# Using Artificial Intelligence to Predict Students’ Academic Performance in Blended Learning

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Mathematical Modeling

#### 3.1. Firefly Algorithm

_{i}at time t+1, N represents the total number of fireflies (the dimension of the solution vector). The value of ${\beta}_{0}$ is considered as 1, α represents a random vector over [0, 1], ${\gamma}^{*}$ is absorption coefficient that distributed over [0, ∞], ${r}_{ij}^{2}$ is the distance between any two fireflies. ${\in}_{i}^{t}$ represents a random parameter at time t, where Figure 1 illustrates the FFA structure.

#### 3.2. ANN

## 4. Research Methodology and Framework

**H**

_{1}.**H**

_{2}.**H**

_{3}.**H**

_{4}.## 5. Results and Discussions

- Multicollinearity tests: Table 2 shows the correlation between input and output variables. The variables are removed because of multicollinearity between input variables. The “no multicollinearity” refers to the absence of perfect multicollinearity, which is an exact (non-stochastic) linear relation among the input values. According to the conducted tests, we removed some variables from input variables that are strongly related to other input variables. The result shows weak correlations between input variables because it is less than 50%.
- Furthermore, there is a strong correlation between assignments and mid-exam. There are strong negative correlations between attendance and final exams.
- The first plot in Figure 4, “Residuals vs. Fitted,” aids in evaluating Linearity and Homoscedasticity: If the residuals (points on the plot) are primarily spread around the zero line, zero red line (fitted line), linearity is present. The x-axis is the fitted value, and the y-axis is the residual that refers to the different distance between the fitted value in the red line and observation; the residuals are said to be normally distributed if the red trend line is approximately flat and near zero. Homoscedasticity refers to the absence of a clear pattern in the residuals. This is also referred to as a residual distribution. The second plot is a scatterplot with two sets of quantiles against one another. It is called a Q-Q plot (or quantile–quantile plot). Plotting the theoretical quantiles of the normal distribution on the x-axis and the quantiles of the residual distribution on the y-axis allows you to determine if the residuals are normally distributed. It is acceptable to infer that the residuals follow a normal distribution if the Q-Q plot forms a diagonal line. As we can see, this is generally true for the observed values. By looking at the scale-location plot, sometimes referred to as the spread-location plot, the third plot, this assumption may be verified. This graphic demonstrates if residuals are distributed similarly throughout the predictor ranges. A horizontal line with evenly spaced points is ideal. This is the case in the scenario we provide. The final plot, also known as the residuals vs. leverage plot, is a diagnostic diagram that shows which observations in a regression model are most important. Within the plot, each observation from the dataset is represented by a single point. Each point’s leverage is shown on the x-axis, and its standardized residual is shown on the y-axis. Leverage measures how much the regression model’s coefficients would change if particular datasets were left out. High-leverage observations have a significant impact on the regression model’s coefficients. The coefficients of the model will change dramatically if we remove these observations. The residual is the uniform difference between a value that was predicted and the observation’s actual value. Any site in this plot outside of Cook’s range (the red dashed lines) is regarded as a significant finding. Any position in this plot outside Cook’s distance (the red dashed lines) is regarded as a significant finding. In our model, there are no influential points. In the end, the least-squares estimation is significantly based on previous assumptions.
- OLS, fixed effects, and random-effects models for input variables issues: A statistical approach used to analyze the relationship between a single output variable and input variables is multiple regression. The ordinary least square (OLS) aims to use the input variables known to predict the value of the single output value by their values. The weights are weighed for each predictor value, which denotes their relative contribution to the overall prediction.$${Y}_{i}=\propto +{\displaystyle \sum}_{i=1}^{n}{\beta}_{i}{x}_{i}+{\epsilon}_{i}$$

_{2}, H

_{3}, and H

_{4}. However, there are adverse effects between attendance on final exams, with a significant level < 5%. Therefore, we reject H

_{1}. The R-square is 70%, the adjusted R-square is 69.63%, and F-statistic is 134.6 with a significant level < 1%.

