Factor that Affects the Students’ Performance in Mathematics Subject using Logistic Regression First Author\[1\]^\*, Second Author² (Double Blind Review: Please do not type or edit anything here until final-camera ready submissions) *¹First affiliation, City and Country (Please do not type or edit anything here, until final camera-ready paper submission)* *²Second affiliation, City and Country (Please do not type or edit anything here, until final camera-ready paper submission)*

ARTICLE INFO

ABSTRACT

Article history:

Received

Revised

Accepted

Online first

Published 1 March 2024

Predicting students' academic performance plays an important role in academics. Mathematics is a science concerned with the logic of shape, quantity, and order. This subject is one of the most important subjects in the school curriculum. Mathematics is a basic knowledge that students should have the expertise in order for them to score in the other subjects. However, most students find Mathematics a difficult subject, they will have difficulty scoring in this subject. Therefore, this paper aims to determine the factors that affect students’ performance in Mathematics subject which is the pre-calculus subject among students of Diploma in Computer Sciences (CS110) in UiTM Cawangan Melaka Kampus Jasin. During the analysis, gender, assessment marks, place of students, time spent studying pre-calculus subject per week, whether the student took additional mathematic in SPM, act as independent variables whereas grade for pre-calculus subject as the dependent variable, were examined. The assessments refer to test 1, test 2, lab assignment, quiz 1, quiz 2 and written assignment. The logistic regression model was applied, and the results showed that the gender, test 2 and quiz2 are variables that are significant to the model. When examining the variables influencing the academic performance of CS110 students at UiTM Cawangan Melaka Kampus Jasin, there are certain knowledge gaps and restrictions. It is advised that future studies collect data from more respondents and keep the question simple but clear in order to get more accurate results.

Keywords:

Prediction

Academic

Performance

Logistic Regression

Mathematics

DOI:

