upload_2n2fmzcwhqdlmkrg3noytyzuix.pdf

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ISSN: 2992-7161

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VALIDATION OF A PREDICTIVE MODEL USING LINEAR

REGRESSION AND ANOVA

VALIDACIÓN DE UN MODELO PREDICTIVO MEDIANTE

REGRESIÓN LINEAL Y ANOVA

López Tarango Daniel Axel

Tecnológico Nacional de México/I. T. De Chihuahua II

https://orcid.org/0009-0005-7829-7275

daniel.lt@chihuahua2.tecnm.mx

Barraza Álvarez Alberto Guerrero

Tecnológico Nacional de México/I. T. De Chihuahua II

https://orcid.org/0000-0002-0197-1859

alberto.ba@chihuahua2.tecnm.mx

García Aguirre Ilse Haydeé

Tecnológico Nacional de México/I. T. De Chihuahua II

https://orcid.org/0009-0000-4012-476X

ilse.ga@chihuahua2.tecmn

Gallegos Orozco Carmen Angelina

Tecnológico Nacional de México/I. T. De Chihuahua II

https://orcid.org/0000-0002-4872-4927

carmen.go@chihuahua2.tecnm.mx

Orduño Aguirre Edgar Gerardo

Tecnológico Nacional de México/I. T. De Chihuahua II

https://orcid.org/0009-0007-8975-6734

edgar.oa@chihuahua2.tecnm.mx

DOI:

https://doi.org/10.61273/neyart.v4i4.221

| Received:

18/05/2026

|

Accepted:

24/07/2026

|

Published:

28/08/2026

This work is licensed under

an international

Creative Commons Attribution 4.0 license.

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ISSN: 2992-7161

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Original Research Article

Abstract--

This paper verifies a simple linear regression prediction model, whose function is to predict

in advance the monthly number of new customers of an institution. This verification uses the institution's

full five-year historical monthly customer growth data. The tools used to verify the reliability of the model

are

the

commonly

used

Excel,

and

the

professional

statistical

software

Minitab

19.

The

specific

verification

method

is

analysis

of

variance,

which

is

the

ANOVA

mentioned

in

studies.

After

the

verification, the model draws a clear conclusion: the correlation between the passage of time and customer

growth

is

very

high.

The

three

statistical

values

supporting

this

conclusion

are

the

coefficient

of

determination

R²=0.8094,

the

F-value=246.37,

and

the

p-value≈0.

Finally,

the

authors

of

the

paper

propose that in the future, these variables that may affect customer growth can all be incorporated into

the

model

to

carry

out

multiple

regression

analysis,

to

further

help

the

institution

formulate

more

reasonable decisions.

Keywords—

Forecasting, Mathematical model, Planning, Quantitative methods, Statistical analysis

.

Resumen—

Este artículo verifica un modelo de predicción de regresión lineal simple, cuya función es

predecir con anticipación el número mensual de nuevos clientes de una institución. Esta verificación

utiliza el conjunto completo de datos históricos de crecimiento

mensual

de clientes de la institución

durante cinco años. Las herramientas utilizadas para verificar la confiabilidad del modelo son el programa

Excel,

de

uso

común,

y

el

software

estadístico

profesional

Minitab

19.

El

método

específico

de

verificación es el análisis de varianza, conocido como ANOVA, mencionado en diversos estudios. Tras

la verificación, el

modelo llega

a una conclusión clara:

la correlación

entre el paso del

tiempo

y el

crecimiento de la clientela es muy alta. Los tres valores estadísticos que respaldan esta conclusión son el

coeficiente de determinación R² = 0,8094, el valor F = 246,37 y el valor p ≈ 0.. Finalmente, los autores

del artículo proponen que, en el futuro, estas variables que pueden afectar el crecimiento de la clientela

se incorporen al modelo para realizar un análisis de regresión múltiple, con el fin de ayudar aún más a la

institución a tomar decisiones más razonables.

Palabras

Clave—

Previsión,

Modelo

matemático,

Planificación,

Métodos

cuantitativos,

Análisis

estadístico.

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Original Research Article

INTRODUCTION

At present, institutions and enterprises in all walks of life all face an unavoidable demand—they need

reliable statistical tools to help predict the trends of several core operational indicators in advance. For

example, they need to have a clear idea ahead of time of figures such as the market demand for their own

products, the level of current-period sales that can be achieved, and whether the factory's output can keep

up. Currently, tools that can accurately support such predictions still cannot fully meet everyone's needs,

and this study is carried out to fill this gap.

To complete the prediction of such operational indicators, the most widely used quantitative analysis

method in the industry at present is linear regression. If linear regression is paired with another statistical

method, the ANOVA mentioned in the original text, two key functions can be achieved: not only can a

complete prediction model be built, but the reliability of this model can also be strictly verified from a

statistical perspective—confirming whether it can really be used for prediction, and whether its ability to

explain the causes of indicator changes is sufficiently strong.

