alireza Bahadori, A new decision tree based algorithm for prediction of hydrogen sulfide solubility in various ionic liquids, Journal of Molecular Liquids, Volume 242, 2017, Pages 701-713, ISSN 0167-7322, https://doi.org/10.1016/j.molliq.2017.07.075. (http://www.sciencedirect.com/science/article/pii/S0167732217305123)

Examples

# dummy inputs, independent variable
# integers from 0 to 19
inputs <- 0:19

# dummy targets/observed values, dependent variable
# a product of 2*times inputs minus 5 with some normal noise
targets <- -5 + inputs*1.2 + rnorm(20)

# linear regression model
model<-lm(targets~inputs)

# model's predicted values against targets
predicted<-model$fitted.values

# using library ehaGoF for goodness of fit.
library(ehaGoF)

# Goodness of fit - Pearson's correlation coefficient
gofPC(targets, predicted)

Root Mean Square Error

Description

Calculates and returns root mean square error (RMSE).

Usage

gofRMSE(Obs, Prd, dgt = 3)

Arguments

Value

Author(s)

Prof. Dr. Ecevit Eyduran, TA. Alper Gulbe

References

Comparison of the Predictive Capabilities of Several Data Mining Algorithms and Multiple Linear Regression in the Prediction of Body Weight by Means of Body Measurements in the Indigenous Beetal Goat of Pakistan - Ecevit Eyduran, Daniel Zaborski, Abdul Waheed, Senol Celik, Koksal Karadas, Wilhelm Grzesiak

Prediction of Selected Reproductive Traits of Indigenous Harnai Sheep under the Farm Management System via various Data Mining Algorithms - Daniel Zaborski, Muhammad Ali, Ecevit Eyduran, Wilhelm Grzesiak, Mohammad Masood Tariq, Ferhat Abbas, Abdul Waheed, Cem Tirink - Pakistan journal of zoology, 2019

Indirect Estimation of Structural Parameters in South African Forests Using MISR-HR and LiDAR Remote Sensing Data - Precious Nokuthula Wistebaar Mahlangu, Renaud Mathieu, Konrad Wessels, Laven Naidoo, Michel M Verstraete, Gregory P Asner, Russell Main, Remote Sens. 2018, 10, 1537 ; doi:10.3390/rs10101537.

Examples

# dummy inputs, independent variable
# integers from 0 to 19
inputs <- 0:19

# dummy targets/observed values, dependent variable
# a product of 2*times inputs minus 5 with some normal noise
targets <- -5 + inputs*1.2 + rnorm(20)

# linear regression model
model<-lm(targets~inputs)

# model's predicted values against targets
predicted<-model$fitted.values

# using library ehaGoF for goodness of fit.
library(ehaGoF)

# Goodness of fit - root mean square error (RMSE)
gofRMSE(targets, predicted)

Standard Deviation Ratio

Description

Calculates and returns standard deviation ratio (SDR).

Usage

gofSDR(Obs, Prd, dgt=3)

Arguments

Value

Author(s)

Prof. Dr. Ecevit Eyduran, TA. Alper Gülbe

References

Comparison of the Predictive Capabilities of Several Data Mining Algorithms and Multiple Linear Regression in the Prediction of Body Weight by Means of Body Measurements in the Indigenous Beetal Goat of Pakistan, Ecevit Eyduran, Daniel Zaborski, Abdul Waheed, Senol Celik, Koksal Karadas and Wilhelm Grzesiak, Pakistan J. Zool., vol. 49(1), pp 257-265, 2017.

Prediction of Selected Reproductive Traits of Indigenous Harnai Sheep under the Farm Management System via various Data Mining Algorithms - Daniel Zaborski, Muhammad Ali, Ecevit Eyduran, Wilhelm Grzesiak, Mohammad Masood Tariq, Ferhat Abbas, Abdul Waheed, Cem Tirink - Pakistan journal of zoology, 2019

Comparison of Different Data Mining Algorithms for Prediction of Body Weight From Several Morphological Measurements in Dogs - S Celik, O Yilmaz

Examples

##---- Should be DIRECTLY executable !! ----
##-- ==>  Define data, use random,
##--	or do  help(data=index)  for the standard data sets.