10.24191/jcrinn.v9i1

# introduction The scientific and technical advancement of nations depends on mathematics. This is due to the fact that knowledge of mathematics is crucial in comprehending other fields, such as engineering, physics, social science, and even arts (Patena & Dinglasan, 2013). Mathematics is a science concerned with the logic of shape, quantity, and order. Mathematics is present in every aspects of real lives. Many students consider mathematics to be the most tough and difficult subject. According to (Ashaari et al., 2011), the majority of students find mathematics to be challenging because they lack knowledge of the topic, its techniques, and its conceptual framework. In addition, (Omar et al., 2022) revealed that for a high performing group of students, emotion has been found to be a significant predictor of mathematics anxiety. Several studies were conducted to reveal the factors that affect students’ performance in mathematics. (Mazana et al., 2018) discovered that, the students' ability, instructional, and social-psychological contextual elements were the ones that affected whether they like or dislike mathematics. The findings also indicate that ineffective learning and assessment strategies, institutional resources, failure to comprehend instructions, and instructor didactic strategies are all factors in exam failure. Another study conducted by (Kuppusamy & Musa, 2021) aims to investigate the six factors that influence International School secondary student’s attitude towards their mathematics’ performance. The factors are self-efficacy, self-judgement, seeking-help, self-reaction, mathematical anxiety, beliefs in utility of mathematics in real life and teachers’ involvement. The result disclosed that, self-efficacy is the attitude characteristic that affects students' performance the most. The results give educators, schools, and other organizations a clearer picture of how to improve teaching and learning methods to raise students' self-efficacy in classrooms. In order to forecast characteristics that affect students' achievement in mathematics, (Bakar et al., 2019) used five factors which are difficult problems, steps, understanding, word problem and effort. It was discovered that students’ achievement in mathematics was greatly influenced by difficult problems, steps, and understanding. While in studying factor that contribute to a students’ success in a subject, which was conducted by (Farooq et al., 2011),a socioeconomic status (SES), such as a higher level of SES is the best indicator contributing to the quality of a student's achievement. In the same way, (Soule, 2017) carried out a study to improve prediction techniques regarding the future performance of students in the selected university. The variables that the researcher used in the study are based on pre-test, homework, quiz and test score, and attendance. As a result, homework has an almost linear relationship early semester, whereas the mid-semester plot rapidly approaches a success probability of 1. Similarly, (Shedriko, 2021) conducted a study to predict students’ graduation in a subject using the independent variables such as homework, mid-test and final-test. It was revealed that the homework variable is very significant factor in student graduation. Logistic regression was firstly developed by statistician D.R. Cox in 1958 as a statistical method. Logistic regression is a process of modelling the probability of a discrete outcome given an input variable. It is used to model the probability of a certain class or event, such as pass or fail, win or lose, alive or dead or healthy or sick. (Sperandei, 2014) stated that logistic regression could be used to obtain the odds ratio in the presence of more than one explanatory variable. Furthermore, it avoids confounding effects by analyzing the association of all the variables. Logistic regression has also been considered by many analysts to be an important procedure in predictive analytics. Logistic regression can be used for three purposes which are to predict the probability of the outcome or response variable, to categorize outcomes or predictions and to access the odds or risks associated with model predictors. Surveys conducted by (Zou et al., 2019) stated that logistic regression has many iterations. It also takes a long time to bring a large amount of data, which is not applicable. Most researchers will use logistic regression as a broad data processing method in terms of binary classification and predictions. Logistic regression mainly focuses on application. Researchers rarely explore deeply the underlying theoretical models and assumptions when applying logistic regression algorithms, so, there will be unreasonable applications. In recent years, there has been an increasing amount of literature on logistic regression analysis. An example is, one of the applications reviewed b y(Ramosacaj et al., 2015) in the study of students' performance levels. As we all know, many factors contribute to a student's success. The results are divided into two categories which are less than 30% credits and more than 30% credits. They calculated the probability of success