The following section will first sort out the background of applied research on these methods at both the

international and domestic levels, that is, what relevant studies at home and abroad in the past have

adopted the combined method of linear regression plus ANOVA; then clarify the practical application,

theoretical, and research-methodological reasons for carrying out this study, explaining why this research

is conducted from three dimensions; after that, list the overall objectives of this study, that is, what core

tasks this research will ultimately achieve; finally, it will also point out various constraints that limit the

scope of this study, clarifying what boundaries this research will not exceed, and explicitly defining the

coverage of this study.

International Background

Globally, the two methods of linear regression and ANOVA are widely used in a large number of research

fields to validate predictive models; that is, they are used to judge whether a model used for prediction is

reliable and usable. Research by Jahan (2017) points out that when non-normal errors occur in the process

of

multiple

linear

regression

análisis

to

put

it

simply,

the

calculated

errors

do

not

conform

to

the

conventional situation of normal distribution the stability of ANOVA F-test's will be mainly disturbed by

two factors, and the originally stable and reliable test characteristics will encounter problems: one is excess

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kurtosis, which means the kurtosis of the data is too high, and the other is insufficient sample size, meaning

the number of collected samples is too small. These problems will ultimately affect people's interpretation

of the model's significance, making it impossible to accurately judge whether the model is actually useful,

whether it can pass statistical tests, and clarify its true value.

In the healthcare field, Zou et al. (2024) developed and validated multiple linear regression models to

predict the diameter of the acetabular prosthesis used in total hip arthroplasty, demonstrating that this type

of model, based on analysis of variance, allows for the generation of clinically useful predictive tools from

anthropometric variables.

In the energy sector, scholars Amral, Özveren, and King completed a relevant study in 2007. The research

method they adopted was multiple linear regression, which was used to forecast electricity demand over

a short period in the future, that is, to calculate the total amount of electricity that would be consumed

during

that

period.

During

the

research,

they

also

conducted

statistical

significance

tests

a

set

of

specialized statistical tests designed to verify whether results are reliable, which ultimately confirmed that

two types of data can be stably and reliably used for prediction: one is various climate-related variables,

and the other is historically recorded historical electricity consumption data.

There is another similar study completed by Kandananond in (2011). At that time, he conducted a set of

comparative tests, using two methods, linear regression and artificial neural networks, to calculate the

forecast

values of Thailand's electricity demand respectively,

and then

carefully compared the

actual

performance of the two methods after application. Finally, he reached a clear conclusion: no matter which

of the two methods is used, rigorous statistical verification must be carried out to ensure that the final

calculated forecast results are sufficiently accurate, and this verification step cannot be skipped to directly

use the results.

In relevant research in the field of project management, Ottaviani and De Marco launched a new set of

tools in (2022), which is the multiple linear regression model. The core purpose of their development of

this model is to improve the accuracy of predicting the final cost of a project this predicted final cost is

the estimate at completion mentioned in the original text. After completing the model, they did not put it

directly into use. Instead, they first used the method of analysis of variance to test the significance of each

regression variable used in the model one by one, to confirm that the influencing factors added to the

model can indeed play a role in prediction. Compared with the traditional earned value management

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Original Research Article

method commonly used in the industry in the past, this new method has indeed reduced the fluctuation

degree of prediction errors, and the prediction stability is better than the old method.

Within the research scope of renewable energy, Arias Velásquez (2022) carried out a relevant study. This

study adopted analysis tools such as regression models, which included the specific regression model

Ridge regression, and these regression models were not used alone; instead, they were combined with

deep learning technologies to jointly conduct analysis and calculation, with the goal of predicting the

energy output of photovoltaic power stations, that is, solar power stations. To verify the reliability of these

prediction results, he also used two types of indicators for testing: one type is error measurement indicators

used to measure the size of errors, and the other type is statistical significance indicators, and finally

completed the verification of the accuracy of these prediction results.

In environmental research, Abdullah et al. (2020) constructed a multiple linear regression model to predict

the concentration of inhalable particulate matter PM10 during cross-border haze periods in Malaysia. The

cross-border haze mentioned here refers to haze weather that drifts into Malaysia from foreign countries,

while PM10 is inhalable particulate matter with a diameter not exceeding 10 micrometers, which directly

affects air quality and public health. Predicting its concentration changes in advance is of great importance

for

responding

to

such

sudden

air

pollution

events.

After

building

the

model,

they

also

used

two

professional statistical methods, analysis of variance and the coefficient of determination, to verify the

reliability of the model and confirm that it could produce sufficiently accurate prediction results.

In another study in the same field, Yusuf et al. (2019) tested the multiple linear regression model and the

artificial neural network model respectively to explain the fluctuation pattern of PM10 concentration

during haze periods in Malaysia that is, why PM10 concentrations in the air can vary in level and change

constantly even on all haze days. They conducted a comparative assessment of these two commonly used

models, and finally concluded that using ANOVA for statistical verification is the key to selecting the

model with the strongest predictive ability, and this step is indispensable.

