Prediction of Online Students Performance by Means of Genetic Programming

Figures & data

Figure 1. Tree representation of a CP

Figure 2. Crossover representation

Figure 3. A semester, data gathering period

Figure 4. B semester, data gathering period

Table 1. Data sample description, A semester

	Enrollment	Course dropouts	Course passes	Course fails	U1 passes	U1 fails	U1 dropouts
Female	27	8	5	14	8	11	9
Male	139	25	40	74	52	62	29
Total	166	33	45	88	60	73	38
% of class	100%	20%	27%	53%	36%	44%	23%

Table 2. Results of multiple variable analyses on 12 variables

	Standard Deviation	Coefficient of Variation (%)	Pearson Correlations (r)	P-value of Correlations
FG	33.50	86.24	-	-
FA	27.53	72.64	0.46	0.0000
FM	2.38	76.79	0.39	0.0000
FP	2.58	65.20	0.43	0.0000
FT	0.80	94.44	0.21	0.0130
FV	25.48	75.08	0.46	0.0000
OF	1.06	360.57	0.12	0.1660
V1	1.83	15.64	0.30	0.0004
V2	13.53	69.57	0.61	0.0000
V3	14.35	67.43	0.59	0.0000
TA	38.99	65.56	0.55	0.0000
U1	7.64	59.70	0.78	0.0000

FG: Final grades; FA: Total forum activity; FM: Number of forum messages; FT: Number of forum threads; FP: Total forum posts; FV: Forum views; OF: Other forum activity; V1: Resource views; V2: Page views; V3: Total views; U1: Unit 1 scores; TA: Total activity

Figure 5. Normality plot for FG

Figure 6. Normality plot for U1

Table 3. Genetic programming parameters

Objective:	To find a mathematical model in symbolic form that fits by improving the sum of the error differences for all values of its independent variables, given a sample of 133 pairs of grades
Terminal set:	x1 = U1; r(−1.0, +1.0)
Function set:	(+), (-), (×), (÷)
Fitness:	The 133 pairs of (x, y), where xi are the grades of Unit 1 (X1) and where yi are the values of the given mathematical expression
Raw fitness:	The sum, taken over the 133 fitness cases, of the absolute value of the difference between yi and the value produced by the S-expression of xi
Parameters:	Generations: Populations: Probability of crossover Probability of reproduction Probability of mutation Maximum depth of new individuals: Maximum depth of individuals after crossover: Selection method: Generation method: Runs:	15 133 pairs/500 iterations 0.20 0.10 0.00 6 17 Fitness-proportionate Ramped half-and-half 15

Table 4. Test for normality of differences between AR of each model for training data set

Test	P-value
Chi-Squared	0.0001
Shapiro-Wilk W	0.0000
Skewness Z-score	0.6651
Kurtosis Z-score	0.0000