and failure. The odd ratio is a good indicator that shows the chances of success against failure under specific conditions of the data. Next, null hypothesis (H\_0) was made, and then, a test was run to decide whether to accept or reject the (H\_0). By using the dependent variable, logistic regression analysis was performed. They assumed that the student with less than 30 credits failed in one or more subjects. The result concluded that the factors that contributed to students’ success are gender, types of private or public school and their location or environment. A similar study was conducted by (Adejumo & Adetunji, 2013). They applied logistic regression analysis to evaluate the students’ performance of Nigerian students. The objectives of the study were to study the factors that contribute to the students’ performance. The results indicated that the mode of entry, age at entry, department, and gender of students are the factors that contributed to students' success in academics. Syuhada et al. (2023) used logistic regression analysis to identify the factor influencing students’ performance in statistics subject. The analysis showed that test 2 and final test marks are the variables that affect to the result of the subject. Logistic regression can also be used in other fields, such as epidemiological studies. Jin (2015) have studied an epidemiological study. The study aims to determine the relationship between bovine tuberculosis (bTB) incidence in cattle herds and potential risk factors (explanatory variables) from 2005 to 2009 using the logit model. Since they have many explanatory variables, which are more than 30, they examined associations between the response variable and each explanatory variable in a univariate analysis using Spearman's rank correlation coefficient first. The correlation among the variables then being tested using Pearson's and Spearman's rank correlation. While in studying factor that contribute to a students’ success in a subject, which was conducted by Farooq et al. (2011),a socioeconomic status (SES), such as a higher level of SES is the best indicator contributing to the quality of a student's achievement. In the same way, Soule (2017) carried out a study to improve prediction techniques regarding the future performance of students in the selected university. The variables that the researcher used in the study are based on pre-test, homework, quiz and test score, and attendance. As a result, homework has an almost linear relationship early semester, whereas the mid-semester plot rapidly approaches a success probability of 1. Similarly, Shedriko (2021) conducted a study to predict students’ graduation in a subject using the independent variables such as homework, mid-test and final-test. It was revealed that the homework variable is very significant factor in student graduation. Logistic regression was firstly developed by statistician D.R. Cox in 1958 as a statistical method. Logistic regression is a process of modelling the probability of a discrete outcome given an input variable. It is used to model the probability of a certain class or event, such as pass or fail, win or lose, alive or dead or healthy or sick. Sperandei (2014) stated that logistic regression could be used to obtain the odds ratio in the presence of more than one explanatory variable. Furthermore, it avoids confounding effects by analyzing the association of all the variables. Logistic regression has also been considered by many analysts to be an important procedure in predictive analytics. Logistic regression can be used for three purposes which are to predict the probability of the outcome or response variable, to categorize outcomes or predictions and to access the odds or risks associated with model predictors. Surveys conducted by Zou et al. (2019) stated that logistic regression has many iterations. It also takes a long time to bring a large amount of data, which is not applicable. Most researchers will use logistic regression as a broad data processing method in terms of binary classification and predictions. Logistic regression mainly focuses on application. Researchers rarely explore deeply the underlying theoretical models and assumptions when applying logistic regression algorithms, so, there will be unreasonable applications. In recent years, there has been an increasing amount of literature on logistic regression analysis. An example is, one of the applications reviewed by Ramosacaj et al. (2015) in the study of students' performance levels. As we all know, many factors contribute to a student's success. The results are divided into two categories which are less than 30% credits and more than 30% credits. They calculated the probability of success and failure. The odd ratio is a good indicator that shows the chances of success against failure under specific conditions of the data. Next, null hypothesis (H\_0) was made, and then, a test was run to decide whether to accept or reject the (H\_0). By using the dependent variable, logistic regression analysis was performed. They assumed that the student with less than 30 credits failed in one or more subjects. The result concluded that the factors