Latin American Context

In

Mexico,

linear

regression

and

analysis

of

variance

have

been

applied

in

various

productive

and

academic sectors for the construction and validation of forecasting models, demonstrating the relevance

of this line of research in the national context.

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Morales Castro, Ramírez Reyes, and Rodríguez Albor (2019) forecasted sales for Mexican companies in

the food sector—including Bachoco, Bimbo, and Grupo Lala—by comparing multiple linear regression

models with artificial neural networks, finding that the linear models outperformed the 90% adjustment

level in most of the cases analyzed.

Enríquez Zárate and Rodríguez Lozada (2021) applied and compared various forecasting techniques,

including simple linear regression, for inventory planning at a small-to-medium-sized enterprise— —a

building materials distributor in Tlaxcala, Mexico, and statistically validated the fit of each model against

actual demand behavior.

Baeza-Serrato and Vázquez-López (2014), in a study conducted at a company in the Mexican textile

sector,

proposed

transitioning

from

a

predictive

multiple

linear

regression

model

to

an

explanatory

nonlinear regression model, using analysis of variance and mean squared error as validation criteria to

increase the reliability of the predictions.

Ruiz Mendoza and Hernández González (2021), at the Celaya campus of the National Technological

Institute of Mexico, applied quantitative forecasting methods—including linear regression—to determine

the future demand for a plastic part manufactured by a company in the Bajío region, comparing the

performance of each technique by calculating the forecast error.

Limones López, in his thesis developed at the Mexican Corporation for Materials Research (COMIMSA),

used

the

linear

regression

model

and

its

corresponding

analysis

of

variance

table

as

part

of

the

methodology for the statistical control of defective production within an industrial process, validating the

significance of the relationship between the variables under study.

Morantes-Quintana,

Rincón-Polo,

and

Pérez-Santodomingo

(2019),

in

an

article

published

in

the

International

Journal

of

Environmental Pollution (published in

Mexico), developed

a multiple linear

regression model to estimate particulate matter concentration, validating the model using the adjusted

coefficient of determination and the global significance test.

Scholars Fierro Torres, Castillo Pérez, and Torres Saucedo conducted a comparative analysis in 2022.

The two types of models they compared are all demand forecasting tools that can be used in small and

medium-sized enterprises in Mexico — simply put, they are tools to help these small and medium-sized

businesses predict how much of their own products or services the market will need. One category is

traditional

models,

and

the

other

is

modern

models

of

the

same

type.

Throughout

the

comparative

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analysis, the three scholars specifically pointed out the limitations of the multiple linear regression model:

when encountering scenarios where data does not change linearly following a fixed trend, that is, when a

non-linear change occurs, or when encountering unconventional sudden special events, this model cannot

function properly and becomes unusable.

Pérez Paredes, Cruz de los Ángeles, Guatemala Villalobos, and Juárez Fonseca (2018) analyzed the

importance of forecasting methods—including linear regression—in decision-making at Latin American

micro,

small,

and

medium-sized

enterprises,

emphasizing

the

need

for

managers

to

understand

the

statistical fundamentals of these techniques before using automated computational tools.

Study Objective

To

statistically

validate

a

forecasting

model

based

on

linear

regression

using

analysis

of

variance

(ANOVA), in order to determine the significance of the predictor variables and the reliability of the model

for estimating the future behavior of the study variable.

Rationale for the Study

From the perspective of practical application, conducting this research is necessary. For any institution,

the decisions that need to be made actually fall into two categories: one is operational decisions that

manage daily operations, and the other is strategic decisions that set long-term directions. Regardless of

the

category,

forecasting

is

an

indispensable

core

support.

With

reliable

forecasting,

various

future

conditions linked to demand, production, and sales can be clarified in advance, so that one will not be

caught off guard when problems arise, and there will be a solid basis for making decisions. Pérez Paredes

et al. (2018) proposed that if decision-makers can master multiple forecasting methods and apply them

correctly, they

can

systematically anticipate the

daily operational activities of the institution, reduce

uncertainty, allocate the resources at their disposal to the areas that need them most, and achieve more

reasonable resource allocation.

From a theoretical perspective, the study is grounded in the statistical foundations of linear regression

and analysis of variance, which allow the total variability of a response variable to be broken down into

the portion explained by the model and the portion attributable to error, serving as the basis for testing

the hypothesis of the model’s significance. In this regard, analysis of variance is considered essential for

comparing

the explained and unexplained variability within a regression model and

for determining

whether the observed relationship between the variables is statistically significant (FasterCapital, 2024).

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From a methodological perspective, the research is justified by the need to employ a rigorous statistical

procedure that allows not only for the generation of a predictive model but also for the validation of its

assumptions

and

significance

through

formal

tests.

In

this

regard,

Jahan

(2017)

emphasizes

that

the

ANOVA

procedure

applied

to

multiple

linear

regression

models

constitutes

the

appropriate

methodological

approach

for

testing

the

hypothesis

of

the

model’s

overall

significance,

although

its

validity may be compromised when the assumptions of normality and homogeneity of variance are not

met, which requires a systematic review of these assumptions before accepting the forecast results.

