*3.3. Multiple Linear Regression Analysis*

The multiple linear regression analysis is applied to investigate to what extent the iPEP scale is able to predict the performance in Mathematics and Arts. Stepwise method has been conducted.

On the one hand, the prediction of mathematical performance displays a 6-variable model (V3, V6, V7, V11, V4 and V9) that explains 7.2 per cent of the dependent variable. In addition, the value of

the Durbin-Watson statistic (1.758) indicates compliance with the assumption of the independence of the residuals (Table 6). On the other hand, the prediction of performance in Arts establishes a model of 2 variables (V6 and V9) that explains 3.7 per cent of the dependent variable. The Durbin-Watson statistic is 1.408, which complies the assumption of independence of the residuals.


**Table 6.** Multiple linear regression results.

Table 6 shows the Pearson correlations. In the first model (dependent variable = Mathematics grade), the independent variables V3, V6, V11 and V9 obtain positive values reveal a direct relationship. While the variables V7 and V4, indicate an inverse relationship with mathematical performance. In the second model, both variables (V6 and V9) indicate a direct relationship with arts performance.

The validity of the models depends on the verification of the assumptions, such as the non-existence of perfect multicollinearity. The collinearity diagnosis is made through the Variance Inflation Factor (VIF), whose values are close to 1, indicating that the assumption is met (see Table 7).


**Table 7.** Global regression model for model 1 and 2.

One of the premises sought to explore whether these influences could be related to the academic level. For this purpose, multiple linear regression analyzes have been conducted for each course (see Table 8).

**Table 8.** Multiple linear regression results.


Concerning mathematics performance of the fourth course, a model of four variables (V6, V4, V5 and V3) has been obtained that explain 14.1 per cent. In the fifth course, the percentage explained is 9.6 per cent for two variables (V7 and V1). In the sixth course, the V7 explains 10.1 per cent of the performance in mathematics. With regards to the performance in Arts in the fourth course, it is explained in 13.5 per cent by two variables (V6 and V4). In the fifth course, five variables explain 32.1 per cent (V9, V6, V2, V7 and V3). In the sixth course, this performance is explained in 10.1 per cent by two variables (V8 and V9).

Table 9 shows the standardized Beta coefficients that indicate whether the relationship of each variable in the model is direct or inverse towards mathematics performance. In the fourth course the V6, V5 and V3 have a direct relationship and the V4 an inverse relationship. In the fifth course V7 indicates an inverse relationship with the dependent variable and V1 a direct relationship. Moreover, in the sixth course the relation of V7 indicates a direct relation.


**Table 9.** Global regression model by course (predictor variable: Mathematics performance).

Table 10 shows the results regarding the multiple linear regression models regarding the art performance. In the fourth course both variables show a direct relationship with the dependent variable. In the fifth course, V9, V6 and V3 indicate a direct relationship and V2 and V7 an inverse relationship. In the sixth course, V8 indicates a direct relationship and V9 an inverse relationship.


**Table 10.** Global regression model by course (predictor variable: Art performance).