that contributed to students’ success are gender, types of private or public school and their location or environment. A similar study was conducted by Adejumo and Adetunji (2013). They applied logistic regression analysis to evaluate the students’ performance of Nigerian students. The objectives of the study were to study the factors that contribute to the students’ performance. The results indicated that the mode of entry, age at entry, department, and gender of students are the factors that contributed to students' success in academics. (Syuhada et al., 2023) used logistic regression analysis to identify the factor influencing students’ performance in statistics subject. The analysis showed that test 2 and final test marks are the variables that affect to the result of the subject. Logistic regression can also be used in other fields, such as epidemiological studies.(Jin, 2015) have studied an epidemiological study. The study aims to determine the relationship between bovine tuberculosis (bTB) incidence in cattle herds and potential risk factors (explanatory variables) from 2005 to 2009 using the logit model. Since they have many explanatory variables, which are more than 30, they examined associations between the response variable and each explanatory variable in a univariate analysis using Spearman's rank correlation coefficient first. The correlation among the variables then being tested using Pearson's and Spearman's rank correlation. # METHODOLOGY ## Data Collection Method The This study was conducted among 122 students Diploma in Computer Sciences from UiTM Cawangan Melaka Kampus Jasin which involved all students who took pre-calculus subjects for semester October 2021 – February 2022. A questionnaire was distributed online to the respondents. The questionnaire consists of two sections which are section A and section B. In section A, respondents needed to fill in their information which are gender, place of residence and grade for pre-calculus subject. In section B, there are questions about, assessment marks; test 1, test 2, quiz 1, quiz 2, lab assignment, written assignment, time spent studying pre-calculus subject per week and whether the student took additional mathematic during SPM. The factors that affect students passing or failing of MAT133 subject was analyzed using logistic regression. Logistic regression is a technique that is suitable for examining the relationship between a categorical response variable and one or more categorical or continuous predictor variables. In a nutshell, logistic regression will be used if the dependent variable is categorical and binary. There are only two categories of variables in logistic regression. In general, the occurrence of the event is denoted as 1 and its absence as 0. ## Set of Variables The study analyzed the factors that affect students’ performance in pre-calculus subject by measuring students’ grade on ten factors which are gender, place of residence, test 1, test 2, quiz 1, quiz 2, lab assignment, written assignment, time spent studying pre-calculus subject per week and whether the student took additional mathematic during SPM as shown as in Table 1. Table 1: Set of variables | | | | | ----------------------------------- | ---------------------------------------- | ----------------- | | **Variable** | **Type of variable** | **Variable Code** | | Gender | Qualitative (0 = male, 1 = female) | Gender | | Place of residence | Qualitative (0 = off campus, 1 = hostel) | Place | | Test 1 | Quantitative continuous | T1 | | Test 2 | Quantitative continuous | T2 | | Quiz 1 | Quantitative continuous | Q1 | | Quiz 2 | Quantitative continuous | Q2 | | Lab Assignment | Quantitative continuous | Lab | | Written Assignment | Quantitative continuous | Written | | Time spent studying MAT112 per week | Quantitative continuous | Time | | Took Additional Mathematics in SPM | Qualitative (0 = no, 1 = yes) | SPM | ## Binary Logistic Regression The specific form of the logistic regression model is: | | | | ----------------------------------------- | --- | | ![](65ae90b80e846_media/media/image1.wmf) | (1) | The transformation of the conditional mean ![](65ae90b80e846_media/media/image2.wmf) logistic function is known as the logit transformation: | | | | ----------------------------------------- | --- | | ![](65ae90b80e846_media/media/image3.wmf) | (2) | where ![](65ae90b80e846_media/media/image2.wmf) is the probability of the outcome of interest or event, ![](65ae90b80e846_media/media/image4.wmf) is the intercept, ![](65ae90b80e846_media/media/image5.wmf) ,…, ![](65ae90b80e846_media/media/image6.wmf) are regression coefficients![](65ae90b80e846_media/media/image7.wmf) ,…![](65ae90b80e846_media/media/image8.wmf)are independent variables. For this study, the dependent variable is success or failure and ten independent variables, the binary logistic regression model is estimated to be | | | | ----------------------------------------- | --- | | ![](65ae90b80e846_media/media/image9.wmf) | (3) | # result and discussion ## Determining the Model Fit To determine the fit model, the model must be validated using a number of statistical criteria. There are two statistical criteria used which are Omnibus and Hosmer and Lemeshow. **Omnibus** H₀: The logistic model is a good fit for the data, H₁: The logistic model is not a good fit for the data *p*-value = 0.428 Decision: Reject H0 since p-value less than 0.05 Conclusion: The model fits the data **Hosmer and Lomeshow** H₀: The logistic model is not a good fit for the data H₁: The logistic model is a good fit for the data *p*-value = 0.000 Decision: Reject H0 since p-value less than 0.05 Conclusion: The model fits the data ## Determining the Model Fit # Table 2: Logistic Regression Model Coefficient | **Variables** | **B** | **WALD** | **Sig.