Study Limitations

This study itself has limitations, and all these issues are directly related to the types of models used. First

of all, the linear regression model applied in the study has a core premise for its validity: there must exist

a linear corresponding variation relationship between all the variables it analyzes—when one variable

changes by a certain amount, another changes by a fixed proportion accordingly. However, if the variable

that is the key focus of the actual research does not exhibit such linear variation at all, whether it shows

curved fluctuations that rise and fall, periodic cyclic changes that follow a certain pattern, or is affected

by

a

special

event

that

has

never

appeared

in

historical

records,

the

predictive

ability

of

this

linear

regression model will be greatly weakened, and the calculated results will be completely unreliable.

Second is the ANOVA used in this study. For the results derived from it to be valid, three strict premises

must be met simultaneously: first, the residuals conform to a normal distribution; second, the residuals

have homogeneity of variance; third, the residuals are independent of one another. If any one of these

requirements is not met, it becomes impossible to correctly interpret the statistical significance of the

model, the final assessment results will be skewed, and no accurate conclusions can be drawn from the

analysis.

In addition to these inherent problems of the models themselves, the historical data used in the study has

additional limitations. Whether these data can be successfully obtained, whether the quality of the data

itself meets standards, and whether the total accumulated records are sufficient—each of these factors

will

affect

the

final

results

of

the

study.

If

the

observation

data

used

for

analysis

is

too

small,

the

conclusions drawn from the estimation will be untenable, unable to remain stable and reliable, and even

less able to be directly applied to other scenarios or other time periods..

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DEVELOPMENT

Research Approach

This research was conducted using a quantitative approach, as it is based on the numerical measurement

of the study variables—the number of customers served over time—and on the use of statistical analysis

to identify behavioral patterns and generate a forecasting model. In this regard, Acosta Faneite (2023)

notes that the quantitative approach is characterized by predictions, which constitute interpretations of

observed facts, such that their direction is predictable; he also specifies that this approach is based on the

measurement of numerical data to answer research questions and test hypotheses through sequential

statistical processes.

Research Paradigm

The study was conducted within the positivist paradigm, also known as the quantitative or empirical-

analytical paradigm, whose main objective is to explain, predict, and control phenomena by verifying

theories and laws through empirical observation and statistical analysis. According to Herrera Castrillo

(2024), quantitative research is grounded in this paradigm by employing rigorous methods and techniques

to collect and analyze numerical and statistical data, with the aim of obtaining precise and verifiable

results, which is consistent with the statistical validation of the forecasting model proposed in this study.

Research Method

The hypothetical-deductive method was employed, which begins with the formulation of an assumption

or hypothesis regarding the relationship between the study variables, to subsequently test it empirically

through statistical analysis of the collected data. De la Cruz Sullca (2020) notes that the validity of a

scientific idea is established by deriving its implications for the real world and verifying whether the

resulting prediction is correct or not; thus, the scientific method is, in essence, hypothetical-deductive;

this approach is relevant to the present study, in which a regression model was derived from historical

data and tested using analysis of variance.

Research Design

The research design was non-experimental, longitudinal, and retrospective, since the study variables were

not deliberately manipulated; rather, historical data spanning a five-year period were analyzed, observing

the behavior of the variables as they occurred in their real-world context. In this regard, Sienes Bailo et

al. (2021), in their retrospective observational study on crystalluria, illustrate how this type of design

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Original Research Article

allows for the analysis of existing data, collected over a defined period of time, to identify relationships

between variables without direct intervention by the researcher in the events under study.

Type of Research

The study was descriptive-correlational in nature, as it sought, first, to describe the historical trends of

the variable “number of patients seen” and, subsequently, to determine the degree of relationship between

this

variable

and

time

(months),

with

the

aim

of

constructing

and

validating

a

predictive

model.

Cairampoma Carrillo (2015) notes that correlational research is a type of study that seeks to measure the

degree of relationship between two or more variables without experimentally manipulating any of them,

relying instead on observation and statistical analysis of the available data.

Participants

The sample for this pilot study consisted of a total of 15 students enrolled in the first semester of their

vocational training at a public university, covering the academic term from January to June 2025. The

group

of

students

participating

in

the

study

did

not

use

a

professional

sampling

method

that

could

guarantee sample randomness; instead, they adopted non-probability convenience sampling—in simple

terms, only selecting individuals that were easily accessible to the researchers. They were chosen because

these students were all participating in the school’s new technology literacy course at that time, so the

research team could easily gather this group regardless of coordinating schedules or securing a venue,

which met the selection requirements for convenience sampling.

A total

of 15 participants were included in

this study. The gender distribution of their demographic

characteristics was as follows: 11 males, accounting for 73.33%, and 4 females, accounting for 26.67%.

All participants were first-year university students who had just enrolled, with ages ranging from 18 to

20 years old. The researchers believed that selecting this group for the assessment was perfectly suitable,

as it could accurately measure one specific thing—the baseline level of numeracy that students bring with

them when they transition from high school to the university environment, which is the baseline numeracy

to be measured in the study.