# Input values, independent variable
input <- 0:4

# Target vector, observed values
target <- c(1.9, 4.1, 5.89, 7.9, 10.01)

# Simple linear regression target across input like target = a * input + b,
# where a and b are coefficients.
model <- lm(target~input)

# Information about the model
summary(model)

# Values predicted by the model
predicted <- predict(model)

# using library ehaGoF for goodness of fit.
library(ehaGoF)

# Goodness of fit - standard deviation ratio (SDR)
gofSDR(target, predicted)

Adjusted Coefficient of Determination (Adjusted R-Squared)

Description

Calculates and returns adjusted coefficient of determination (adjusted R-squared).

Usage

gofACoD(Obs, Prd, nTermInAppr = 2, dgt = 3)

Arguments

Value

Author(s)

Prof. Dr. Ecevit Eyduran, TA. Alper Gulbe

References

Comparison of Different Data Mining Algorithms for Prediction of Body Weight From Several Morphological Measurements in Dogs - S Celik, O Yilmaz.

A new decision tree based algorithm for prediction of hydrogen sulfide solubility in various ionic liquids - Reza Soleimani, Amir Hossein Saeedi Dehaghani, Alireza Bahadori.

Examples

# dummy inputs, independent variable
# integers from 0 to 19
inputs <- 0:19

# dummy targets/observed values, dependent variable
# a product of 2*times inputs minus 5 with some normal noise
targets <- -5 + inputs*1.2 + rnorm(20)

# linear regression model
model<-lm(targets~inputs)

# About the model
summary(model)

# Number of Terms
n = length(model$coefficients)

# model's predicted values against targets
predicted<-model$fitted.values

# using library ehaGoF for goodness of fit.
library(ehaGoF)

# Goodness of fit : adjusted coefficient of determination (adjusted R-squared)
gofACoD(targets, predicted, dgt=4,nTermInAppr=n)

Adjusted R-Squared (Adjusted Coefficient of Determination)

Description

Caclulates and returns adjusted coefficient of determination (adjusted R-squared).

Usage

gofARSq(Obs, Prd, nTermInAppr = 2, dgt = 3)

Arguments

Value

Author(s)

Prof. Dr. Ecevit Eyduran, TA. Alper Gulbe

References

Comparison of Different Data Mining Algorithms for Prediction of Body Weight From Several Morphological Measurements in Dogs - S Celik, O Yilmaz.

A new decision tree based algorithm for prediction of hydrogen sulfide solubility in various ionic liquids - Reza Soleimani, Amir Hossein Saeedi Dehaghani, Alireza Bahadori.

Examples

# dummy inputs, independent variable
# integers from 0 to 99
inputs <- 0:99

# dummy targets/observed values, dependent variable
# a product of 2*times inputs minus 5 with some normal noise
targets <- -5 + inputs*1.2 + rnorm(100)

# linear regression model
model<-lm(targets~inputs)

# About the model
summary(model)

# Number of Terms
n = length(model$coefficients)

# model's predicted values against targets
predicted<-model$fitted.values

# using library ehaGoF for goodness of fit.
library(ehaGoF)

# Goodness of fit : adjusted R-squared
gofARSq(targets, predicted, dgt=4, nTermInAppr=n)

Akaike's Information Criterion

Description

Calculates and returns Akaike's information criterion (AIC).

Usage

gofAIC(Obs, Prd, nTermInAppr=2, dgt = 3)

Arguments

Value

Note

When n/k is not greater than 40, where n is the number of observations and k is the number of terms in approximation, Corrected Akaike's Information Criterion (gofCAIC) is used.

