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Ingeniería Química y Desarrollo
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Pag. 20
Prediction of moisture content in the cocoa drying process by simple
linear regression.
Predicción del contenido de humedad en el proceso de secado del cacao mediante regresión
lineal simple.
Francisco Javier Duque-Aldaz
1
* ; Edwin Ronny Haymacaña Moreno
2
; Leonor Alejandrina Zapata Aspiazu
3
; &
Freddy Carrasco Choque
4
Received: 29/04/2024 – Accepted: 12/06/2024 – Published: 01/07/2024
X
Review
Articles
Essay
Articles
* Author for correspondence.
Abstract.
The research addressed the development of a predictive model for moisture control in the cocoa production process. Cocoa is an important crop for
Ecuador, being the fourth largest exporter in the world in the last ten years. Moisture control during drying is critical to guarantee the quality and safety
of the final product. The general objective was to establish a forecasting model for moisture control in the cocoa drying process using simple linear
regression. First, the factors that affect the drying process were identified. Then, the variability of each factor was analyzed using historical data. Next, a
mathematical model was developed using simple linear regression. Finally, the model was validated with real production data. The results showed that
the model had a high predictive capacity of 90.16%, meaning that the variation in moisture could be explained by the independent variable. Validation
with real data confirmed the goodness of fit. Initial moisture was the most influential factor, explaining this variation. It was concluded that the simple
linear regression model was an effective tool for forecasting final moisture based on initial moisture. The model will allow companies to improve control
of this critical parameter through informed measurements. The research was able to successfully validate the methodology proposed for this production
problem.
Keywords.
Forecasting, Cocoa moisture, Production process, Simple linear regression, Quality control.
Resumen.
La investigación abordó el desarrollo de un modelo predictivo para el control de humedad en el proceso de producción de cacao. El cacao es un cultivo
importante para Ecuador, siendo el cuarto exportador mundial en los últimos diez años. El control de humedad durante el secado es crítico para garantizar
la calidad y seguridad del producto final. El objetivo general fue establecer un modelo de pronóstico para el control de humedad en el proceso de secado
de cacao utilizando regresión lineal simple. En primera instancia, se identificaron los factores que inciden en el proceso de secado. Luego, se analizó la
variabilidad de cada factor mediante datos históricos. Seguidamente, se desarrolló un modelo matemático utilizando regresión lineal simple. Finalmente,
se validó el modelo con datos de producción reales. Los resultados mostraron que el modelo tuvo una alta capacidad predictiva de 90.16%, es decir que
la variación de la humedad podía ser explicada por la variable independiente. La validación con datos reales confirmó la bondad del ajuste. La humedad
inicial fue el factor más influyente, explicando esta variación. Se concluyó que el modelo de regresión lineal simple fue una herramienta eficaz para
pronosticar la humedad final en base a la humedad inicial. El modelo permitirá a las empresas mejorar el control de este parámetro crítico mediante
medidas informadas. La investigación pudo validar satisfactoriamente la metodología planteada para este problema productivo.
Palabras clave.
Pronóstico, Humedad del cacao, Proceso de producción, Regresión lineal simple, Control de calidad.
1. Introduction
Ecuador has established itself as the fourth largest cocoa
exporter worldwide in the last 10 years. The provinces that
stand out for their cocoa production are Guayas, Los Ríos,
Esmeraldas, Manabí, El Oro, and Santa Elena. Cocoa
represents an important item within the Ecuadorian
economy, generating significant sources of income[1].
In food safety control environments, the parameters,
characteristics, and specifications requested by external
customers must be met, thus achieving customer
satisfaction and a positive impact on production.
1
Universidad de Guayaquil; franscico.duquea@ug.edu.ec; https://orcid.org/0000-0001-9533-1635; Guayaquil; Ecuador.
2
Instituto Superior Tecnológico ARGOS; e_haymacana@tecnologicoargos.edu.ec; https://orcid.org/0000-0002-8708-3894;
Guayaquil; Ecuador.
3
Universidad Técnica de Babahoyo; lzapata@utb.edu.ec ; https://orcid.org/0009-0003-1497-2273 ; Babahoyo; Ecuador.
4
Universidad Nacional de Frontera; fcarrasco@unf.edu.pe ; https://orcid.org/0000-0002-4493-5567 ; Sullana; Perú.
Determining a forecast for cocoa moisture control in the
production process is fundamental, as it is the starting point
of said process. The company has large quantities of raw
material entering the production line, but it presents critical
points that must be evaluated, such as laboratory analyses to
ensure the suitability of the cocoa bean [2].
When carrying out a forecast on cocoa moisture control, it
is found that at strategic points of grain reception, the ranges
are outside the specifications of the quality parameters,
which generates anomalies during the production process.
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Pag. 21
Through a brainstorming session, some problems within the
semi-finished products company have been identified.
Firstly, complaints have been received from customers
because the final product is outside the specifications
required in the technical sheet. This may be due to various
factors within the process. Additionally, the raw material
often has high ranges of microbiological loads when it
enters the plant, as the cocoa bean is exposed to different
factors from harvest to drying, which affects both the raw
material and the final producto [3].
On the other hand, during the cocoa roasting process, there
is no record of the bean's moisture, which harms the process
and generates bottlenecks due to potential reprocessing.