Procedure

The entire process of this study was completed within the semester from January to June 2025. During

the six months of the research's advancement, we first retrieved all historical data from the previous five

years. These data detailed the total number of clients we had served each month, and we conducted

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dedicated analysis centering on these data. There were two clear goals to achieve for this data analysis:

first, to clarify the exact nature of the correlation between the two variables; second, to build a set of

models that can be used for prediction, relying on the statistical analysis method of linear regression.

After the preliminary construction of this prediction model, we did not put it into use directly; instead,

we launched a statistical verification process, and the verification method used was analysis of variance,

that is, the originally marked ANOVA. The purpose of conducting this verification was also clear: first,

to confirm the significance of the model, meaning that it is valid and has research value; second, to test

whether its actual prediction ability can meet the requirements.

After completing all verification steps, we finally produced a prediction model with higher reliability for

the institution involved in this study..

Ethical Considerations

Throughout this research, the fundamental ethical principles governing scientific practice were upheld,

including

the

confidentiality

of

the

information

obtained

and

the

responsible

use

of

historical

data

provided by the organization, which were used exclusively for academic and statistical analysis purposes.

In this regard, Iriarte et al. (2017) note that human rights violations throughout history have led to the

development of ethical guidelines in scientific research, with respect for life, autonomy, confidentiality,

and the responsible handling of information being some of the fundamental ethical principles that every

researcher must uphold during their research work—principles that were observed in the handling of the

information used in this study.

Procedure for Data Analysis and Statistical Analysis

When processing the collected data, Microsoft Excel was used for the first step of data organization and

statistical analysis. First, it was used to sort out the accumulated historical database, then the built-in data

analysis tool of Excel was called to generate a linear regression model. With this model, all coefficients

in the regression equation and the corresponding coefficient of determination were calculated.

After the first round of analysis results were obtained, the statistical software Minitab 19 was used to

conduct

subsequent

verification.

The

verification

to

be

completed

included

two

parts:

first,

to

check

whether the results previously calculated with Excel were accurate; second, to confirm statistically that

the model was qualified and usable through the method of analysis of variance.

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The statement in Gestión de Operaciones, published in (2016), is fully consistent with this set of operation

procedures. The book mentions that to build a regression model that can be used for prediction, there are

two optional tools: one is the Excel data analysis tool used just now, and the other is the statistical software

Minitab. It also clearly states that when these two tools are used to complete the same analysis process,

the only difference is the way the results are presented, and the final calculated coefficients are completely

identical.

Data Analysis

Model Fit

We conducted a simple linear regression analysis and calculated the multiple correlation coefficient as

0.8997. This coefficient is a value used to measure the strength of the linear correlation between two

types of data, with a range from 0 to 1. The closer it is to 1, the stronger the linear correlation between

the two variables, and it is a positive correlation—that is, when one value rises, the other will also rise

accordingly. The value calculated this time is close to 0.9, very near to 1, which means that between the

passage of time counted on a monthly basis and the number of customers served in the same period, there

exists a strong positive linear correlation—the longer the time that passes, the larger the cumulative

number of customers served, and the trend of synchronous growth of the two is very obvious.

Next, the coefficient of determination of the model we calculated, that is, R², has a value of 0.8094. The

coefficient of determination helps us judge how much of the variation in another set of data can be

explained by the variables included in the model. The situation here is that the number of customers we

serve

each

month

is

not

fixed,

it

fluctuates

up

and

down

every

month,

and

this

kind

of

numerical

fluctuation

is

called

"volatility".

This

R²

value means

that

approximately

80.9%

of

all the

observed

volatility in the number of customers served can be clearly explained by the time variable incorporated

into the model—only the factor of "how many months have passed" can explain the vast majority of the

causes of fluctuations in the number of customers.

The remaining 19.1% of the volatility in the number of customers comes from various factors that were

not included in the model's calculation, and these fluctuations cannot be explained by the time variable.

These factors that were not included in the model are also listed in the original text, including seasonal

changes, marketing activities, market environment, and all external events that are not controlled by the

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model's input variables; all of these are possible sources of that part of the volatility that cannot be

explained by time.

The adjusted R², which corrects the coefficient of determination based on the number of observations and

the number of included predictor variables, was 0.8062. The closeness between R² and the adjusted R²

confirms that the model’s explanatory power is not artificially inflated by the sample size, and that the

independent

variable

provides

genuinely

relevant

information

for

explaining

the

behavior

of

the

dependent variable.

Meanwhile, the standard error of the estimate was 30.04 customers, representing the expected average

deviation

between

the

observed

values

and

the

values

predicted

by

the

model.

Considering

that

the

number

of

customers

served

ranged

from

relatively

low

values

at

the

beginning

of

the

period

to

considerably

higher

values

toward

the

end,

this

margin

of

error

can

be

considered

reasonable

and

consistent with the nature of the data analyzed.

