Chapter 4 Experimental Methods
4.3 Research Methods
4.3.5 Building a MATLAB Toolbox Based on Taylor Approximation
Start
End
Step 2: Determine the requirements that the program must satisfy
Step 3: Draw flowcharts of the program
Step 5: Using the MATLAB software to write the program
Step 6: Test the program
Step 1: Determine the purpose of the program design
Yes
No Step 4: Test flowcharts
Yes
No
Fig. 4-6 Progress of designing the MATLAB toolbox
Software Specifications and Requirements
(1) Windows XP, Windows 7 or upgrade versions.
(2) Screen resolution 1280×800.
(3) MATLAB version 7.10 or upgrade versions.
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This dissertation presents a sample program that is developed by MATLAB including many scientific functions due to the provision of experimental environment on the computer, and then a reliable program can be developed. The program for the prediction models has been developed by the MATLAB software.
Progress for Building a MATLAB Toolbox
The progress for designing the toolbox includes six basic steps and is described in Fig. 4-6.
Step 1: Determine the purpose of the MATLAB toolbox design
The MATLAB toolbox was designed for prediction and evaluation in educational information and measurement.
Step 2: Determine the requirements that the program must satisfy
After completion, the program must be accurate, fast and easy to use.
Step 3: Construct the flowcharts of the program
The algorithms of the overall program and each subroutine are specifically built and represented by the flowcharts.
Step 4: Test the flowcharts of the program
Step 5: Using the MATLAB software write the program
In this study, the program is developed by the MATLAB software.
Step 6: Test the program
The program will be tested several times to ensure it satisfies the requirements determined. If not satisfied, the program continues to be tested, repaired and improved.
Graphical User Interface (GUI) of MATLAB for TAMGP
GUI of MATLAB for TAMGP includes GUI of MATLAB for T-GM(1,1), T-GVM, and T-GM(2,1), GUI of MATLAB for T-GM(1,n) and T-GM(2,n), GUI of MATLAB for Taylor approximation method in RaschGSP IRT, GUI of MATLAB for predicting and evaluating the academic achievement of students, and GUI of MATLAB to set the standard for tests. They are designed as follows:
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Fig. 4-7 GUI of MATLAB for T-GM(1,1), T-GVM, and T-GM(2,1)
The graphical user interface starts up when file “TAMGP1.m” is opened, the graphical user interface of the program is displayed on the screen of the computer (as Fig. 4-7). Firstly, the user needs to click the button “Input Data” to input the data. In this study, the input data are the number of foreign students studying in Taiwan that are numerical and written in *.xlsx file. Secondly, the user selects the prediction model (T-GM(1,1) or T-GVM or T-GM(2,1)) . Thirdly, the user can type the number of Times K, the number of Delta h, and the number of Coefficient H; then clicks the button “OK”, the program will process the data, and then the program will display results and graphs.
In the panel, the user can click the button “Save Results” to save the results to *.csv file or *.xlsx file or *.xls file formatted, and can click the button “Save Graphs” to save the graphs to *.JPG file formatted. Finally, if new data is selected, the program will continue, or else if the user clicks the button “Exit” the program will be ended.
Example 4-1:
In this study, the experimental data are taken from the website of the Ministry of Education, Taiwan. Data are the number of students from three countries
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(Vietnam, Japan, and Malaysia) studying in Taiwan from the 2003-2004 academic year to the 2012-2013 academic year. These are three countries with large numbers of students studying in Taiwan in recent years. The prediction results for the next three years and the accuracy of three prediction models (GM(1,1), GVM, and T-GM(2,1)) from the experimental data are shown in the Table 4-1. The results will provide the important information for educational administrators to proactively propose the appropriate policy, and building the educational development strategy in accordance with the new conditions.