_{2}, H

_{3}, and H

_{4}. However, there is no effect between attendance on final exams, with a significant level < 5%. Therefore, we accept H

_{1}. The R-square is 64.2%, the adjusted R-square is 24.85%, and F-statistic is 49.76, with a significant level of less than 1%.

_{2}, H

_{3}, and H

_{4}. However, there are adverse effects between attendance on final exams with a significant level < 5%. Therefore, we reject H

_{1}. The R-square is 69.23%, the adjusted R-square is 68.69%, and F-statistic is 518.514 with a significant level < 1%.

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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Variables | Mean | Std. Dev. | Min. | Max. | Skewness | Kurtosis | ||
---|---|---|---|---|---|---|---|---|

Statistic | Std. Error | Statistic | Std. Error | |||||

Final exams | 35 | 15.111 | 0 | 50 | −1.051 | 0.159 | 0.141 | 0.317 |

Mid-exams | 16.06 | 6.227 | 0 | 25 | −0.674 | 0.159 | 1.389 | 0.317 |

Assignments | 21.2 | 6.253 | 0 | 25 | −2.349 | 0.159 | 4.729 | 0.317 |

Attendance | 2.71 | 2.942 | 0 | 8 | 1.867 | 0.159 | 4.557 | 0.317 |

Virtual/Face | 0.49 | 0.501 | 0 | 1 | 0.034 | 0.159 | −2.016 | 0.317 |

Final Exam | Virtual/Face | Mid-Exam | Assignment | Attendance | |
---|---|---|---|---|---|

Final exam | 1 | 0.474 ** | 0.573 ** | 0.633 ** | −0.646 ** |

Virtual/Face | 1 | 0.132 * | 0.059 | −0.06 | |

Mid-exam | 1 | 0.494 ** | −0.476 ** | ||

Assignment | 1 | −0.484 ** | |||

Attendance | 1 |

Variables | OLS | Fixed Effect | Random Effect | |||
---|---|---|---|---|---|---|

Coefficient | Std. Err. | Coefficient | Std. Err. | Coefficient | Std. Error | |

(Intercept) | 10.1592 * | 3.3144 | 9.7678 * | 3.3421 | ||

Virtual/Face | 12.4691 * | 1.0986 | 9.3633 * | 11.0740 | 12.4444 * | 1.1963 |

Mid exam | 0.4303 * | 0.1104 | 0.4163 * | 0.1518 | 0.4298 * | 0.1096 |

Assignment | 0.7639 * | 0.1167 | 0.898 * | 0.1700 | 0.7847 * | 0.1169 |

Attendance | −1.6207 * | 0.2622 | −1.6325 | 0.4080 | −1.6334 * | 0.2643 |

Observations | 234 | 234 | 234 | |||

R-square | 0.7015 | 0.6420 | 0.6923 | |||

Adjusted R-square | 0.6963 | 0.2485 | 0.6869 | |||

F-statistic/Chisq | 134.6000 * | 49.7612 * | 518.514 * |

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**MDPI and ACS Style**

Hamadneh, N.N.; Atawneh, S.; Khan, W.A.; Almejalli, K.A.; Alhomoud, A.
Using Artificial Intelligence to Predict Students’ Academic Performance in Blended Learning. *Sustainability* **2022**, *14*, 11642.
https://doi.org/10.3390/su141811642

**AMA Style**

Hamadneh NN, Atawneh S, Khan WA, Almejalli KA, Alhomoud A.
Using Artificial Intelligence to Predict Students’ Academic Performance in Blended Learning. *Sustainability*. 2022; 14(18):11642.
https://doi.org/10.3390/su141811642

**Chicago/Turabian Style**

Hamadneh, Nawaf N., Samer Atawneh, Waqar A. Khan, Khaled A. Almejalli, and Adeeb Alhomoud.
2022. "Using Artificial Intelligence to Predict Students’ Academic Performance in Blended Learning" *Sustainability* 14, no. 18: 11642.
https://doi.org/10.3390/su141811642