Author(s)

Prof. Dr. Ecevit Eyduran, TA. Alper Gulbe

References

Comparison of the Predictive Capabilities of Several Data Mining Algorithms and Multiple Linear Regression in the Prediction of Body Weight by Means of Body Measurements in the Indigenous Beetal Goat of Pakistan - Ecevit Eyduran, Daniel Zaborski, Abdul Waheed, Senol Celik, Koksal Karadas, Wilhelm Grzesiak.

Prediction of Selected Reproductive Traits of Indigenous Harnai Sheep under the Farm Management System via various Data Mining Algorithms - Daniel Zaborski, Muhammad Ali, Ecevit Eyduran, Wilhelm Grzesiak, Mohammad Masood Tariq, Ferhat Abbas, Abdul Waheed, Cem Tirink - Pakistan journal of zoology, 2019.

Examples

# dummy inputs, independent variable
# integers from 0 to 99
inputs <- 0:99

# dummy targets/observed values, dependent variable
# a product of 2*times inputs minus 5 with some normal noise
targets <- -5 + inputs*1.2 + rnorm(100)

# linear regression model
model<-lm(targets~inputs)

# About the model
summary(model)

# Number of Terms
n = length(model$coefficients)

# model's predicted values against targets
predicted<-model$fitted.values

# using library ehaGoF for goodness of fit.
library(ehaGoF)

# Goodness of fit : Akaike's information criterion (AIC)
gofAIC(targets, predicted, dgt=4, nTermInAppr=n)

Coefficient of Determination (R-Squared)

Description

Calculates and returns coefficient of determination (R-squared).

Usage

gofCoD(Obs, Prd, dgt = 3)

Arguments

Value

Author(s)

Prof. Dr. Ecevit Eyduran, TA. Alper Gulbe

References

Comparison of Different Data Mining Algorithms for Prediction of Body Weight From Several Morphological Measurements in Dogs - S Celik, O Yilmaz.

A new decision tree based algorithm for prediction of hydrogen sulfide solubility in various ionic liquids - Reza Soleimani, Amir Hossein Saeedi Dehaghani, Alireza Bahadori.

Examples

# dummy inputs, independent variable
# integers from 0 to 99
inputs <- 0:99

# dummy targets/observed values, dependent variable
# a product of 2*times inputs minus 5 with some normal noise
targets <- -5 + inputs*1.2 + rnorm(100)

# linear regression model
model<-lm(targets~inputs)

# About the model
summary(model)

# model's predicted values against targets
predicted<-model$fitted.values

# using library ehaGoF for goodness of fit.
library(ehaGoF)

# Goodness of fit : coefficient of determination (R-squared)
gofCoD(targets, predicted)

Corrected Akaike's Information Criterion

Description

Calculates and returns corrected Akaike's information criterion.

Usage

gofCAIC(Obs, Prd, nTermInAppr = 2, dgt = 3)

Arguments

Value

Note

When n/k is greater than 40, where n is the umber of observations and k is the number of terms in approximation, Akaike's Information Criterion (gofAIC) is used.

Author(s)

Prof. Dr. Ecevit Eyduran, TA. Alper Gulbe

References

Comparison of the Predictive Capabilities of Several Data Mining Algorithms and Multiple Linear Regression in the Prediction of Body Weight by Means of Body Measurements in the Indigenous Beetal Goat of Pakistan - Ecevit Eyduran, Daniel Zaborski, Abdul Waheed, Senol Celik, Koksal Karadas, Wilhelm Grzesiak.

Prediction of Selected Reproductive Traits of Indigenous Harnai Sheep under the Farm Management System via various Data Mining Algorithms - Daniel Zaborski, Muhammad Ali, Ecevit Eyduran, Wilhelm Grzesiak, Mohammad Masood Tariq, Ferhat Abbas, Abdul Waheed, Cem Tirink - Pakistan journal of zoology, 2019.