Table 4-1
The prediction results and the accuracy of three prediction models
Unit: Person
School Year Measured Data Prediction Results Vietnam Japan Malaysia Vietnam Japan Malaysia
2003-2004 438 1825 194 - - -
2004-2005 503 1879 332 - - -
2005-2006 671 2126 425 - - -
2006-2007 836 2188 671 - - -
2007-2008 1276 2297 872 - - -
2008-2009 1779 2182 1001 - - -
2009-2010 2592 2142 1560 - - -
2010-2011 3282 2302 1961 - - -
2011-2012 3687 2861 2286 - - -
2012-2013 3706 3097 2722 - - -
2013-2014 - - - 3190 3011 3613
MAPE (%) - - - 8.40 6.07 9.81
RMSPE (%) - - - 15.87 7.39 14.27
Model T-GVM T-GM(2,1) T-GM(1,1)
The graphical user interface starts up when file “TAMGP2.m” is opened, the graphical user interface of the program is displayed on the screen of the computer (as Fig. 4-8). Firstly, the user needs to click the button “Input Data” to input the data. In this study, the input data are the number of students and teachers for admission that are
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numerical and written in *.xlsx file. Secondly, the user selects the prediction model (T-GM(1,n) or T-GM(2,n)) . Thirdly, the user needs to type the number of Times K, the number of Delta h, and the number of Coefficient H; then clicks the button “OK”, the program will process the data, and then the program will display results and graphs. In the panel, the user can click the button “Save Results” to save the results to *.csv file or
*.xlsx file or *.xls file formatted, and can click the button “Save Graphs” to save the graphs to *.JPG file formatted. Finally, if new data is selected, the program will continue, or else if the user clicks the button “Exit” the program will be ended.
Fig. 4-8 GUI of MATLAB for T-GM(1,n) and T-GM(2,n)
Example 4-2:
In this study, data are taken from the website of the Ministry of Education and Training of Vietnam. Data are the number of teachers and students at all preschools from the 2003-2004 to the 2012-2013 academic year in Vietnam. The prediction results and the accuracy of two prediction models (T-GM(1,n) and T-GM(2,n)) are shown in the Table 4-2.
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Table 4-2
The prediction results and the accuracy of two prediction models
Unit: Person
School Year Measured Data Prediction Results
Teachers Students GM(1,n) T-GM(1,n) GM(2,n) T-GM(2,n) 2003-2004 150335 2588837 150335 150335 150335 150335 2004-2005 155699 2754094 149720 159037 176992 156370 2005-2006 160172 3024662 164965 162292 228198 159597 2006-2007 163809 3147252 171755 166453 295284 165532 2007-2008 172978 3195731 174334 170555 383145 174064 2008-2009 183443 3305391 180114 181074 498184 185138 2009-2010 195852 3409823 185520 193370 648784 198754 2010-2011 211225 3599663 195724 207024 845907 214956 2011-2012 229724 3873445 210583 223397 1103901 233834 2012-2013 244478 4148356 225329 243865 1441535 255521
MAPE (%) - - 4.31 1.40 183.14 1.29
RMSPE (%) - - 5.13 1.61 241.03 1.78
Fig. 4-9 GUI of MATLAB for Taylor approximation method in RaschGSP IRT The graphical user interface starts up when file “T_RGSP.m” is opened, the graphical user interface of the program is displayed on the screen of the computer (as Fig. 4-9). Firstly, the user needs to click the button “Input Data” to input the data. In this study, the input data are the test result of students that are numerical and written in *.xlsx
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file. Secondly, the user need to type the number of Times K, the number of Delta h, and the number of Coefficient H; then clicks the button “OK”, the program will process the data, and then the program will display results. In the panel, the user can click the button
“Save Results” to save the results to *.csv file or *.xlsx file or *.xls file formatted, and can click the button “Save Graphs” to save the graphs to *.JPG file formatted. Finally, if new data is selected, the program will continue, or else if the user clicks the button “Exit”
the program will be ended.