** | **Exp(B)** | | ------------- | -------- | -------- | -------- | ---------- | | Constant | \-13.580 | 14.409 | .000 | .000 | | Gender | 2.264 | 4.633 | .031 | 9.624 | | Place | \-.707 | .280 | .597 | .493 | | T1 | .101 | .919 | .338 | 1.107 | | T2 | .213 | 6.022 | .014 | 1.238 | | Q1 | .012 | .020 | .888 | 1.012 | | Q2 | .572 | 8.902 | .003 | 1.771 | | Lab | .335 | 3.784 | .052 | 1.399 | | Written | .056 | .847 | .358 | 1.058 | | Time | \-.160 | 2.641 | .104 | .852 | | SPM | .538 | .388 | .533 | 1.713 | Table 2 shows that only three variables are significant which are Gender (Sig = 0.031, *p* \< 0.05), T2 (Sig = 0.014, *p* \< 0.05) and Q2 (Sig = 0.003, *p* \< 0.05) since *p*-value is less than alpha=0.05, while the other seven variables are not significant to the model. Table 2 displays the value of the odd ratio for variables. The odd ratio for first significant variable which is 9.624 for gender. Therefore, this value indicates that most of female students are approximately 9.6 times more likely to pass examination compared to male students, while for T2, the result shows that the value of 1.238 which means that for every one-mark increase in test 2, the odds of passing the examination will increase by 1.238 or 23.8%. This indicates that the chance of students was taking the test 2 and getting good score is 1.238 times higher than the students who taking the exam but get bad score. The last significant variable which is Q2 produced the value of an odd ratio of 1.771 which means that for every one-mark increase in quiz 2, the odds of passing the examination will increase 17.71%. This explains that the probability of students who taking quiz 2 and get good score is 1.771 times higher than the students was taking the quiz 2 but get a bad score. Table 2 also shows the result of Wald statistics. The value of Wald statistics for gender (4.633), T2 (6.022) and Q2 (8.902) are more than ![](65ae90b80e846_media/media/image10.wmf)=3.841. This indicates that, there is a significant effect between the independent variable (Gender, Test 2 and Quiz 2) and grade for pre-calculus subject. Therefore, the best model using Binary Logistic Model is | | | | ------------------------------------------ | --- | | ![](65ae90b80e846_media/media/image11.wmf) | (4) | Table 3: Classification Table | | | **Predicted** | **Percentage corrects** | | | -------- | ------------------ | ------------- | ----------------------- | ---- | | | | Fail | Pass | | | Observed | Fail | 23 | 7 | 76.7 | | | Pass | 5 | 87 | 94.6 | | | Overall Percentage | | | 90.2 | Table 3 shows the result comparing the outcome predicted using the proposed Binary Logistic Regression Model with the actual data outcome. The data accuracy was 90.2%, which is more than the cut-off point of 50%, which shows that the model possesses good predictive efficiency. # conclusion To achieve the objective of the study, which is to determine the factors that affect students' performance in Mathematics subject, gender, the grade for MAT133, place of residence, status whether the student took additional mathematics during SPM, time that students spent studying for the subject and the assessments were analysed. The assessments refer to test 1, test 2, lab assignment, quiz 1, quiz 2 and written assignment. From the results, it is shown that the variables that are significant are gender, test 2 and quiz 2. The most important factor is test 2 and quiz 2. This is because test 2 and quiz 2 usually covers topics on the last syllabus of the subject. If the students understand the last syllabus, usually they would also understand the whole syllabus because pre-calculus subject’s syllabus are related to each other from the beginning to the end. Gender also is an important factor because mathematics requires students to do more exercises so that they know whether they understand the topic or not. Female students are usually more hardworking than male students. Findings regarding the other variables such as place of residence, status whether the student took additional mathematics during SPM, test 1, lab assignment, quiz 1, and written assignment tend to be insignificant might be because students had to study online or online distance learning (ODL). In addition, students had different situations and problems at home. Sometimes, the assessment does not affect much in their result because some students tend to copy others without understanding them. Thus, they will have difficulties with their final assessment. In order to increase their students' sense of mastery and