Examples

# dummy inputs, independent variable
# integers fron 0 to 79
inputs <- 0:79

# dummy targets/observed values, dependent variable
# a product of 2*times inputs minus 5 with some normal noise
targets <- -5 + inputs*1.2 + rnorm(80)

# linear regression model
model<-lm(targets~inputs)

# About the model
summary(model)

# Number of Terms
n = length(model$coefficients)

# model's predicted values against targets
predicted<-model$fitted.values

# using library ehaGoF for Goodness of Fit function (GoF)
library(ehaGoF)

# Goodness of Fit : Corrected Akaike's Information Criterion
gofCAIC(targets, predicted, dgt=4, nTermInAppr=n)

Global Relative Approximation Error

Description

Calculates and returns global relative approximation error (RAE).

Usage

gofRAE(Obs, Prd, dgt = 3)

Arguments

Value

Author(s)

Prof. Dr. Ecevit Eyduran, TA. Alper Gulbe

References

Comparison of the Predictive Capabilities of Several Data Mining Algorithms and Multiple Linear Regression in the Prediction of Body Weight by Means of Body Measurements in the Indigenous Beetal Goat of Pakistan - Ecevit Eyduran, Daniel Zaborski, Abdul Waheed, Senol Celik, Koksal Karadas, Wilhelm Grzesiak.

Prediction of Selected Reproductive Traits of Indigenous Harnai Sheep under the Farm Management System via various Data Mining Algorithms - Daniel Zaborski, Muhammad Ali, Ecevit Eyduran, Wilhelm Grzesiak, Mohammad Masood Tariq, Ferhat Abbas, Abdul Waheed, Cem Tirink - Pakistan journal of zoology, 2019.

Comparison of Different Data Mining Algorithms for Prediction of Body Weight From Several Morphological Measurements in Dogs - S Celik, O Yilmaz.

The Connection Dependent Threshold Model for Finite Sources -A Generalization of the Engset Multirate Loss Model - Ioannis D. Moscholios and Michael D. Logothetis.

Examples

# dummy inputs, independent variable
# integers from 0 to 99
inputs <- 0:99

# dummy targets/observed values, dependent variable
# a product of 2*times inputs minus 5 with some normal noise
targets <- -5 + inputs*1.2 + rnorm(100)

# linear regression model
model<-lm(targets~inputs)

# About the model
summary(model)

# model's predicted values against targets
predicted<-model$fitted.values

# using library ehaGoF for goodness of fit.
library(ehaGoF)

# Goodness of fit : global relative approximation error (RAE)
gofRAE(targets, predicted)

Mean Absolute Deviation

Description

Calculates and returns mean absolute deviation (MAD).

Usage

gofMAD(Obs, Prd, dgt = 3)

Arguments

Value

Author(s)

Prof. Dr. Ecevit Eyduran, TA. Alper Gulbe

References

Comparison of the Predictive Capabilities of Several Data Mining Algorithms and Multiple Linear Regression in the Prediction of Body Weight by Means of Body Measurements in the Indigenous Beetal Goat of Pakistan - Ecevit Eyduran, Daniel Zaborski, Abdul Waheed, Senol Celik, Koksal Karadas, Wilhelm Grzesiak.

Prediction of Selected Reproductive Traits of Indigenous Harnai Sheep under the Farm Management System via various Data Mining Algorithms - Daniel Zaborski, Muhammad Ali, Ecevit Eyduran, Wilhelm Grzesiak, Mohammad Masood Tariq, Ferhat Abbas, Abdul Waheed, Cem Tirink - Pakistan journal of zoology, 2019.

Comparison of Different Data Mining Algorithms for Prediction of Body Weight From Several Morphological Measurements in Dogs - S Celik, O Yilmaz.

