**3. Results**

The results indicate that there is a direct and positive relationship between the grades of the first weeks of activity and the final result or AP of the subject. Likewise, it was established that, from 8 points out of a possible ten, in the first measurement of the academic activity, students pass more than those who fail. **Figure 2** shows the behavior of academic performance at the end of the semester, depending on the AP of the first weeks. As an example of the reading of the results, we point out the following cases:


**Figure 2** shows the positive relationship between the first moment of APt1 and APt4, the higher the grade in t1 the more likely it is that the subject will be passed, especially when the first moment has more than eight points. Between the AP measured at t1 and the AP measured at t4 there is a correlation of 86%.

The relationship between the moments of academic performance over time, initially measured with a simple regression, Model 1: *Yi* ¼ *δ*<sup>0</sup> þ *δ*1*Xi* þ *μ*<sup>1</sup> (Ec. (1)) the results are positive and conform to the initial theoretical approach.

#### **Figure 2.**

*Number of students according to promotion at the end of semester t4 compared to the results in the first weeks of study.*


The 74% of the changes that could occur in the academic performance at the end of the semester (APt4)) are explained by the academic performance at the first moment of the semester evaluation (APt1). The APt4 that does not depend on APt1 is 4.24 points, a very low value in relation to the 40 points that can be accumulated; while, the APt4 that depends on APt1 has a positive effect and increases to an average of 2.73 for each additional point of APt1. The estimated results passed all the tests of correct specification and therefore, the prediction is valid and confirms the proposed relationship.

Model 2: *ln PA PR* <sup>¼</sup> *<sup>δ</sup>*<sup>0</sup> <sup>þ</sup> *<sup>δ</sup>*1*Xi* <sup>þ</sup> *<sup>μ</sup>*<sup>1</sup> (Ec. (2)), shows the relationship between the natural logarithm of the probability that APt4 is above the minimum necessary (75%) to pass the course versus not passing, as a function of APt1 or *Xi*. The results of the five-iteration logit model suggest a relationship with positive effects (0.87) and a null probability (�6.99) of APt4 for the cases in which APt1 is null.

The marginal effect (0.15), determines that unit changes in APt1 have a positive effect equivalent to 15% on the probability that APt4 is greater than or equal to the 75% grade required to pass. Alternatively, we can say that as APt1 increases by one point, the probability of having APt4 = 1 increases by 15%. This model predicts very well, according to the ROC curve, 89% of the cases were well classified.


*Influence of Initial Study Activities on Final Academic Performance – An Analysis… DOI: http://dx.doi.org/10.5772/intechopen.99804*


Finally, Model 3: *ln PA PR* <sup>¼</sup> *<sup>δ</sup>*<sup>0</sup> <sup>þ</sup> *<sup>δ</sup>*1*D*<sup>1</sup> <sup>þ</sup> *<sup>μ</sup>*3(Ec. (3)), raises the possibility of the relationship between the natural logarithm of the probability ratio (PR) that APt4 is above the minimum necessary (75%) to pass the subject, versus that it is not, this as a function of a dichotomous variable *D*<sup>1</sup> that is equal to one when APt1 > 75% and zero when APt1 < 75%. The results of model 3, are conclusive to test the hypothesis proposed in the theoretical model "The student who in the first measurement *t*<sup>1</sup> of the APt1 have results that are equal to or higher than 75% of the grade have the highest probability of passing the subject".


The estimation of the -logit- model, with four iterations, confirms the positive effects of models one and two. The logarithm of the likelihood ratio is positive (3.45) when *D*1=1, otherwise the probability is zero. Therefore, a student who has less than 75% of the grade, in the first weeks of study (APt1), is unlikely to pass the subject or have an APt4 > 75%. The marginal effect is 65% for unit changes in APt1. The ROC curve (0.82) certifies the adequate classification of the predictions of this model.
