Learning Interest Modelling of  Poliwangi Students to Learn Mathematics Engineering Through MOOCs Using Dummy Regression


CAUCHY –Jurnal Matematika Murni dan Aplikasi 
Volume 6(4) (2021), Pages 181-187 
p-ISSN: 2086-0382; e-ISSN: 2477-3344 
 

Submitted: August 29, 2020 Reviewed: March 17, 2021 Accepted: April 11, 2021 
DOI: http://dx.doi.org/10.18860/ca.v6i4.10212  

Learning Interest Modelling of  Poliwangi Students to Learn Mathematics 
Engineering Through MOOCs Using Dummy Regression 

Ika Yuniwati1, Aprilia Divi Yustita2, Siska Aprilia Hardiyanti3, I Wayan Suardinata4 

1,2,3,4Politeknik Negeri Banyuwangi 
Email: ika@poliwangi.ac.id  

ABSTRACT  

MOOCs is a learning system in the form of online courses that is massive and open to allow 
participants to enjoy unlimited content and can be accessed via the web. Mathematical 
techniques taught using MOOCs which will be developed in the following year are expected to be 
liked by students. The purpose of this study was to determine student interest in studying 
MOOCs. This study uses a dummy regression model on learning hours in each category. Dummy 
regression is considered a suitable model because dummy regression can quantify qualitative 
data. Qualitative data were obtained from a questionnaire distributed to 240 students. The 
questionnaire contains indicators of student MOOCs interest, including cognitive, affective, and 
psychomotor interests. The result of this study is the amount of time studying mathematics 
influenced by students' interest in learning mathematics through MOOCs by 60.7%, and the rest 
39.3% is influenced by other factors. The model is Yi = 1,562 + 4,729 D1 + 1,461 D2 + 𝜀𝑖 . So it can 
be concluded that the interest of students who want to study mathematics through MOOCS is the 
highest with an average student learning hours of 4,729 minus 1,562 equal to 3,647 hours. 
 
Keywords: Dummy Regression Model; Learning Interest; MOOCs 

INTRODUCTION  

Massive Open Online Courses (MOOCs) can be qualified as revolution education 
has begun to grow and become popular today. Individuals can get training in the areas 
needed and developed with educational training that is open to all students throughout 
the world [1]. MOOCs caters to a large number of students and provides a combination 
of open online courses, short video lectures, automated conversations, quizzes, peer and 
self-talk, and student collaboration through discussion forums. There are various kinds 
of MOOCs designed according to the level of thinking since 2016 [2]. Massive open 
online courses (MOOCs) contribute significantly to individual empowerment because 
they can help people learn about various topics [3]. 

The goal of MOOCs is the best learning resource and new ways of learning in the 
classroom. Learning can help students learn fully, work together, and is also supported 
by expert guidance [4]. The use of MOOCs in learning already exists in various countries. 
Singapore MOOCs can reduce university and university level tuition fees improve 
community access to such courses. They also provide skills and job training for 
community members [5]. This contradicts the results of research which state that 
MOOCs can provide new forms of learning through technology and save significant costs 
for education [6]. In Portugal, there is a study that states there is a relationship between 
interest in educational success [7]. Other studies add learning competencies that can 
influence participation, perseverance, and sustainability [8]. A good formal education 
system supports the students involved. factors that affect this performance according to 

http://dx.doi.org/10.18860/ca.v6i4.10212
mailto:ika@poliwangi.ac.id


Learning Interest Modelling of  Poliwangi Students to Learn Mathematics Engineering Through 
MOOCs Using Dummy Regression 

Ika Yuniwati 182 

a survey conducted at the Nigerian Private University (Redeemer University) namely 
hours of study [9]. While the learning domain that must be learned in learning can be 
categorized as the cognitive domain (knowledge), the psychomotor domain (skills), and 
the affective domain (attitude) according to Bloom [10]. Because this research analyzed 
interests published in the domain which is an indicator that shows interest in MOOCs. 
The analysis used dummy analysis. Dummy analysis can be used to predict interest. The 
research that has been done is the students' interest in soap [11]. The Dummy 
regression model is also used for the performance of students majoring in mathematics 
FMIPA [12]. Dummy variables have often been used in strategy research to study the 
effects of categorical variables [13,14]. The advantage of using these puppet variables, 
variables 1 and 0 is that they can be questioned and interpreted as the resulting 
regression estimates [15]. 