Example 4-3:
There was an examination with a 25-questions Math test for a class including 30 junior high school students in Taichung, Taiwan. The obtained data were tested for reliability with Cronbach’s Alpha reaching 0.879. Firstly, data are calculated by S-P chart. The original data are processed and arranged according to the rule of S-P chart. Secondly, Gamma values for students and Gamma values for problems are calculated based on GRA. Next, data are arranged in order of Gamma values for students and problems with GSP chart. Thirdly, parameters α, β and γ are calculated based on RaschGSP IRT. Next, TAM is used in RaschGSP IRT to obtain the optimal parameters and making the convergent error reduce to the minimum. Finally, conclusions are drawn from the results of TAM in RaschGSP IRT.
Table 4-3
Parameters α, β, γ, and error analysis
α β γ MAPE (%) RMSPE (%)
RaschGSP IRT (Students) 0.0328 -0.1622 -0.9360 7.6185 9.0986 T-RGSP (Students) 0.0266 -12.5661 -1.6952 3.9164 5.1465 RaschGSP IRT (Problems) 0.0305 0.3783 -0.7386 5.8627 6.9916 T-RGSP (Problems) 0.0359 3.9291 -0.6840 5.3839 6.3959
The graphical user interface starts up when file “TAMGP_GRA.m” is opened, the graphical user interface of the program is displayed on the screen of the computer (as Fig. 4-10). Firstly, the user needs to click the button “Input Data” to input the data. In this study, the input data are the academic achievement of students that are numerical
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and written in *.xlsx file. Secondly, the user types the number of Times K, the number of Delta h, and the number of Coefficient H; then clicks the button “OK”, the program will process the data, and then the program will display results. In the panel, the user can click the button “Save TS-GRA” to save the results to *.csv file or
*.xlsx file or *.xls file formatted, and can click the button “Save TAMGP-GRA” to save the results to *.csv file or *.xlsx or *.xls file formatted. Finally, if new data is selected, the program will continue, or else if the user clicks the button “Exit” the program will be ended.
Fig. 4-10 GUI of MATLAB for predicting and evaluating the academic achievement of students
Example 4-4:
The study has performed an experiment to predict and evaluate for the academic achievement of 30 students in Mathematics in Taichung, Taiwan. Data are the academic achievement of students for three years corresponding to six semesters in junior high school (as shown in the Table 4-4). Firstly, the measured data are transformed to T scores. Secondly, GRA is used to calculate Gamma values based on T scores. Thirdly, Taylor approximation method in grey prediction is used to
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calculate parameters and determine predicted values, then error analysis is also performed. Results of error analysis showed that the MAPE are all relatively low and satisfy condition of less than 10%, so the predicted results are accepted. Thirdly, GRA is used to calculate Gamma values based on T scores and the predicted results. Finally, drawing conclusions from the results of the combination of TAMGP and GRA for predicting and evaluating the academic achievement of 30 students in Mathematics.
The results for predicting and evaluating the academic achievement of 30 students based on the combination of TAMGP and GRA are shown in the Fig. 4-10 GUI of MATLAB for predicting and evaluating the academic achievement of students.
Table 4-4
The academic achievement in Mathematics of 30 students in six semesters in junior high school
ID The academic achievement of students
ID The academic achievement of students Sem1 Sem2 Sem3 Sem4 Sem5 Sem6 Sem1 Sem2 Sem3 Sem4 Sem5 Sem6
S1 82 90 90 96 90 97 S16 83 84 84 89 78 91
S2 82 82 81 86 84 90 S17 89 90 86 88 80 93 S3 97 97 95 99 95 97 S18 72 69 66 70 58 69 S4 95 88 91 95 88 96 S19 97 96 93 94 86 96 S5 95 91 93 95 90 96 S20 93 93 91 91 85 94 S6 83 81 82 85 84 92 S21 80 80 74 83 74 83 S7 91 81 79 86 81 88 S22 85 83 80 88 85 91 S8 43 43 48 55 34 40 S23 75 82 76 85 74 82 S9 97 96 92 96 92 98 S24 95 94 93 89 80 87 S10 97 95 88 94 90 96 S25 99 98 95 98 89 95 S11 68 56 45 53 34 46 S26 85 84 75 79 68 77 S12 98 97 98 96 90 94 S27 84 85 79 84 82 89 S13 54 52 49 57 41 50 S28 98 97 95 96 92 95 S14 81 83 84 84 74 83 S29 70 58 60 73 54 63 S15 78 77 70 79 70 80 S30 96 97 91 96 88 93 Note. “Sem” is the abbreviation of semester.