Overall Significance of the Model (Analysis of Variance)

We can use Analysis of Variance (ANOVA) to determine whether the regression model we have on hand

truly has overall statistical significance, or if it is merely an invalid result derived from accumulated

random errors. After conducting analysis with this tool, we calculated two key values: the first is the F-

statistic, which is 246.37, and the second is the critical F-value, which is 1.53×10⁻²². There is a general

judgment threshold in the field of statistics, that is, a significance level of 0.05, and the critical F-value

we just calculated is far smaller than this threshold. With this result, we can reject the null hypothesis we

initially set—the preliminary judgment that there is no linear relationship between variables. In addition

to rejecting the null hypothesis, we can also draw two definite conclusions: first, the regression model we

proposed has high statistical significance and is indeed a valid model with reference value; second, the

independent variables in the model can indeed effectively explain the changes in the dependent variable,

and their explanatory power is qualified.

Interpretation of the Regression Coefficients

The estimated regression equation, based on the coefficients obtained, can be expressed as follows:

Ŷ = 47.503 + 3.515 (X)

The intercept coefficient (47.503) represents the estimated number of customers served at the origin of

the period analyzed, that is, the baseline level of service before considering the effect of the passage of

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months. This value has a t-statistic of 6.049 and an associated probability of 1.13×10⁻⁷, confirming that

the intercept is statistically different from zero and, therefore, significant within the model.

The

Month

(X)

coefficient

of

3.515

indicates

an

average

monthly

increase

of

approximately

3.5

customers

served.

This

positive

effect

is

highly

statistically

significant

(t=15.696,

p=1.53×10⁻²²),

supported by a 95% confidence interval of 3.066 to 3.963 that excludes zero.

Discussion

The results obtained in this study, summarized by a coefficient of determination (R²) of 0.8094 and a

highly significant F-test (F = 246.37; p < 0.05), empirically confirm the theoretical and methodological

approaches outlined in the reviewed literature, according to which analysis of variance (ANOVA) is the

ideal statistical method for testing the overall significance of a regression model and for decomposing the

total variability of the dependent variable into the portion explained by the model and that attributable to

error. In this regard, the finding of an F-value with an associated probability of virtually zero (1.53×10⁻²)

aligns with the role that FasterCapital (2024) attributes to ANOVA as a tool for determining whether the

observed relationship between variables is statistically significant and not the result of chance.

The magnitude of the R² obtained in this study is consistent with the findings reported by Morales Castro,

Ramírez Reyes, and Rodríguez Albor (2019) in their study on sales forecasting for Mexican companies

in the food sector, where multiple linear regression models achieved levels of fit exceeding 90% in most

of the cases analyzed. Although the goodness-of-fit obtained here (80.9%) is slightly lower, both results

point in the same direction: linear regression models, when applied to variables with systematic behavior

and a defined trend over time, offer satisfactory explanatory performance within the Mexican business

context,

without

necessarily

requiring

the

use

of

more

complex

techniques

such

as

artificial

neural

networks.

Similarly, the pattern of sustained growth identified in the “customers served” variable corresponds to

that reported by Amral,

Özveren, and King (2007) and by Ottaviani and De Marco (2022), who, in

different contexts—short-term electricity demand forecasting and the estimation of final project costs,

respectively—confirmed through statistical significance tests that the variables included in their multiple

linear

regression

models

were

reliable

predictors,

capable

of

reducing

error

variability

compared

to

alternative methods. The present study reinforces this evidence by showing that even a simple regression

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model, with a single explanatory variable of a temporal nature, can achieve robust levels of statistical

significance when the underlying phenomenon exhibits a clear and sustained trend.

However, it is important to contrast these results with the warnings issued by Jahan (2017), who noted

that the robustness of the F-test in ANOVA procedures applied to regression models is compromised

when the error does not follow a normal distribution, particularly in the presence of excessive kurtosis or

small

sample

sizes.

In

the

case

analyzed,

the

number

of

observations

(sixty

monthly

data

points,

equivalent to five years) can be considered adequate to mitigate this risk; however, the interpretation of

the model’s overall significance must be made with the methodological caveat that, within the framework

of this analysis, full compliance with the assumptions of normality and homogeneity of variance of the

residuals was not exhaustively verified—an aspect that Jahan (2017) identifies as critical to the validity

of inferential conclusions.

Furthermore, it is important to consider the fit obtained within the limitations inherent in linear regression

models, as pointed out by Fierro Torres, Castillo Pérez, and Torres Saucedo (2022), who note that this

type of model loses predictive power when faced with scenarios involving nonlinear behavior or atypical

events not captured in the historical data series. The 19.1% of variability not explained by the model

estimated here could, in fact, be associated with factors of this nature—seasonality, sales campaigns, or

changing market conditions—that a simple regression model, based exclusively on the passage of time,

is unable to capture. Along the same lines, Kandananond (2011) argues that both linear regression models

and alternative approaches, such as artificial neural networks, require rigorous statistical validation to

ensure the accuracy of their estimates, which confirms the importance of having subjected the proposed

model to an ANOVA test before accepting its results as a basis for decision-making.