Examples

# dummy inputs, independent variable
# integers from 0 to 99
inputs <- 0:99

# dummy targets/observed values, dependent variable
# a product of 2*times inputs minus 5 with some normal noise
targets <- -5 + inputs*1.2 + rnorm(100)

# linear regression model
model<-lm(targets~inputs)

# model's predicted values against targets
predicted<-model$fitted.values

# using library ehaGoF for Goodness of Fit function (GoF)
library(ehaGoF)

# Goodness of Fit : Mean Absolute Deviation
gofMAD(targets, predicted, dgt=4)

Mean Error

Description

Calculates and returns mean error (ME).

Usage

gofME(Obs, Prd, dgt = 3)

Arguments

Value

Author(s)

Prof. Dr. Ecevit Eyduran, TA. Alper Gulbe

References

Comparison of the Predictive Capabilities of Several Data Mining Algorithms and Multiple Linear Regression in the Prediction of Body Weight by Means of Body Measurements in the Indigenous Beetal Goat of Pakistan - Ecevit Eyduran, Daniel Zaborski, Abdul Waheed, Senol Celik, Koksal Karadas, Wilhelm Grzesiak.

Prediction of Selected Reproductive Traits of Indigenous Harnai Sheep under the Farm Management System via various Data Mining Algorithms - Daniel Zaborski, Muhammad Ali, Ecevit Eyduran, Wilhelm Grzesiak, Mohammad Masood Tariq, Ferhat Abbas, Abdul Waheed, Cem Tirink - Pakistan journal of zoology, 2019.

Examples

# dummy inputs, independent variable
# integers from 0 to 19
inputs <- 0:19

# dummy targets/observed values, dependent variable
# a product of 2*times inputs minus 5 with some normal noise
targets <- -5 + inputs*1.2 + rnorm(20)

# linear regression model
model<-lm(targets~inputs)

# About the model
summary(model)

# model's predicted values against targets
predicted<-model$fitted.values

# using library ehaGoF for goodness of fit.
library(ehaGoF)

# Goodness of fit : mean error (ME)
gofME(targets, predicted)

Mean Relative Approximation Error

Description

Calculates and returns mean relative approximation error (MRAE).

Usage

gofMRAE(Obs, Prd, dgt = 3)

Arguments

Value

Author(s)

Prof. Dr. Ecevit Eyduran, TA. Alper Gulbe

References

The Connection Dependent Threshold Model for Finite Sources -A Generalization of the Engset Multirate Loss Model - Ioannis D. Moscholios and Michael D. Logothetis.

Competitive adsorption equilibrium modeling of volatile organic compound (VOC) and water vapor onto activated carbon - Imranul I. Laskara, Zaher Hashishoa,⁎, John H. Phillipsb, James E. Andersonc, Mark Nichols.

A new decision tree based algorithm for prediction of hydrogen sulfide solubility in various ionic liquids - Reza Soleimani, Amir Hossein Saeedi Dehaghani, Alireza Bahadori.

Examples

# dummy inputs, independent variable
# integers from 0 to 19
inputs <- 0:19

# dummy targets/observed values, dependent variable
# a product of 2 times inputs minus 5 with some normal noise
targets <- -5 + inputs*1.2 + rnorm(20)

# linear regression model
model<-lm(targets~inputs)

# About the model
summary(model)

# model's predicted values against targets
predicted<-model$fitted.values

# using library ehaGoF for goodness of fit.
library(ehaGoF)

# Goodness of fit : mean relative approximation error (MRAE)
gofMRAE(targets, predicted)

Performance Index

Description

Calculates and returns performance index (PI).