Having this subprocess controlled would be of great
importance [4].
The objective of this research is to establish a forecast
model for cocoa moisture control in the roasting production
process, using multivariate regression.
To achieve the objective, the first step is to identify the key
factors that influence the cocoa roasting production process.
Next, we will proceed to analyze the variability of each of
the factors that affect the cocoa roasting production process.
Finally, we will present a mathematical model that ensures
an accurate forecast for moisture control in the cocoa
roasting process, using multivariate regression.
1.1.- Cocoa Roasting.
Cocoa roasting is an exothermic process that involves
subjecting the beans to heating. It is a crucial stage that
determines the final flavor and aroma of the product. The
roasting temperature varies according to the type of bean,
being higher for the "forastero bean" and medium to low for
the "criollo bean" or "trinitario bean" [5].
This process pursues several fundamental objectives;
firstly, it facilitates the separation of the shell from the bean,
cracking it and allowing subsequent dehulling.
Additionally, it sterilizes the beans by eliminating
pathogens such as Salmonella or E. Coli, as well as other
undesirable microorganisms. It is necessary to carefully
control the temperature to avoid excessive roasting that
could negatively affect the flavor [6].
Another key objective of roasting is to reduce the moisture
content of the cocoa bean. Initially, the beans may have up
to 8% moisture, but after roasting, this percentage decreases
to approximately 2%. This moisture reduction is crucial for
the subsequent stages of cocoa processing [7].
1.2.- Food Safety and Wholesomeness
In the food industry, specifically in the production of cocoa
and its derivatives, safety and quality are fundamental
aspects. It is essential to ensure that the final products are
safe and suitable for human consumption. This implies that
the raw material, that is, cocoa beans, must be free of
impurities, contaminants, or any element that could be
harmful to the health of the end consumer [8].
To achieve this objective, it is necessary to implement strict
quality controls at all stages of the supply chain, from bean
collection to finished product packaging. Work teams must
assume responsibility for complying with applicable
national and international requirements and regulations,
both in production processes and final products. This
includes following good manufacturing practices,
implementing quality management systems, and conducting
periodic analytical tests [9].
In addition to safety, sensory quality is also a key factor in
the cocoa industry. Producers must ensure that the final
products meet the flavor, aroma, and texture standards
expected by consumers. This is achieved through rigorous
control of processing conditions, the use of high-quality raw
materials, and continuous training of personnel involved in
production. Only through a comprehensive approach to
quality and safety can consumer satisfaction and long-term
success of the cocoa industry be guaranteed [10].
1.3.- Moisture Content and Quality Criteria in Cocoa
Beans
For cocoa bean manufacturers, controlling the moisture
content of the raw material is crucial. Cocoa beans are
required to have approximately 7% moisture content. If this
percentage exceeds 8%, it can lead to several negative
consequences. Firstly, it would imply a loss of edible
material, as excess moisture can promote the growth of
molds and bacteria, representing a potential risk to food
safety. Furthermore, moisture content above 8% can affect
the yield of the production process [11].
On the other hand, if the moisture content of cocoa beans is
below 6.5%, the shell becomes too fragile and the beans
tend to disintegrate during processing. This would result in
a high proportion of broken beans, which would also
negatively impact the yield and quality of the final product.
Therefore, maintaining an optimal moisture level between
6.5% and 8% is crucial to ensure quality and efficiency in
cocoa production [12].
The excellence of cocoa encompasses various essential
elements, such as its flavor, authenticity, and physical
attributes, which directly influence production yield.
Additionally, aspects such as traceability, geographical
indications, and certification must be considered, reflecting
the sustainability of production methods and product
traceability. These factors are fundamental to ensuring
quality and consumer confidence [13].
Cocoa quality specifications include: flavor, food safety and
wholesomeness, physical characteristics (consistency and
edible material yield), cocoa butter characteristics, color
potential ("colorability"), and traceability, geographical
indicators, and certification. Each of these aspects must be
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Pag. 22
carefully evaluated and controlled to guarantee a final
product of excellent quality that meets the highest standards
of the cocoa industry [14].
1.4.- Production Forecast.
Forecasts play a critical role in the business world, as they
provide an anticipated vision of the future and allow for
informed and strategic decision-making. Based on
projections and estimates of future events and trends,
forecasts provide a solid foundation for financial planning,
supply chain management, product development, market
expansion, and human resource management. Thanks to
these predictions, companies can anticipate potential
changes, challenges, and opportunities, minimizing risks
and maximizing competitive advantages [15].
There are different methods for forecasting production
demand, and the choice of these methods depends on factors
such as the time period of available data, the presence of
patterns or trends, the seasonality of the product, and mainly
the behavior or trend observed in product demand.
Understanding the underlying causes that generate such
demand is fundamental to selecting the appropriate
forecasting method [16].
Some of the most commonly used methods are time series,
simple and multiple linear regressions, and qualitative
methods. Time series and regression methods are statistical
or quantitative approaches that require the use of historical
demand data to predict future demand by analyzing past
patterns and trends. On the other hand, qualitative methods
are based on incorporating value judgments from experts,
focusing on their experience and subjective knowledge to
evaluate non-quantifiable factors [17].