The graphical user interface starts up when file “TAMGP_GRA_ROC.m” is opened, the graphical user interface of the program is displayed on the screen of the
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computer (as Fig. 4-11). Firstly, the user needs to click the button “Input Data” to input the data. In this study, the input data are the academic achievement and test scores of students that are numerical and written in *.csv file. Secondly, the user types the number of Times K, the number of Delta h, and the number of Coefficient H; then clicks the button “OK”, the program will process the data, and then the program will display result and graph. In the panel, the user can click the button “Save Result” to save the result to
*.csv file or *.xlsx file or *.xls file formatted, and can click the button “Save Graph” to save the graphs to *.JPG file formatted. Finally, if new data is selected, the program will continue, or else if the user clicks the button “Exit” the program will be ended.
Fig. 4-11 GUI of MATLAB to set the standard for tests Example 4-5:
The study has performed an experiment to set the standard for the Mathematics test. There were 42 students who participated the mid-term test, they are the third grade of senior high school students in Taichung, Taiwan. Measured data are the academic achievement of students in the previous five semesters and test score (as shown in the Table
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4-5). Firstly, the measured data are transformed to T scores. Secondly, Taylor approximation method in grey prediction is used to calculate parameters and determine predicted values, and error analysis is also performed. Results of error analysis showed that the MAPE are all relatively low and satisfy condition of less than 10%, so the predicted results are accepted.
Thirdly, GRA is used to calculate Gamma values based on T scores and the predicted results.
Finally, ROC analysis and the Youden indexes corresponding to possible cut scores are calculated to pick the optimal cut score. The optimal cut score based on the large Youden index is 70, and the AUC of the test is 0.98 in this example.
Table 4-5
The academic achievement of senior high school students in the previous five semesters and test score
ID Academic achievement Test
score ID Academic achievement Test score Sem1 Sem2 Sem3 Sem4 Sem5 Sem1 Sem2 Sem3 Sem4 Sem5 S1 87 87 81 93 86 94 S22 70 72 75 79 79 70 S2 82 86 76 85 82 88 S23 76 70 63 76 73 89 S3 70 75 74 79 78 65 S24 80 82 83 84 85 87 S4 82 82 81 86 84 90 S25 97 96 92 96 92 98 S5 97 97 95 99 95 97 S26 87 92 82 87 85 94 S6 79 77 65 79 77 86 S27 97 95 88 94 90 96 S7 89 82 76 88 80 91 S28 79 80 74 84 85 83 S8 95 88 91 95 88 96 S29 93 88 82 86 86 95 S9 80 62 76 76 55 54 S30 68 56 45 53 34 46 S10 91 87 78 88 87 92 S31 82 76 67 66 54 62
S11 88 87 90 94 92 96 S32 69 67 62 66 53 67
S12 91 85 80 86 83 92 S33 85 75 63 72 58 69 S13 95 91 93 95 90 96 S34 94 88 89 93 78 91 S14 83 81 82 85 84 92 S35 87 81 83 90 80 94
S15 80 82 76 82 80 71 S36 98 97 98 96 90 94
S16 91 81 79 86 81 88 S37 82 90 90 96 90 97 S17 43 43 48 55 34 40 S38 94 91 86 79 72 77 S18 80 80 72 78 80 67 S39 81 83 84 84 74 83 S19 91 90 83 94 88 94 S40 92 91 87 91 78 92 S20 93 91 81 92 89 92 S41 71 68 62 73 61 62 S21 96 91 92 92 93 96 S42 75 64 58 68 60 66
Note. “Sem” is the abbreviation of semester.