Usage

gofPI(Obs, Prd, dgt = 3)

Arguments

Value

Author(s)

Prof. Dr. Ecevit Eyduran, TA. Alper Gulbe

References

Prediction of Selected Reproductive Traits of Indigenous Harnai Sheep under the Farm Management System via various Data Mining Algorithms - Daniel Zaborski, Muhammad Ali, Ecevit Eyduran, Wilhelm Grzesiak, Mohammad Masood Tariq, Ferhat Abbas, Abdul Waheed, Cem Tirink - Pakistan journal of zoology, 2019

Examples

# dummy inputs, independent variable
# integers from 0 to 19
inputs <- 0:19

# dummy targets/observed values, dependent variable
# a product of 2*times inputs minus 5 with some normal noise
targets <- -5 + inputs*1.2 + rnorm(20)

# linear regression model
model<-lm(targets~inputs)

# model's predicted values against targets
predicted<-model$fitted.values

# using library ehaGoF for goodness of fit.
library(ehaGoF)

# Goodness of fit - performance index (PI)
gofPI(targets, predicted)

R-Squared (Coefficient of Determination)

Description

Calculates and returns R-squared (coefficient of determination).

Usage

gofRSq(Obs, Prd, dgt = 3)

Arguments

Value

Author(s)

Prof. Dr. Ecevit Eyduran, TA. Alper Gulbe

References

Comparison of Different Data Mining Algorithms for Prediction of Body Weight From Several Morphological Measurements in Dogs - S Celik, O Yilmaz.

A new decision tree based algorithm for prediction of hydrogen sulfide solubility in various ionic liquids - Reza Soleimani, Amir Hossein Saeedi Dehaghani, Alireza Bahadori.

Examples

# dummy inputs, independent variable
# integers from 0 to 99
inputs <- 0:99

# dummy targets/observed values, dependent variable
# a product of 2*times inputs minus 5 with some normal noise
targets <- -5 + inputs*1.2 + rnorm(100)

# linear regression model
model<-lm(targets~inputs)

# About the model
summary(model)

# model's predicted values against targets
predicted<-model$fitted.values

# using library ehaGoF for goodness of fit.
library(ehaGoF)

# Goodness of fit : coefficient of determination (R-squared)
gofRSq(targets, predicted)

Relative Root Mean Square Error

Description

Calculates and returns relative root mean square error (RRMSE) of the model. The ratio of the mean of square root of residuals squared to the mean of observed values.

Usage

gofRRMSE(Obs, Prd, dgt = 3)

Arguments

Details

RRMSE is calculated by dividing RMSE by the mean of observed values.

Value

Note

For more information: Despotovic, M., Nedic, V., Despotovic, D., & Cvetanovic, S., Evaluation of empirical models for predicting monthly mean horizontal diffuse solar radiation, Renewable and Sustainable Energy Reviews, Volume 56, April 2016, Pages 246-260, ISSN 1364-0321, http://dx.doi.org/10.1016/j.rser.2015.11.058.

Author(s)

Prof. Dr. Ecevit Eyduran, TA. Alper Gulbe

References

Comparison of the Predictive Capabilities of Several Data Mining Algorithms and Multiple Linear Regression in the Prediction of Body Weight by Means of Body Measurements in the Indigenous Beetal Goat of Pakistan, Ecevit Eyduran, Daniel Zaborski, Abdul Waheed, Senol Celik, Koksal Karadas and Wilhelm Grzesiak, Pakistan J. Zool., vol. 49(1), pp 257-265, 2017.

Indirect Estimation of Structural Parameters in South African Forests Using MISR-HR and LiDAR Remote Sensing Data - Precious Nokuthula Wistebaar Mahlangu, Renaud Mathieu, Konrad Wessels, Laven Naidoo, Michel M Verstraete, Gregory P Asner, Russell Main

Examples

# Input values, independent variable
input <- 0:4

# Target vector, observed values, dependent variable
target <- c(1.9, 4.1, 5.89, 7.9, 10.01)

# Simple linear regression, target across input like: target = a * input + b,
# where a and b are coefficients.
model <- lm(target~input)

# Information about the model
summary(model)

# Values predicted by the model
predicted <- predict(model)

# using library ehaGoF for goodness of fit
library(ehaGoF)

# Goodness of fit - relative root mean square error (RRMSE)
gofRRMSE(target, predicted)