On the other hand, the individual significance obtained for the coefficient of the Month variable (t =

15.696; p ≈ 0) is consistent with the findings of Enríquez Zárate and Rodríguez Lozada (2021), who,

when applying forecasting techniques—including simple linear regression—for inventory planning in a

small and medium-sized Mexican company, emphasized the importance of statistically validating the fit

of each model against the actual behavior of the studied variable before using it as a planning tool. In the

case analyzed, both the narrow confidence interval for the slope (3.066 to 3.963) and the absence of the

value zero within that interval support the existence of a positive and stable relationship between time

and the number of customers served, which gives the model an adequate level of reliability for use in

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operational

planning,

in

line

with

the

practical

relevance

highlighted

by

Pérez

Paredes,

Cruz

de

los

Ángeles, Guatemala Villalobos, and Juárez Fonseca (2018) attribute to a correct statistical understanding

of forecasting methods by decision-makers in micro, small, and medium-sized enterprises.

Finally, the standard error of the estimate (30.04 customers) allows us to qualify the practical scope of

the model: while the statistical significance of the forecast is beyond dispute, the absolute magnitude of

this error suggests—in line with the arguments put forward by Zou et al. (2024) regarding predictive

models applied in clinical contexts, that the usefulness of a regression model should not be evaluated

solely on the basis of its statistical significance, but also on the basis of the magnitude of the expected

error

in

relation

to

the

scale

of

the

variable

of

interest.

Overall,

the

evidence

gathered

supports

the

conclusion that the prognostic model validated in this study is statistically robust and consistent with the

reviewed literature, although its practical application must be complemented by continuous monitoring

of

the

model’s

assumptions

and

the

eventual

incorporation

of

additional

variables

that

capture

the

variability not explained by the simple passage of time.

Conclusions

The

objective

set

forth

in

this

study—to

statistically

validate

a

forecasting

model

based

on

linear

regression

using

analysis

of

variance—was

successfully

achieved.

The

results

obtained

allow

us

to

conclude that the “month number” variable significantly explains the behavior of the number of clients

served, with a coefficient of determination of 0.8094, which demonstrates strong explanatory power, and

an F-test (246.37; p < 0.05) that confirms the overall significance of the model as a whole.

The analysis of the regression coefficients reinforced this conclusion by showing that both the intercept

and the slope associated with the time variable were statistically different from zero, with high t-statistics

and associated probabilities that were practically zero. The 95% confidence interval obtained for the

slope—which is

narrow and does not include

zero—supports the

existence of a positive, stable, and

predictable relationship between the passage of time and the growth in the number of customers served,

thereby validating the model as a useful tool for planning the operational capacity of the service under

analysis.

In general terms, it can be stated that simple linear regression, when subjected to a rigorous statistical

validation procedure using ANOVA, is an appropriate technique for building reliable forecasting models

in contexts where the variable of interest exhibits a systematic and sustained trend over time. However,

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the 19.1% of variability not explained by the model, as well as the identified standard error of estimation,

indicate that there is room for improvement that could be addressed by incorporating additional predictor

variables or through complementary methodological approaches.

As a first line of future research, we propose extending the current model to a multiple linear regression

that

incorporates

additional

variables

of

a

seasonal,

commercial,

or

macroeconomic

nature—such

as

marketing campaigns, holidays, local market conditions, or regional economic indicators—with the aim

of

reducing

the

proportion

of

variability

not

explained

by

the

current

model

and

strengthening

its

predictive capacity in more complex scenarios. This line of research would also allow for the evaluation

of multicollinearity among the new predictors and, , the use of ANOVA to test the individual contribution

of each variable to the overall significance of the expanded model.

As

a

second

line

of

future

research,

we

recommend

exploring

the

application

of

alternative

or

complementary

models

to

linear

regression—such

as

time-series

models

with

seasonal

components,

nonlinear regression, or machine learning techniques—in order to compare their predictive performance

against the linear model validated here, particularly in the presence of cyclical behaviors or atypical events

that simple linear regression is unable to capture. This comparison would make it possible to determine,

based

on

error

criteria

and

statistical

significance,

which

approach

offers

the

best

balance

between

predictive accuracy and ease of interpretation for the organization under study.

Conflict of Interest

The authors declare that they have no conflicts of interest.

Data Availability

All datasets relevant to the results of this study are available in their entirety in the article.

Source of Funding

This study was not funded by any organization.

Statement on Generative AI

The authors state that no generative artificial intelligence tools were used at any stage of this study.

References

Aguado, D., González, A., Antúnez, M., & de Dios, T. (2017). Assessment of transferable skills among

college students. Initial psychometric properties of the Transferable Skills Questionnaire.

REICE.

NEYART Journal

ISSN: 2992-7161

Issue 4 | Vol. 4 – No. 4 | July – December 2026 |

Page

109

Original Research Article

Ibero-American Journal on Quality, Effectiveness, and Change in Education

,

15

(2), 129–152.

https://doi.org/10.15366/reice2017.15.2.007

Asonitou,

S.