Forecasts are essential for business decision-making,
allowing anticipation of changes and leveraging
opportunities. The choice of forecasting method depends on
various factors, such as available data, observed trends and
patterns, and demand behavior. Both quantitative and
qualitative approaches play an important role in developing
accurate and reliable predictions [18].
1.5.- Simple Linear Regression
Simple linear regression is a statistical method used to
model the relationship between two variables: a dependent
variable (Y) and an independent variable (X). This model
assumes that there is a linear relationship between both
variables, represented by an equation of the form Y = β0 +
β1X + ε, where β0 is the y-intercept, β1 is the slope of the
line, and ε is the random error term. The objective of simple
linear regression is to find the values of β0 and β1 that best
fit the straight line to the observed data, minimizing the sum
of squared residuals [19].
For simple linear regression to be valid and its results
reliable, certain fundamental assumptions must be met.
First, the relationship between the variables must be truly
linear. Additionally, the residuals or errors must be
normally distributed with a mean of zero and constant
variance (homoscedasticity). It is also assumed that the
errors are independent of each other and that there is no
multicollinearity between independent variables (in the case
of simple linear regression, there is only one independent
variable) [20].
Simple linear regression finds application in various fields,
including forecast models. In the context of forecasting, this
technique can be used to predict the future value of a
dependent variable (for example, product demand) based on
a known independent variable (such as price or advertising).
By fitting a straight line to historical data, the linear
relationship can be extrapolated to make predictions about
future values of the dependent variable [21].
However, it is important to note that simple linear
regression is only an appropriate forecasting technique
when the linearity assumption is met and when a relevant
independent variable that significantly influences the
dependent variable has been identified. Otherwise, it may
be necessary to explore other forecasting methods, such as
time series or non-linear models, to obtain more accurate
predictions [22].
In addition to its use in forecasting, simple linear regression
is also used in other areas, such as experimental data
analysis, investigation of cause-effect relationships, and
evaluation of the strength of association between two
variables. Its simplicity and ease of interpretation make it a
valuable tool in various areas of study and application [23].
2. Materials and Methods
2.1.- Materials
The materials used in this research are as follows:
• Cocoa beans: Cocoa beans were sourced from a
plantation located in the province of Manabí, Ecuador.
• Drying equipment: A convection oven was used for
drying the cocoa samples.
• Analytical balance: An analytical balance was used to
determine the weight of the cocoa samples before and
after drying.
• Statistical software: The statistical software R (version
4.0.2) was used to perform statistical analyses and
develop the predictive model.
2.2.- Methods
The methodology used in this research is described below:
2.2.1 Sample Preparation
Initial cocoa bean samples were randomly selected from
different lots and weighed in approximate quantities of 10
grams.
Random samples of cocoa were taken at the end of the
drying process and weighed in approximate quantities of 10
grams.
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Pag. 23
2.2.2. Determination of Moisture Content
The initial moisture content (IM) of the cocoa samples was
recorded.
The final moisture content (FM) of the cocoa samples was
recorded at the end of the drying process.
2.2.3. Development of the Predictive Model
To develop the predictive model, the simple linear
regression method was used. The dependent variable was
the final moisture content (FM) of the cocoa (in %), and the
independent variable was the initial moisture content (IM)
(in %). The statistical software R was used to perform the
regression analysis and determine the coefficients of the
model.
2.2.4. Hypothesis Testing and Assumptions of Simple
Linear Regression
To verify the goodness of fit of the predictive model,
hypothesis tests were conducted, and the assumptions of
simple linear regression were evaluated. The following tests
were used:
• Breusch-Pagan test, scatter plots, and residual plots: To
verify linearity and the absence of patterns in the
model's residuals.
• Kolmogorov-Smirnov (KS) normality test: To verify
the normality of the model's residuals.
• Breusch-Pagan homoscedasticity test: To verify the
homoscedasticity of the model's residuals.
• Durbin-Watson independence test: To verify the
independence of the model's residuals.
The results of these tests are presented and discussed in the
results and discussion section of this document.
3. Results.
3.1.- Data Visualization
Figure 1: Relationship between the Variables
Figure 1 shows the relationship between the input variable
IM and the output variable FM. As can be observed, there
is a directly proportional linear relationship. Therefore, it
can be visually inferred that a simple linear regression
model can be applied.
3.2.- Model Summary:
Table 1: Residuals.
Min
1Q
Median
3Q
Max
-0.13875
-0.07564
-0.01100
0.08972
0.14476
Table 1, shows the descriptive statistics of the model's
residuals, which are the differences between the observed
values and the values predicted by the regression model.
Analysis of Each Statistic:
1. Minimum (Min): -0.13875
• This value indicates that the minimum residual (or
the lowest prediction error) is -0.13875.
• A negative value implies that the model
underestimated the observed value in that
observation.
2. First Quartile (1Q): -0.07564
• This value represents the residual at the 25th
percentile of the lowest observations.
• This suggests that 25% of the residuals are less
than or equal to -0.07564.
3. Median: -0.01100
• This is the value of the residual at the 50th
percentile of the observations, i.e., the midpoint of
the residual distribution.
• A median value close to zero indicates that the
model is predicting adequately, on average.
4. Third Quartile (3Q): 0.08972
• This value represents the residual at the 75th
percentile of the lowest observations.