self-efficacy, lecturers should assign them more homework and discuss the answer together in class. Lecturers must also make sure that the students do the exercise given, regardless of their gender. Mathematics teaches students to think creatively and critically. Therefore, lecturers can try to develop critical thinking skill while teaching to train the students to think creatively. (Saka, 2021) showed that collaboration among educators can improve student learning. When examining the variables influencing the academic performance of CS110 students in UiTM Jasin, there are certain knowledge gaps and restrictions. It is advised that future studies collect data from more respondents and keep the question simple but clear in order to get more accurate results. To get more precise result, the future research should collect the data from equal number of male and female students. # Acknowledgements/Funding The authors would like to thank to the students of Universiti Teknologi MARA Cawangan Melaka Kampus Jasin who participated in this study. The authors would also like to express gratitude to the reviewers for their insightful comments and ideas. # Conflict of interest statement The authors agree that this research was conducted in the absence of any self-benefits, commercial or financial conflicts and declare the absence of conflicting interests with the funders. # Authors’ contributions XXX carried out the research, wrote and revised the article. XXX conceptualised the central research idea and provided the theoretical framework. XXX and XXX designed the research, supervised research progress; XXX anchored the review, revisions and approved the article submission. # References Adejumo, A. O., & Adetunji, A. A. (2013). Application of ordinal logistic regression in the study of students’ performance. In *Mathematical Theory and Modeling* (Vol. 3, Issue 11).Ashaari, N. S., Judi, H. M., Mohamed, H., & Tengku Wook, T. M. (2011). Student’s attitude towards statistics course. *Procedia - Social and Behavioral Sciences*, *18*. https://doi.org/10.1016/j.sbspro.2011.05.041Bakar, S. A., Ayub, A. F. M., Gopal, K., & Salim, N. R. (2019). The influence of students’ beliefs on mathematical problem solving towards mathematics achievement among Malaysian matriculation students. *Universal Journal of Educational Research*, *7*(10). https://doi.org/10.13189/ujer.2019.071025Farooq, M. S., Chaudhry, a H., Shafiq, M., & Berhanu, G. (2011). Factors affecting students’ quality of academic performance: A case of secondary school level. *Journal of Quality and Technology Management*, *VII*(II).Jin, R. (2015). Application of logistic regression model in an epidemiological study. *Science Journal of Applied Mathematics and Statistics*, *3*(5). https://doi.org/10.11648/j.sjams.20150305.12Kuppusamy, S., & Musa, M. (2021). Investigating International School secondary students ’ attitude towards mathematics. *Jurnal Pendidikan Sains Dan Matematik Malaysia*, *11*(2), 122–130.Mazana, M. Y., Montero, C. S., & Casmir, R. O. (2018). Investigating students’ attitude towards learning mathematics. *International Electronic Journal of Mathematics Education*, *14*(1). https://doi.org/10.29333/iejme/3997Omar, S. H., Aris, S. R. S., & Hoon, T. S. (2022). Mathematics Anxiety and its relationship with mathematics achievement among secondary school students. *Asian Journal of University Education*, *18*(4), 863–878. https://doi.org/10.24191/ajue.v18i4.19992Patena, A. D. C., & Dinglasan, B. (2013). Students performance on departmental examination: Basis for math intervention program. *SSRN Electronic Journal*. https://doi.org/10.2139/ssrn.2276044Ramosacaj, M., Hasani, V., & Dumi, A. (2015). Application of logistic regression in the study of students’ performance level (case study of Vlora University). *Journal of Educational and Social Research*. https://doi.org/10.5901/jesr.2015.v5n3p239Saka, A. O. (2021). Can teacher collaboration improve students’ academic achievement in junior secondary mathematics? *Asian Journal of University Education*, *17*(1), 33–46. https://doi.org/10.24191/ajue.v17i1.8727Shedriko. (2021). *Binary logistic regression in determining affecting factors student graduation in a subject*. *4*(1), 114–120. https://doi.org/10.36378/jtos.v4i1.1401Soule, P. (2017). *Predicting student success : A logistic regression analysis of data from multiple SIU-C courses*. *Fall*.Sperandei, S. (2014). Understanding logistic regression analysis. *Biochemia Medica*, *24*(1). https://doi.org/10.11613/BM.2014.003Syuhada, N., Pazil, M., Mahmud, N., Baharom, N., & Hafawati, S. (2023). Logistic regression in determining affecting factors student success in an introductory statistics subject. *Jurnal Intelek*, *18*(1), 9–16. https://doi.org/https://doi.org/10.24191/ji.v18i1.20133Zou, X., Hu, Y., Tian, Z., & Shen, K. (2019). Logistic regression model optimization and case analysis. *Proceedings of IEEE 7th International Conference on Computer Science and Network Technology, ICCSNT 2019*. https://doi.org/10.1109/ICCSNT47585.2019.8962457

1. ^\* Corresponding author. *E-mail address*: (Please do not type or edit anything here, our editors will do the work for you)