(2022).

Measuring

the

gap

between

academic

hard

skills

training

and

modern

industry

demands in higher education.

Higher Education, Skills and Work-Based Learning

,

12

(3), 455-472.

https://doi.org/10.1108/HESWBL-05-2021-0098

Asonitou, S. (2022). The digital transformation era: Redefining technical mastery and soft skills in higher

education.

European Journal of Higher Education

,

12

(3), 289-305.

García-Vargas, M., López-Maldonado, J., & Restrepo, A. (2022). Gaps in technical training upon entry

into higher education in Latin America.

Ibero-American Journal of Higher Education

,

13

(36), 88-

105.

https://doi.org/10.22201/iisue.20072872e.2022.36.1192

He, T., Zhang, L., & Chang, Y. (2021). The definitive role of hard skills in early engineering employment

outcomes.

Journal

of

Engineering

Education

Research

,

29

(2),

114-129.

https://doi.org/10.1016/j.jeer.2021.02.004

Jones, P., & Broadbent, M. (2020). OECD metrics and the standardization of technical competencies in

global

higher

education.

Educational

Evaluation

Policy

Analysis

,

42

(4),

567-584.

https://doi.org/10.3102/0162373720934521

Martínez-Sánchez, F., & Rodríguez, C. (2023). Technical competencies and professional qualification

frameworks

in

Mexican

higher

education.

Journal

of

Higher

Education

,

52

(206),

45-63.

https://doi.org/10.36857/resu.2023.206.2415

Pérez-Franco, J. (2021). Structural challenges in the assessment of disciplinary skills in the Southern

Cone.

Quality in Education

, (54), 112–139.

https://doi.org/10.31619/caledu.n54.968

Ramírez, G., & González, E. (2023). Digital literacy and diagnostic quantitative skills among first-year

students.

Apertura

,

15

(1), 34–49.

https://doi.org/10.32870/Ap.v15n1.2301

Silva, M., & Santos, R. (2022). Gender gaps in the self-perception of hard technological skills among

college

students.

Latin

American

Journal

of

Educational

Technology

,

21

(2),

75-91.

https://doi.org/10.17398/1695-288X.21.2.75

Smith,

J., & Martínez, K. (2023). Quantitative

deficiencies in

first-year university students

and their

correlation with retention.

Journal of College Student Retention: Research, Theory & Practice

,

25

(1), 142-161.

https://doi.org/10.1177/15210251211011342

NEYART Journal

ISSN: 2992-7161

Issue 4 | Vol. 4 – No. 4 | July – December 2026 |

Page

110

Original Research Article

Torres-Cáceres, L. (2024). The disconnect

between hard academic skills

and Latin American SMEs.

Estudios Gerenciales

,

40

(170), 89-102.

https://doi.org/10.18046/j.estger.2024.170.6120

Tymon,

A.

(2021).

The

4.0

Industry

Paradigm:

Redefining

Technical

Mastery

Within

Academic

Structures.

Studies

in

Higher

Education

,

46

(8),

1611-1624.

https://doi.org/10.1080/03075079.2019.1698532

Valencia-Maldonado, G. (2023). Diagnostic competency-based assessment in Andean higher education.

Formación Universitaria

,

16

(3), 55-66.

https://doi.org/10.4067/S0718-50062023000300055

Wilson, H., & Taylor, S. (2022). Objective performance testing vs. self-assessment of technical instrument

skills

in

freshmen.

Assessment

&

Evaluation

in

Higher

Education

,

47

(5),

789-804.

https://doi.org/10.1080/02602938.2021.1963452

Zhao, Q., & Wang, Y. (2024). Technological hard skills entry requirements and academic adaptations in

STEM

fields.

International

Journal

of

Educational

Research

,

123

,

102-117.

https://doi.org/10.1016/j.ijer.2023.102117

Collaborative Work Table

Role

Author(s)

Conceptualization

Daniel Axel López Tarango

Methodology

Alberto Guerrero Barraza Álvarez, José Roberto Holguín

Beltrán

Software

Ilse

Haydeé

García

Aguirre,

Edgar

Gerardo

Orduño

Aguirre

Validation

Brenda López Martínez

Formal Analysis

Ricardo

García

Parada,

María

Eugenia

Astrid

Macías

Sagarminaga

Research

Víctor Villar Laguna, Fátima Yaraset Mendoza Montero

Resources

Brenda López Martínez

Data Curation

Ricardo

García

Parada,

María

Eugenia

Astrid

Macías

Sagarminaga

Writing - Preparation of the original

draft

Víctor Villar Laguna, Fátima Yaraset Mendoza Montero

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Writing - Review and Editing

Brenda López Martínez

Visualization

Ricardo

García

Parada,

María

Eugenia

Astrid

Macías

Sagarminaga

Supervision

Víctor Villar Laguna, Fátima Yaraset Mendoza Montero

Project Management

Brenda López Martínez

Fundraising

Ricardo

García

Parada,

María

Eugenia

Astrid

Macías

Sagarminaga