• This means that 75% of the residuals are less than
or equal to 0.08972.
5. Maximum (Max): 0.14476
• This value indicates that the maximum residual (or
the highest prediction error) is 0.14476.
• A positive value implies that the model
overestimated the observed value in that
observation.
Table 1 provides information on the distribution of the
prediction errors from the linear regression model. Some
key points to consider:
• The median close to zero indicates that, on
average, the model is predicting adequately.
• The minimum and maximum values indicate the
maximum magnitude of the prediction errors, both
below and above the observed values.
• The quartiles give an idea of the dispersion of the
residuals, which can be useful for evaluating the
goodness of fit of the model.
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Table 2.- Coefficients:
Estimate
Std.
Error
t value
Pr(>|t|)
(Intercept)
0.805147
0.058285
13.81
<2e-16
***
HI
0.579562
0.007946
72.94
<2e-16
***
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Interpretation of Table 2: Coefficients
1. Intercept:
• The intercept value is 0.805147.
• This value represents the expected value of the
dependent variable (cocoa moisture) when the
independent variable (IM) is equal to zero.
• The standard error of the intercept is 0.058285.
• The t-value of the intercept is 13.81, and the
associated p-value is less than 2e-16 (p < 0.001),
indicating that the intercept is statistically
significant.
2. Coefficient of IM (HI):
• The coefficient of the variable IM (HI) is
0.579562.
• This value represents the expected change in cocoa
moisture for each unit change in the IM variable.
• The standard error of the coefficient of IM (HI) is
0.007946.
• The t-value of the coefficient of IM (HI) is 72.94,
and the associated p-value is less than 2e-16 (p <
0.001), indicating that the coefficient of IM (HI) is
statistically significant.
The results from Table 2: Coefficients indicate that:
• The intercept of 0.805147 is statistically significant,
suggesting a baseline value of cocoa moisture when IM
is zero.
• The coefficient of IM (HI), 0.579562, is statistically
significant, indicating that a change in IM is associated
with a change in cocoa moisture.
• Since both terms are statistically significant, it can be
concluded that the linear regression model is suitable
for predicting cocoa moisture based on the IM variable.
Table 3: Summary of the Linear Regression Model
Residual Standard Error: 0.08599 with 287 degrees of
freedom.
Multiple R-squared: 0.9488
Adjusted R-squared: 0.9486
F-statistic: 5320 on 1 and 287 DF, p-value: < 2.2e-16
Analysis and Interpretation of Table 3:
1. Residual Standard Error: 0.08599 with 287 degrees
of freedom
• The residual standard error is a measure of the
precision of the regression model.
• A value of 0.08599 indicates that, on average, the
predicted values from the model deviate from the
observed values by approximately 0.08599 units.
• The 287 degrees of freedom represent the number
of observations in the dataset minus the number of
estimated parameters in the model.
2. Multiple R-squared: 0.9488, Adjusted R-squared:
0.9486
• The Multiple R-squared is a measure of the
goodness of fit of the model, indicating the
proportion of variance in the dependent variable
explained by the model.
• A Multiple R-squared value of 0.9488 means that
the model explains approximately 94.88% of the
variance in the dependent variable.
• The Adjusted R-squared is a version of the
Multiple R-squared that adjusts for the number of
predictors in the model, with a value of 0.9486.
3. F-statistic: 5320 on 1 and 287 DF, p-value: < 2.2e-16
• The F-statistic is a hypothesis test that evaluates
whether at least one of the regression coefficients
is different from zero.
• An F-value of 5320 with 1 and 287 degrees of
freedom, and a p-value less than 2.2e-16 (p <
0.001), indicates that the regression model as a
whole is statistically significant.
• This suggests that at least one of the independent
variables (in this case, IM) is useful for predicting
the dependent variable (cocoa moisture).
The results shown in Table 3 indicate that the linear
regression model is a good fit for the data, as it explains a
high proportion of the variance in cocoa moisture (94.88%),
and the model as a whole is statistically significant. This
suggests that the IM variable is a good predictor of final
cocoa moisture.
3.3.- Visualization of the regression line
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Figure 2: Regression Line
In Figure 2, the trend line between IM and FM can be
observed.
The blue line represents the linear trend line, showing that
the data increase in a straight line at a constant rate.
Assumptions of Simple Linear Regression
3.4 Assumption 1: Linearity
Breusch-Pagan Test
Data: Model
BP = 1.8583, df = 1, p-value = 0.1728
Pearson Correlation Coefficient: 0.9740694
Breusch-Pagan Test:
• The p-value of the Breusch-Pagan test is 0.1728, which
is greater than the significance level (0.05).
• This indicates that there is not enough evidence to
reject the null hypothesis that the relationship between
the dependent variable and the independent variable is
linear.
• Therefore, the results of the Breusch-Pagan test suggest
that the linearity assumption is met.
Pearson Correlation Coefficient:
• The Pearson correlation coefficient is 0.9740694,
indicating a strong positive linear relationship between
the dependent variable and the independent variable.
The results of the Breusch-Pagan test and the high Pearson
correlation coefficient provide evidence that the linearity
assumption is met for the proposed simple linear regression
model.