 

METHODS 

Multiple Linear regression analysis 
The Dummy regression analysis is a double linear regression analysis whose 

variable is qualitative. So before the use of dummy regression analysis, it must first be 
understood the analysis of a double linear regression [12] following 
On each observation, represented the ith bservation, applies the equation 
𝑌𝑖 = 𝛽0 + 𝛽1𝑋1𝑖 + 𝛽2𝑋2𝑖 + ⋯ + 𝛽𝑝𝑋𝑝𝑖 + 𝜀𝑖                                                                 

 (1) 
System equations (1) can be written in the form of a matrix, by defining each matrix into  
the following  matrix: 
 

𝑌 = [

𝑌1
𝑌2
⋮

𝑌𝑛

]  ; 𝑋 = [

1 𝑋11 𝑋12 ⋯ 𝑋1𝑘
1 𝑋21 𝑋22 ⋯ 𝑋2𝑘
⋮
1

⋮
𝑋𝑛1

⋮ ⋯ ⋮
𝑋𝑛2 ⋯ 𝑋𝑛𝑘

] ; 𝛽 = [

𝛽0
𝛽1
⋮

𝛽𝑛

]  ; 𝜀 = [

𝜀1
𝜀2
⋮

𝜀𝑛

]                            

 (2) 
 
or equations (2)  can be written in the form of another matrix   as follows : 
𝐘 = 𝐗𝛃 + ϵ            (3) 
 
Based on the assumptions above𝜀𝑖 ~𝑁(0, 𝜎

2), Then the equation (1) can be written in the 
form of expectation value: 
𝐸(𝑌𝑖 ) = 𝛽0 + 𝛽1𝑋1𝑖 + 𝛽2𝑋2𝑖 + ⋯ + 𝛽𝑘 𝑋𝑖𝑘            
 (4)                                                          
 
Estimation parameters 

The estimation of the parameters can be obtained using the smallest quadratic 
method so that the equation (4)  can be  written in a matrix form : 

�̂� = (X′X)−1X′Y           (5) 
 
Hypothesis testing was conducted to test the overall regression Parameter. Overall test 
of the regression parameters as follows: 
 H0: β0 = β1 … = βk = 0  
 H1: at least one βj ≠ 0 

 



Learning Interest Modelling of  Poliwangi Students to Learn Mathematics Engineering Through 
MOOCs Using Dummy Regression 

Ika Yuniwati 183 

The Sum of Squares Total (SST) is The Total of Sum Squared Regression (SSR) and The 
Sum of Squared Error (SSE), or it can be written: 
SST=SSR+SSE           (6) 
 
Test statistics which used are F test statistics: 

F =
SSR/DFR

SSE/DFE
=

MSR

MSE
  

Explanation  
DFR = Degree of freedom in regression 
DFE = Degree of freedom in error 
MSR = Mean Sum of Squares Regression  
MSE = Mean Sum of Squares Error 
H0 rejected if 𝐹0 > 𝐹(𝛼.𝑘,𝑛−𝑘−1) 

By minimizing the number of squared errors, it is obtained: 

SSE = ∑ (Yi − Ŷi)
2n

i=1           (7) 

SST = ∑ (Yi − Y̅i)
2n

i=1           (8) 
 
From equation (6), (7), and (8) obtained  

𝑆𝑆𝑅 = �̂�′𝑋′𝑌′ −
(∑ 𝑌𝑖

𝑛
𝑖=1 )

2

𝑛
          (9) 

