# Estimating the Academic Performance of Secondary Education Mathematics Students: A Gain Lift Predictive Model

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## Abstract

**:**

## 1. Introduction

#### 1.1. Mathematics and Its Learning

#### 1.2. Interactions in the Educational Environment

#### 1.3. Motivation

#### 1.4. Justification

## 2. Materials and Methods

#### 2.1. Inferential Statistics

#### 2.1.1. Global Adjustment of the Model

#### 2.1.2. Parameters of the Model

- b0 = 8.97 × 10
^{−7}, implies that, if all the independent variables took the value 0, the participants’ scores would be 8.97 × 10^{−7}. - b1 (TGM) = 0.33; b2 (PME) = 0.01; b3 (LJM) = 0.02; b4 (ULT) = 0.001; b5 (UAE) = 0.04; b6 (APM) = −0.04; b7 (MAM) = −0.03; b8 (MFM) = 0.05; b9 (MPM) = −0.01; b10 (ILS) = 0.02; b11 (CLB) = 0.07; b12 (TCE) = −0.03; b13 (PAV) = 0.09; and b14 (PCA) = 0.07.

#### 2.1.3. Marginal Averages Predicted by the Model and Estimated with the Data

## 3. Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

## References

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**Figure 1.**Relative importance of the research predictors: (

**a**) The variance decomposition metric. Method LMG (Lindeman, Merenda, and Gold); (

**b**) method last; (

**c**) method first; and (

**d**) Pratt method.

**Figure 3.**Diagnostics of the linear regression model: (

**a**) Residuals vs. fitted values; (

**b**) Normal Quantil-Quantil; (

**c**) scale-location; and (

**d**) residuals vs. leverage values.

**Figure 8.**Gain chart comparison of the mixed student sample and the gender-differentiated subsamples.

Dimension | Indicators | Code | Items |
---|---|---|---|

B. Learning of Mathematics | B.1 Affinity | TGM | Do you like mathematics? |

B.4 Teaching | PME | Does your mathematics teacher explain things to you well in class? | |

B.5 Study Time | LJM | From Monday to Thursday, how many hours do you dedicate to the study of mathematics? | |

B.6 Resources | ULT | Do you use the course book to study mathematics? | |

UAE | Do you use the notebook or class notes to study mathematics? | ||

B.7 Study Assistance | APM | Does your academy or tutor help you when learning mathematics? | |

B.8 Motivation: | MAM | Do your friends motivate you to study mathematics? | |

MFM | Does your family motivate you to study mathematics? | ||

MPM | Does your teacher motivate you to study mathematics? | ||

C. School Environment | C.1 Educational Center | ILS | Do you think your school is a place where you feel protected and safe? |

C.2 Room | CLB | Do you think your classroom is a good place to learn? | |

C.3 Classmates | TCE | Do you work with your classmates while learning mathematics? | |

C.4 Relationship with teachers | PAV | Do you think your teacher thinks highly of and values you? | |

PCA | Does your mathematics teacher create a suitably respectful environment in class? |

**Note:**Likert-scale for study variables: LJM: 1, none; 2, less than 1 h; 3, from 1 to 2 h; and 4, more than 2 h. For all other items, (1, none; 2, a little; 3, enough; and 4, a lot).

Residuals: | ||||

Min | 1Q | Median | 3Q | Max |

−2.720 | −1.160 | −0.096 | 1.006 | 3.340 |

Coefficients: | ||||

Estimate | Std. Error | T Value | Pr(>|t|) | |

Intercept | 0.661314 | 0.134186 | 4.928 | 8.97 × 10^{−7} *** |

TGM | 0.333891 | 0.023150 | 14.423 | <2 × 10^{−16} *** |

PME | 0.017346 | 0.029916 | 0.580 | 0.562102 |

LJM | 0.029923 | 0.026354 | 1.135 | 0.256334 |

ULT | 0.001705 | 0.026223 | 0.065 | 0.948162 |

UAE | 0.036658 | 0.035496 | 1.033 | 0.301860 |

APM | −0.042089 | 0.026612 | −1.582 | 0.113906 |

MAM | −0.025956 | 0.024325 | −1.067 | 0.286073 |

MFM | 0.051622 | 0.033720 | 1.531 | 0.125943 |

MPM | −0.006691 | 0.026851 | −0.249 | 0.803236 |

ILS | 0.024922 | 0.024280 | 1.026 | 0.304806 |

CLB | 0.077882 | 0.024528 | 3.175 | 0.001520 ** |

TCE | −0.031885 | 0.024563 | −1.298 | 0.194403 |

PAV | 0.094211 | 0.027647 | 3.408 | 0.000668 *** |

PCA | 0.072070 | 0.030587 | 2.356 | 0.018559 * |

^{−16}.

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## Share and Cite

**MDPI and ACS Style**

Trujillo-Torres, J.-M.; Hossein-Mohand, H.; Gómez-García, M.; Hossein-Mohand, H.; Hinojo-Lucena, F.-J.
Estimating the Academic Performance of Secondary Education Mathematics Students: A Gain Lift Predictive Model. *Mathematics* **2020**, *8*, 2101.
https://doi.org/10.3390/math8122101

**AMA Style**

Trujillo-Torres J-M, Hossein-Mohand H, Gómez-García M, Hossein-Mohand H, Hinojo-Lucena F-J.
Estimating the Academic Performance of Secondary Education Mathematics Students: A Gain Lift Predictive Model. *Mathematics*. 2020; 8(12):2101.
https://doi.org/10.3390/math8122101

**Chicago/Turabian Style**

Trujillo-Torres, Juan-Manuel, Hassan Hossein-Mohand, Melchor Gómez-García, Hossein Hossein-Mohand, and Francisco-Javier Hinojo-Lucena.
2020. "Estimating the Academic Performance of Secondary Education Mathematics Students: A Gain Lift Predictive Model" *Mathematics* 8, no. 12: 2101.
https://doi.org/10.3390/math8122101