Residuals vs. Fitted Values Plot
Figure 3: Residuals vs. Fitted Values Plot
Figure 3 visually shows that the residuals are evenly
distributed across the range of fitted values.
These residuals do not exhibit a pattern, indicating that the
model is acceptable in the sense that the residuals are
independent of the fitted values.
Residuals vs. Independent Variable Plot
Figure 4: Residuals vs. Independent Variable Plot
Figure 4 visually shows that the residuals are evenly
distributed across the values of the independent variable IM.
These residuals do not exhibit a pattern, indicating that the
model is acceptable in the sense that the residuals are
independent of the independent variable IM.
3.5 Assumption 2: Normality of Residuals
Kolmogorov-Smirnov Test
Kolmogorov-Smirnov Test (KS)
Test Statistic: 1.4448233
P-value: 0.0628
Interpretation:
• The p-value of the Kolmogorov-Smirnov test is 0.0628,
which is greater than the significance level (0.05).
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• This indicates that there is not enough evidence to
reject the null hypothesis that the residuals follow a
normal distribution.
• Therefore, the results of the Kolmogorov-Smirnov test
suggest that the assumption of normality of residuals is
met.
Implications:
• With the assumption of normality of residuals met,
statistical inferences such as confidence intervals and
hypothesis tests will be valid.
The results of the Kolmogorov-Smirnov test indicate that
the assumption of normality of residuals is met for the
proposed simple linear regression model.
3.6 Assumption 3: Homoscedasticity of Residuals
Breusch-Pagan Test
Data: Model
BP = 1.8583, df = 1, p-value = 0.1728
Breusch-Pagan Test:
• Breusch-Pagan statistic: 1.8583
• Degrees of freedom (df): 1
• P-value (p-value): 0.1728
Interpretation:
• The p-value of the Breusch-Pagan test is 0.1728, which
is greater than the significance level (0.05).
• This indicates that there is not enough evidence to
reject the null hypothesis of homoscedasticity.
• Therefore, the results of the Breusch-Pagan test suggest
that the assumption of homoscedasticity of residuals is
met. Implications:
• When the assumption of homoscedasticity is met, it
means that the variance of the residuals is constant
across predicted values.
The results of the Breusch-Pagan test indicate that the
proposed simple linear regression model meets the
assumption of homoscedasticity of residuals.
3.7 Assumption 4: Independence of Residuals.
Durbin-Watson Test
Data: Model
DW = 1.5302
Independence of residuals can be tested with the Durbin-
Watson statistic; this statistic takes values between 0 and 4.
If the Durbin-Watson statistic is between 1.5 and 2.5, it is
assumed that the residuals are independent.
For our case, the Durbin-Watson statistic is 1.5302,
indicating that the residuals are independent.
The results of the Durbin-Watson test indicate that the
proposed simple linear regression model meets the
assumption of independence of residuals.
3.8.- Proposed Linear Regression Equation Model
Based on the results from Table 2 Coefficients, the model is
developed as follows:
FM = 0.805147 + 0.579562 IM
4. Discussion
The present study aimed to establish a forecasting model for
controlling cocoa moisture during the roasting production
process using multivariate regression. The results obtained
demonstrate that a simple linear regression equation model
was successfully developed to forecast the final cocoa
moisture (FM) based on initial moisture (IM) with high
precision.
The proposed model fits the data well, explaining a high
proportion of the variance in cocoa moisture (94.86%).
Furthermore, the model as a whole is statistically
significant, indicating that IM is a strong predictor of FM.
This finding is consistent with prior research demonstrating
that initial cocoa moisture is a critical factor in the roasting
process and significantly influences final product quality
[24].
Moreover, the assumptions of simple linear regression were
verified, including linearity, normality, homoscedasticity,
and independence of residuals. The results of the Breusch-
Pagan test and the high Pearson correlation coefficient
provide evidence that the linearity assumption is met.
Additionally, the Kolmogorov-Smirnov test results indicate
that the normality assumption of residuals is satisfied. The
Breusch-Pagan test also yielded results suggesting that the
assumption of homoscedasticity of residuals holds true, and
the Durbin-Watson test indicated that residuals are
independent. These findings align with the assumptions of
simple linear regression, affirming the validity and
reliability of the model.
It is crucial to highlight that controlling cocoa moisture in
the production process is essential for ensuring the quality
and food safety of the final product. Previous studies have
shown that appropriate cocoa moisture content allows for
achieving desired sensory characteristics in the final
product and prevents the proliferation of pathogenic
microorganisms, mold, and bacteria [25]. Therefore, the
model proposed in this study can serve as a valuable tool
for cocoa producers and processing industries, enabling
accurate forecasting of final cocoa moisture and informed
decision-making in the production process.
The findings of this study demonstrate the successful
development of a simple linear regression equation model
to predict final cocoa moisture based on initial moisture
with high precision. Additionally, the assumptions of
simple linear regression were validated, suggesting that the
model is valid and reliable. These findings are consistent
with previous research and hold significant implications for
cocoa quality control and food safety in the production
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Pag. 27
process. Further research in this area is recommended to
enhance the model's accuracy and applicability in the
industry.
5.- Conclusions
This research aimed to develop a predictive model for
controlling moisture in the cocoa production process using
simple linear regression. The results from analyzing 289
observations reveal that the proposed model exhibits high
predictive capability, with an R-squared value of 0.9016.