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3.4 Conclusion of Chapter 4
This chapter introduced experimental methods relevant to using Taylor approximation method in grey prediction for prediction problems of uncertainty systems in educational information and measurement. Firstly, this study used Taylor approximation method in grey prediction to predict the number of students and teachers for admission, the number of foreign students studying in Taiwan. Secondly, this study used Taylor approximation method in RaschGSP IRT to improve the accuracy of RaschGSP IRT curves for students and problems. Thirdly, this study used the combination of Taylor approximation method in grey prediction and grey relational analysis to predict and evaluate the academic achievement of students. Fourthly, this study used the combination of Taylor approximation method in grey prediction, grey relational analysis, and receiver operating characteristic to set the standard for tests.
Finally, this study described to develop a MATLAB toolbox based on Taylor approximation method in grey prediction for prediction problems of uncertainty systems in educational information and measurement.
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Chapter 5 Applications of TAMGP
In this chapter, experimental data, research results and discussion are introduced.
Firstly, Taylor approximation method in grey prediction (TAMGP) is applied to educational information and measurement to predict the number of teachers and students for admission, andthe number of foreign students studying in Taiwan. Secondly, Taylor approximation method (TAM) is applied in RaschGSP IRT to determine the slope of RaschGSP IRT curve and the test difficulty. Thirdly, the combination of TAMGP and GRA is applied to predict and evaluate the academic achievement of students. Fourthly, the combination of TAMGP, GRA, and ROC is applied to set the standard of test. Finally, conclusions of this chapter are drawn.
5.1 Applying TAMGP to Educational Information and Measurement
5.1.1 Using TAM in GM(1,1), GVM, and GM(2,1)
Experimental Data
In this study, the experimental data are taken from the website of the Ministry of Education, Taiwan. The data are the number of students from three countries (Vietnam, Japan, and Malaysia) studying in Taiwan from the 2003-2004 academic year to the 2012-2013 academic year (Sheu et al., 2014b). These are three countries with large numbers of students studying in Taiwan in recent years. The data are shown in the Table 5-1.
Results
According to the original data showed that GVM and T-GVM have high predictable power for the number of Vietnam students studying in Taiwan (Data1). Establishing the
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original sequence for Data1:
x
(0)= (438, 503, 671,
, 3282, 3687, 3706). Using the GVM model to calculate parameters a and b, the result obtained a = 0.4805 and b = -1.54E-05; the predicted valuesˆx
(0)= (438, 264, 418,
, 2770, 3375, 3713, 3652); and the predicted error of the GVM model: Q = 9.39E+05, MAPE = 19.0%, RMSPE = 23.7%.Using the T-GVM model to calculate parameters a and b, the result obtained a= -0.5263 and b = -1.83E-05; the predicted values
ˆx
(0)= (438, 296, 487,
, 3288, 3717, 3678, 3190); and the predicted error of the T-GVM model: Q = 8.77E+04, MAPE = 8.4%, RMSPE = 15.9%.Fig. 5-1 The graphs for results and error analysis based on the T-GVM model
Fig. 5-2 The graphs for results and error analysis based on the T-GM(2,1) model
According to the original data showed that GM(2,1) and T-GM(2,1) have high predictable power for the number of Japan students studying in Taiwan (Data2).
Establishing the original sequence for Data2:
x
(0)= (1825, 1879, 2126,
, 2302, 2861,83
3097). Using the GM(2,1) model to calculate parameters a1, a2, and b; the result obtained a1 = -0.6009, a2 = 0.0192, and b = -1.04E+03; the predicted values
ˆx
(0)= (1825, 459, -2302,
, -72817, -130220, -231480, -410100); and the predicted error of the GM(2,1) model: Q = 8.10E+10, MAPE = 1.99E+03%, RMSPE = 3.09E+03%.Using the T-GM(2,1) model to calculate parameters a1, a2, and b, the result obtained a1 = 1.07E+12, a2 = -5.58E+10, and b = 1.85E+15; the predicted values
ˆx
(0)= (1825, 1879, 1980,
, 2573, 2711, 2857, 3011); and the predicted error of the T-GM(2,1) model: Q = 3.03E+05, MAPE = 6.1%, RMSPE = 7.4%.Fig. 5-3 The graphs for results and error analysis based on the T-GM(1,1) model
According to the original data showed that GM(1,1) and T-GM(1,1) have high predictable power for the number of Malaysia students studying in Taiwan (Data3).