 
When Variable a free variable is inserted one by one gradually into a regression 
equation, it is performed a sequential F test [16] 
 
Hypothesis testing for partial regression coefficient parameters    
The F test is used to determine the effect of the independent variable on the dependent 
variable simultaneously. After the F test is carried out, the T-test or partial regression 
test is carried out. This test is used to determine the effect of each independent variable 
on the dependent variable. Partial regression hypothesized will be testing 
H0 : βj = 0 
H1 : βj ≠ 0 

Test statistics: thit =
β̂j

Se(βj)
        

 (10) 
H0 Rejected if |thit| > 𝑡(𝛼

2
;𝑛−𝑘−1)

 

 
Coefficient of determination 
After knowing the effect simultaneously and the effect of each independent variable. The 
next step of analysis is to find the percentage of the independent variables as a whole to 
the dependent variable. Multiple coefficients of determination R2 measures the 
proportion of total diversity in the Y-free variables that can be explained by the 
regression equation model together. Size of regression coefficient determined by the 
formula: 

R2 =
SSR

SST
                       (11) 

 
Then from the independent variable and the dependent variable, the model is 
determined. There are many ways to build a regression model whose free variables 
contain. Variable A qualitative variable, one of which is using a variable doll or 
commonly called a dummy variable. Dummy variables are used as an attempt to see how 



Learning Interest Modelling of  Poliwangi Students to Learn Mathematics Engineering Through 
MOOCs Using Dummy Regression 

Ika Yuniwati 184 

the classifications in the sample affect the estimation parameters. Variables dummy also 
tries to make the quantification of Qualitative variables. For example, if you want to 
estimate Variable. The value of a variable Y is influenced by one Variable quantitative 
variable (X) and one Variable qualitative free variable that has two categories, such as 
Category 1 and Category 2.   The dummy model of the example is 
a. Y = a + bX + cD1  (Dummy Intercept Model) 
b. Y = a + bX + c(D1X)   (Dummy Slope Model) 
c. Y = a + bX + c(D1X) + dD1  (Dummy Intercept and Slope Model) 

 
This research used Dummy Intercept Model or Sympel Dummy Regression Model by 
Modupe by the formula [9]  
Yi =bo+b1Zi+ei 
bo = intercept 
b1 = Regression coefficient 
zi = 1 If the unit to I is a group that is 
    = 0 If the unit to I as the reference group 
 

RESULTS AND DISCUSSION  

Data Presentation 

Respondents, in this case, were 240 students. These students have been given 
knowledge about the MOOCs that was developed. Students are given a questionnaire 
totaling 20 questions. The questionnaire was designed to contain indicators of interest 
in the cognitive, affective, and psychomotor domains. After completing the questionnaire 
then make groups of them. It is namely students into students who are interested in 
learning mathematics through MOOCs (A), students who do not like to learn 
mathematics through MOOCs (B), and students who do not want to learn mathematics 
through MOOCs (C). The grouping scores can be seen in Table 1.  

 
Table 1. Student Interest Grouping Score 

Category Score Interval 
A 60-80 
B 40-59 
C 20-39 

 

The data in the research has been categorized as in Table 1 then it was changed 
to dummy variables. The reference category is chosen. It is C Category. So that Category 
C becomes D0, Category A becomes D1, and Category C becomes D2.  
 

Test of Significance and Coefficient of Determination 

The Significance Test is divided into 2 tests, namely the F-Test to find out the 
significance simultaneously and the T-Test to find out the partial significance. F-Test is 
used to test a regression that is by testing hypotheses that involve more than one 
coefficient. The F-Test can also be used to test the linearity of a regression equation. It 
can also be used to see the effect between independent and dependent variables. F-Test 
on the results of this study can be seen in Table 2. 