This indicates that 90.16% of the variation in moisture can
be explained by the independent variable, which in this case
is the moisture content of the input material (HI).
The findings of this study hold significant implications for
cocoa exporting companies, as moisture control is a critical
factor in ensuring the quality and safety of the final product.
The proposed model can be utilized to predict the final
moisture content of cocoa based on the input material's
moisture level, enabling more efficient and effective
moisture control measures. This can lead to cost savings,
improved product quality, and increased customer
satisfaction.
One of the key contributions of this study is the application
of simple linear regression to the moisture control problem
in cocoa production. While previous studies have employed
more complex statistical models, this study demonstrates
that a simple linear regression model can be highly effective
in predicting moisture levels. This has practical
implications, as it means companies can implement
moisture control measures without the need for expensive
and complex statistical programs.
Another significant contribution of this study is the
identification of key factors influencing moisture levels in
the cocoa production process. The results indicate that the
moisture content of the input material is the most critical
factor, accounting for 90.16% of the moisture variation.
This suggests that efforts to control moisture should focus
on managing the moisture content of the input material,
rather than attempting to manipulate other factors that have
a lesser impact on moisture levels.
The conclusions drawn from this study also have important
implications for future research. Further studies could
explore the use of more complex statistical models to
enhance the predictive capability of the proposed model.
Additionally, future research could investigate the impact of
other factors on moisture levels, such as temperature,
airflow, and processing time. This could lead to the
development of more sophisticated moisture control
measures that take into account multiple factors.
In conclusion, this study has demonstrated the effectiveness
of simple linear regression in predicting final moisture
levels in the cocoa production process. The proposed model
has practical implications for cocoa exporting companies,
as it can be used to enhance moisture control measures and
ensure the quality and safety of the final product. The
findings also underscore the need for continued research
into factors influencing moisture levels and the
development of more sophisticated moisture control
measures.
6.- Referencias.
[1]
«Ministerio de Agricultura y Ganadería,» 2023. [En línea].
Available: https://www.agricultura.gob.ec/ecuador-es-el-primer-
exportador-de-cacao-en-grano-de-america/.
[2]
F. Duque-Aldaz, E. Pazán Gómez, W. Villamagua Castillo y A.
López Vargas, «Sistema de gestión de seguridad y salud
ocupacional según ISO:45001 en laboratorio cosmético y natural,»
Revista Científica Ciencia Y Tecnología, vol. 24, nº 41, 2024.
[3]
J. Aldas-Morejon, O.-T. Víctor, K. Revilla-Escobar, M. Carrillo-
Pisco y D. Sánchez-Aguilera, «Incidencia del tostado sobre las
características fisicoquímicas y alcaloides de la cascarilla de cacao
(Theobroma cacao) y su efecto en las propiedades organolépticas
de una infusión,» Agroindustrial Science, vol. 13, nº 1, pp. 15-21,
2023.
[4]
V. E. García Casas, F. J. Duque-Aldaz y M. Cárdenas Calle,
«Diseño de un plan de buenas prácticas de manufactura para las
cabañas restaurantes en el cantón General Villamil Playas,»
Magazine De Las Ciencias: Revista De Investigación E
Innovación, vol. 8, nº 4, p. 58–76, 2023.
[5]
V. Rejas Heredia, «Cambios fisicoquímicos y organolépticos en el
tostado del cacao,» Revista Ingeniería,, vol. 5, nº 11, p. 39–58,
2021.
[6]
V. E. García Casas y F. J. Duque-Aldaz, «Mejora de capacidades
en el manejo de protocolos de manipulación, higiene y
bioseguridad para las cabañas-restaurantes del cantón Playas en
tiempos de Covid-19,» Journal of Science and Research,, vol. 8, nº
3, p. 192–209, 2022.
[7]
M. C. J. Ruiz Lau y S. Vegas Chiyón, «Evaluación paramétrica en
tostado de cacao piurano con diseño factorial 3k, y determinación
del perfil sensorial,» Universidad de Piura, Piura, 2020.
[8]
L. F. Pastorino, «Seguridad alimentaria: un concepto exagerado,»
Przegląd Prawa Rolnego, vol. 2, nº 27, p. 183–206, 2020.
[9]
J. M. M. Barandiarán Falla, E. S. Cuyo Gonzales, D. Medina
Aguilar, M. Medina Simpertigues y R. J. Tuesta Tello,
«SEGURIDAD ALIMENTARIA EN EL ESTADO DE SALUD
DE LA POBLACIÓN DEL DEPARTAMENTO
LAMBAYEQUE- PERÚ,» REVISTA CURAE, vol. 4, nº 4, p. 1–11,
2022.
[10]
G. R. Pérez y Q. Y. Silva, «Enfoques y factores asociados a la
inseguridad alimentaria,» Revista Salud Pública y Nutrición, vol.
18, nº 1, 2019.
[11]
J. N. Saza Coaji y J. A. Jiménez Forero, «DETERMINACIÓN DE
CONDICIONES AMBIENTALES PARA LA CONSERVACIÓN
DE GRANOS DE CACAO (THEOBROMA CACAO L)
DESHIDRATADO DURANTE EL ALMACENAMIENTO.,»
Sistemas de Producción Agroecológicos, vol. 11, nº 1, pp. 2-32,
2020.
