Research on the Optimization of English Teaching Mode and Personalized Learning Path in Colleges and Universities Based on Big Data Regression Analysis

Full model parameter estimation result

Variable	Coefficient	Standard error	T value
Intercept 1|2	4.47	1.71	2.47
Intercept 2|3	4.03	1.69	2.87
Intercept 3|4	6.02	1.66	3.48
Intercept 4|5	8.11	1.66	4.67
Learner factor (x1)	1.27	0.28	4.44
Teacher factor (x2)	0.29	0.32	0.83
Online course factor (x3)	0.68	0.35	1.86
Environmental factor (x4)	0.53	0.81	0.62
Learner motivation (x5)	0.02	0.01	1.84
Learning strategy (x6)	-0.01	0.01	-1.02
Professional literacy (x7)	-0.69	0.36	-1.79
Teaching guidance (x8)	-12.57	0.88	-13.92
Content form (x9)	0.02	0.01	3.31
Platform design (x10)	0.43	0.03	12.41
Teaching interaction (x11)	0.35	0.05	2.47
Residual error	409.00	AIC	439.00

Test result

Variable	LR card	Freedom	Significance	95% confidence interval
				Lower limit	Upper limit
learner factor (x1)	19.2045	1	5.786e-05***	1.1963	1.3457
course factor (x3)	4.3988	1	0.018675*	0.75478	0.84279
Environment factor (x4)	8.7842	1	0.001679**	-0.8317	-0.9167
Residual error	421.78
AIC value	435.78
-2 log likelihood	1317.39

Individual learning path types and Numbers

Type	Path process	The number of people in the path	Mean capacity
1	ks4→ks11	121	0.41
2	ks1→ks11	55	0.265
3	ks8→ks11	15	-0.102
4	ks3→ks11	85	-0.614
5	ks6→ks11	76	0.574
6	ks2→ks6→ks11	27	-0.201
7	ks7→ks4→ks11	25	0.004
8	ks5→ks7→ks4→ks11	15	0.011
9	ks5→ks8→ks11	6	-0.052
10	ks5→ks1→ks11	15	-0.025
11	ks10→ks5→ks7→ks4→ks11	52	-1.635
12	ks9→ks10→ks5→ks7→ks4→ks11	10	-1.835
13	ks9→ks2→ks6→ks11	3	-1.263
14	ks9→ks3→ks11	4	-1.236
15	Master of	22	1.041

The number is 107 students’ properties

	A1	A2	A3	A4	A5	A6	A7	T1	T2	θ
mp	0.9927	0.9965	0.4527	0.041	0.0332	0.9645	0.5115	0.2601	0.2347	0.113
ks	1	1	0	0	0	1	1	0	0

Complete learning path type and number

Type	Path process	The general number of cognitive states
1	ks9→ks3→ks11	117
2	ks9→ks10→ks5→ks8→ks11	154
3	ks9→ks10→ks5→ks1→ks11	179
4	ks9→ks2→ks6→ks11	245
5	ks9→ks10→ks5→ks7→ks4→ks11	235

Model regression

Variable	Coefficient	Standard error	T value
Intercept 1|2	-4.41	0.61	-6.97
Intercept 2|3	-3.91	0.52	-7.48
Intercept 3|4	-2.91	0.38	-7.48
Intercept 4|5	-0.89	0.29	-2.95
learner factor (x1)	1.28	0.26	4.45
course factor (x3)	0.79	0.35	2.18
Environment factor (x4)	-0.85	0.30	-2.01

The properties of the clustering are the probability

Categories	A1	A2	A3	A4	A5	A6	A7	T1	T2	Mean
Ks1	0.977	0.99	0.262	0.172	0.737	0.965	0.839	0.396	0.178	0.613
Ks2	0.751	0.949	0.699	0.272	0.521	0.174	0.358	0.284	0.125	0.459
Ks3	0.751	0.949	0.699	0.272	0.521	0.174	0.358	0.284	0.125	0.534
Ks4	0.992	1	0.883	0.933	0.423	0.99	0.592	0.395	0.792	0.778
Ks5	0.948	0.955	0.381	0.095	0.179	0.902	0.539	0.308	0.242	0.505
Ks6	0.968	0.962	0.686	0.688	0.762	0.95	0.467	0.481	0.556	0.724
Ks7	0.836	0.936	0.223	0.307	0.332	0.974	0.838	0.467	0.809	0.636
Ks8	0.814	0.96	0.244	0.211	0.458	0.841	0.646	0.802	0.161	0.571
Ks9	0.000	0.409	0.001	0.275	0.066	0.000	0.229	0.192	0.005	0.131
Ks10	0.000	0.01	0.137	0.01	0.037	0.042	0.003	0.961	0.48	0.187
Ks11	0.968	0.962	0.686	0.688	0.762	0.951	0.556	0.792	0.539	0.767

The proposed effect of the predicted value is analyzed

Predictive value (grade)	True value
	1	2	3	4	5
1	0	0	0	0	0
2	0	0	0	0	0
3	0	0	0	0	0
4	0	0	0	0	1
5	0	1	4	14	95