 
  



Learning Interest Modelling of  Poliwangi Students to Learn Mathematics Engineering Through 
MOOCs Using Dummy Regression 

Ika Yuniwati 185 

Tabel 2. Result of  F  test 
F-statistic F p-value 
183,313 2 0.000 

 

Table 2 indicate that the value of the F-Test is 183.313 with  a p-value of 0,000, it can be 
stated that the model or independent variable factors, in this case, the variable of 
interest in studying Engineering Mathematics through MOOCs affects the dependent 
variable, the amount of time studied 

The T-Test can be used to test hypotheses about individual coefficients, the T-
Test is also often called a partial test. The results of the T-Test can be seen in Table 3. 

Tabel 3. Result of T test 
Coefficient t-value sig 

D0 6.282 0.000 
D1 16.040 0.000 
D2 5.257 0.000 

 

Based on Table 3 above, it is known that all predictor variables significantly influence 
the model. It can be seen sig value which has a value less than 0,05. So, the regression 
coefficient in each category produced on the variable significantly influences the number 
of learning hours. 

The coefficient of determination is used to find out how much influence is 
dependent on the independent variable. It can be seen in Table 4.  

 
Tabel 4. Table of effect from the amount of time studying in mathematics towards students 

interest to MOOCs 
 

Model R R2 

1 0.779a 0.607 

a. Predictors: (Constant), D2, D1 
b. Dependent Variable: the amount of time studying mathematics 
 

Table 4 reflected the correlation between the amount of time studying 
mathematics and students’s interest in learning mathematics through MOOCs. R-value is 
0,779. This value shows that their correlation is strong. Besides, R2 shows a value of 
60.7%, This gives the meaning of the amount of time studying mathematics influenced 
by students' interest in learning mathematics through MOOCs by 60.7%, and the rest 
39.3% is influenced by other factors. 
 

Interpretation of Dummy Regression Model 

The data in this model uses the results of the data which are categorized into 3 
dependent variables. It can be seen in Table 5. 

 
Tabel 5. The estimated Learning Interest through The Amount of Time Studying Mathematics  

in 3 Categories  

Model Unstandardized Coefficient Sig. 
 B Std. Error  

1        (Constat) 1,562 0,249 0,000 
D1 4,729 0,295 0,000 
D2 1,461 0,278 0,000 

 



Learning Interest Modelling of  Poliwangi Students to Learn Mathematics Engineering Through 
MOOCs Using Dummy Regression 

Ika Yuniwati 186 

Table 5 shows that they are students who do not want to learn mathematics through 
MOOCs (D0), students who are interested in learning through MOOCs (D1), students 
who do not like to learn through MOOCs (D2) and 1 independent variable the average 
hours of study (Y) are dummy and a linear regression model is obtained 
Yi = 1,562 + 4,729 D1 + 1,461 D2 + 𝜀𝑖  

The interpretation of the regression model above is the average study time for 
students who do not want to learn engineering mathematics by 1,562 hours. The 
average difference in hours of study for students interested in learning engineering 
mathematics through MOOCs with students who do not want to learn engineering 
mathematics through MOOCs is 4,729 hours or in other words the interest of students 
who do not want to study engineering mathematics through MOOCs is lower than the 
interest of students interested in learning engineering mathematics through MOOCs. 
The average study time for students who interested in learning engineering 
mathematics by 3,467 hours. The average difference in hours of study for students who 
do not like to study engineering mathematics through MOOCs with students who do not 
want to study engineering mathematics through MOOCs is 1,461 hours or in other 
words the interest of students who do not likes to study engineering mathematics 
through MOOCs is lower than that of students who do not want to study engineering 
mathematics through MOOCs. The average study time for students who do not like study 
engineering mathematics by 0,101 hours or equals to 6 minutes. 

 

CONCLUSIONS 

The results of this study are interest of students who do not want to study engineering 
mathematics through MOOCs is lower than the interest of students who are interested in 
learning engineering mathematics through MOOCs. Moreover, the interest of students 
who do not want to study engineering mathematics through MOOCs is lower than the 
interest of students who do not like to study engineering mathematics through MOOCs. 

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