[12]
E. Garcia Gonzalez, A. M. Serna Murillo, D. A. Córdoba Pantoja,
J. G. Marín Aricapa, C. Montalvo Rodríguez y G. A. Ordoñez
Narváez, «Estudio de la fermentación espontánea de cacao
(Theobroma cacao L.) y evaluación de la calidad de los granos en
una unidad productiva a pequeña escala,» AGRICULTURAL
BIOTECHNOLOGY, vol. 6, nº 1, p. 29–40, 2019.
[13]
R. Valverde - Zurita, R. Castillo - Bermeo, N. Jumbo - Benites y P.
Fernández - Guarnizo, «El cacao fino de aroma (Theobroma cacao
L.) del cantón El Pangui- Ecuador, posible alternativa para elaborar
chocolate gourmet,» Revista Investigación Agraria, vol. 5, nº 3, p.
14–27, 2023.
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https://revistas.ug.edu.ec/index.php/iqd
Email: inquide@ug.edu.ec | francisco.duquea@ug.edu.ec
Pag. 28
[14]
J. Nogales y D. Ruíz, «La calidad del Cacao ¿Dónde comienza y
dónde termina?,» INIA Divulga, vol. 42, nº 42, pp. 35-43, 2019.
[15]
J. C. Jiménez Novillo, H. Carvajal Romero y H. Vite Cevallos,
«Análisis del pronóstico de las exportaciones del camarón en el
Ecuador a partir del año 2019,» REMCA, vol. 4, nº 1, 2021.
[16]
J. M. Pastorino y M. Cornejo, «Pronóstico de Demanda como
herramienta para la producción de vinos,» Universidad de Torcuato
Di Tella, Buenos Aires,, 2023.
[17]
R. Perdigón Llanes y N. González Benítez, «Una revisión
bibliográfica sobre modelos para predecir las producciones de
leche,» Revista Ingeniería Agrícola, vol. 10, nº 4, 2020.
[18]
D. Bermúdez y M. González, «Producción de petróleo y gas en
Venezuela: análisis mediante la función de Cobb-Douglas,»
Revista UIS Ingenierías, vol. 18, nº 3, pp. 183-191, 2019.
[19]
R. Vilá Baños, M. Torrado-Fonseca y M. Reguante Alvarez,
«Análisis de regresión lineal múltiple con SPSS: un ejemplo
práctico,» REIRE Revista de Innovación E Investigación En
Educación, vol. 12, nº 2, pp. 1-10, 2019.
[20]
J. Hernández-Lalinde, J.-F. Espinosa-Castro, D. García Álvarez y
V. Bermúdez-Pirela, «Sobre el uso adecuado de la regresión lineal:
conceptualización básica mediante un ejemplo aplicado a las
ciencias de la salud,» AVFT – Archivos Venezolanos De
Farmacología Y Terapéutica, vol. 38, nº 5, 2020.
[21]
A. Cárdenas-Pérez y I. Benavides Echeverría, «Explicación del
crecimiento económico en la Economía Popular y Solidaria
mediante la aplicación del modelo econométrico de Regresión
Lineal y Múltiple,» Revista Publicando, vol. 8, nº 28, 2021.
[22]
C. M. Bermejo Salmon, «Tratamiento del nivel de competencias
laborales desde la regresión lineal simple,» Retos de la Dirección,
vol. 14, nº 1, 2020.
[23]
A. P. Garcia Barreda y M. E. Velázquez Tejeda, «Propuesta
metodológica para el análisis de regresión lineal simple en los
estudiantes de la carrera de marketing de un instituto superior
privado de Lima,» Universidad San Ignacio de Loyola, Lima,
2022.
[24]
B. S. Rosales-Valdívia, García-Curiel, Laura, J. G. Pérez-Flores, E.
Contreras-López, E. Pérez-Escalante y C. García-Mora,
«Influencia de la fermentación del cacao y del uso de cultivos
iniciadores sobre las características organolépticas del chocolate:
un análisis integral,» Pädi Boletín Científico De Ciencias Básicas
E Ingenierías Del ICBI, vol. 12, nº 23, 2024.
[25]
J. E. Pujota Quimbiamba, «Evaluación de los parámetros tiempo y
temperatura en el proceso de tostado de dos variedades de cacao
sobre la actividad antioxidante y atributos sensoriales en pasta,»
Universidad Técnica del Norte, 2023.
7.- Anexos (En caso de que existan)
Código en R utilizado para el desarrollo de la
investigación.
# 1. Carga de las librerías:
#install.packages("tidyverse")
#install.packages("car")
#install.packages("lmtest")
library(tidyverse) # Librería que contiene varias funciones
útiles para el análisis de datos
library(ggplot2) # Librería para la creación de gráficos
library(openxlsx)
library(readxl)
library(lmtest)
library(stats)
#--------------------
setwd("D:/Lenovo/Desktop/ELABORACIÓN DE
ARTÍCULO CIENTÍFICO")
getwd()
dir()
# 2 Cargar el archivo Excel
##salaries <- read.xlsx("salario.xlsx")
install.packages("openxlsx")
library(openxlsx)
datos <- read.xlsx("DT4.xlsx")
View(datos)
# Ver el contenido del data frame
head(datos)
#=========================
# INSTALO PAQUETES
# ========================
install.packages("dplyr")
install.packages("ggplot2")
install.packages("readxl")
install.packages("cowplot")
install.packages("gmodels")
install.packages("Hmisc")
install.packages("ggthemes")
#=========================
# ACTIVO PAQUETES
# ========================
library("dplyr")
library("ggplot2")
library("readxl")
library("gmodels")
library("Hmisc")
library("ggthemes")
library("cowplot")
# 3. Visualización de los datos:
ggplot(datos, aes(x = HI, y = HF)) +
geom_point() +
labs(title = "Relación entre las variables")
#------------------------------
# 4. Estimación del modelo de regresión lineal:
modelo <- lm(HF ~ HI, data = datos)
#------------------------------
# 5. Resumen del modelo:
summary(modelo)
# install.packages("knitr")
# library(knitr)
# knitr::kable(summary(modelo)$coefficients)
# knitr::kable(summary(modelo))
#------------------------------
# 6. Visualización de la línea de regresión:
ggplot(datos, aes(x = HI, y = HF)) +
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geom_point() +
labs(title = "Relación entre las variables")
ggplot(datos, aes(x = HI, y = HF)) +
geom_point() +
labs(title = "Relación entre las variables") +
geom_smooth(method = "lm")
# Ecuación de regresión lineal
ecuacion <- paste("HF ~", format(coef(modelo), digits =
2))
# Mostrar la ecuación
ecuacion
# =================================
# 7. Gráfica de dispersión
ggplot(datos, aes(x = HI, y = HF)) +
geom_point() +
labs(title = "Relación entre las variables")
# =================================
# Supuestos de La Regresión Lineal Simple.
# ===============================
# 8. Prueba de linealidad
# Crear la gráfica QQ
ggplot(modelo, aes(x = ".resid", y = ".fitted")) +
geom_abline(lty = 2) +
labs(title = "Gráfica QQ de los residuos") +
annotate("point", x = ".resid", y = ".fitted", size = 1.5)
# Realizar la prueba de Breusch-Pagan
library(lmtest)
bptest(modelo)
# Calcular el coeficiente de correlación de Pearson
cor_pearson <- cor(datos$HF, datos$HI)
# Imprimir el resultado
print(cor_pearson)
# Gráfica de residuos vs. valores ajustados:
# Obtener los residuos y valores ajustados del modelo
residuos <- residuals(modelo)
valores_ajustados <- fitted(modelo)
# Crear la gráfica de residuos vs. valores ajustados
plot(valores_ajustados, residuos, xlab = "Valores
ajustados", ylab = "Residuos",
main = "Gráfica de residuos vs. valores ajustados")
abline(h = 0, lty = 2, col = "red") # Agregar una línea
horizontal en y = 0
# Gráfica de residuos vs. variable independiente:
# Obtener los residuos del modelo
residuos <- residuals(modelo)
# Crear la gráfica de residuos vs. variable independiente
plot(datos$HI, residuos, xlab = "Variable independiente
(HI)",
ylab = "Residuos", main = "Gráfica de residuos vs.
variable independiente")
abline(h = 0, lty = 2, col = "red")
# ================================
# 9. Prueba de Homocedasticidad:
library(lmtest)
# Creamos un modelo de regresión lineal simple
fit <- lm(HF ~ HI, data = datos)
# Aplicamos la prueba de Breusch-Pagan
bptest(fit)
# ================================
# 10. Prueba de Normalidad:
# Utilizamos la función ks.test() para realizar la prueba de
normalidad
# Prueba de Kolmogorov-Smirnov (KS)
install.packages("nortest")
librar("nortest")
residuos <- unique(residuos)
resultados <- ks.test(residuos, "pnorm")
# Imprimimos los resultados
cat("Statística de la prueba:", resultados$statistic, "\n")
cat("Valor crítico:", resultados$critical, "\n")
cat("P-valor:", format(resultados$p.value, digits = 10),
"\n")
cat("P-valor:", resultados$p.value, "\n")
# Obtener los residuos del modelo
residuos <- residuals(modelo)
# Gráfico de histograma de los residuos
ggplot(data.frame(residuos = residuos), aes(x = residuos))
+
geom_histogram(aes(y = ..density..), color = "black", fill
= "white") +
geom_density(alpha = 0.2, fill = "#FF6666") +
labs(title = "Histograma de los residuos",
x = "Residuos", y = "Densidad")
# Gráfico de probabilidad normal (Q-Q plot)
ggplot(data.frame(residuos = residuos), aes(sample =
residuos)) +
stat_qq() +
stat_qq_line() +
labs(title = "Gráfico de probabilidad normal (Q-Q plot)",
x = "Valores teóricos", y = "Valores observados")
# ================================
# 11. Prueba de Independencia:
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Pag. 30
# Prueba de Durbin-Watson
# install.packages("lmtest")
library(lmtest)
dwtest(modelo)
# ====================================
# 12. Prueba de No hay colinealidad:
#En el caso de la regresión lineal simple, este supuesto se
cumple automáticamente, ya que solo hay una variable
independiente.