Establishing the original sequence for Data3:
x
(0)= (194, 332, 425,
, 1961, 2286, 2722). Using the GM(1,1) model to calculate parameters a and b, the result obtained a = -0.2375 and b = 349.5198; the predicted valuesˆx
(0)= (194, 447, 566,
, 1856, 2354, 2985, 3785); and the predicted error of the GM(1,1) model: Q = 1.54E+05, MAPE = 11.9%, RMSPE = 16.6%.Using the T-GM(1,1) model to calculate parameters a and b, the result obtained a= -0.2362 and b = 336.2659; the predicted values
ˆx
(0)= (194, 431, 546,
, 1779, 2253, 2853, 3613); and the predicted error of the T-GM(1,1) model: Q = 1.12E+05, MAPE =84
9.8% , RMSPE = 14.3%.
The prediction results and the accuracy comparison of the prediction models from the experimental data are described as follows:
Table 5-1
The prediction results and the accuracy of three prediction models
Unit: Person Year Measured Data T-GVM T-GM(2,1) T-GM(1,1)
Vietnam Japan Malaysia Vietnam Japan Malaysia
2003-2004 438 1825 194 438 1825 194
2004-2005 503 1879 332 296 1879 431
2005-2006 671 2126 425 487 1980 546
2006-2007 836 2188 671 786 2087 691
2007-2008 1276 2297 872 1233 2199 876 2008-2009 1779 2182 1001 1847 2317 1109 2009-2010 2592 2142 1560 2584 2442 1404 2010-2011 3282 2302 1961 3288 2573 1779 2011-2012 3687 2861 2286 3717 2711 2253 2012-2013 3706 3097 2722 3678 2857 2853
2013-2014 - - - 3190 3011 3613
a (a1) - - - -0.5263 1.07E+12 -0.2362
a2 - - - - -5.58E+10 -
b - - - -1.83E-05 1.85E+15 336.2659
Q - - - 8.77E+04 3.03E+05 1.12E+05
MAPE(%) - - - 8.40 6.07 9.81
RMSPE(%) - - - 15.87 7.39 14.27
Discussion
The experimental results showed that the accuracy of three prediction models T-GM(1,1), T-GVM, and T-GM(2,1) were better than three original models GM(1,1), GVM, and GM(2,1), respectively. In addition, the experimental results indicated that the MATLAB toolbox can help to process data quickly, accurately, which can display the results and the graphs on the graphical user interface to predict the number of foreign students studying in Taiwan. The predicted result of the number of Vietnamese students studying in Taiwan for 2013-2014 academic year was 3190 persons, the number of Japanese students studying in Taiwan for 2013-2014
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academic year was 3011 persons, and the number of Malaysian students studying in Taiwan for 2013-2014 academic year was 3613 persons. The MAPE values of three prediction models (T-GM(1,1), T-GVM, T-GM(2,1)) were less than 10%. The results not only can conduce to serve as a reference for the educational administrators in Taiwan, but also can assist the government in developing future policies regarding educational management. The predicted data were required reliable and high accuracy to contribute to the success in the educational development of the country in the future.
5.1.2 Using TAM in GM(1,1) and GM(1,n)
Experimental Data
In this study, the experimental data are taken from the website of the Ministry of Education and Training of Vietnam. The data are the number of teachers and students at all preschools, primary schools, lower secondary schools, and upper secondary schools from the 2003-2004 to the 2012-2013 academic year in Vietnam, respectively (Nguyen et al., 2014b). The data are shown in the Table 5-2.
Table 5-2
The number of teachers and students for admission
Unit: Person Year Preschool Primary Lower Secondary Upper Secondary
T S T S T S T S
2003-2004 150335 2588837 362627 8350191 280943 6612099 98714 2616207 2004-2005 155699 2754094 360624 7773484 295056 6670714 106586 2802101 2005-2006 160172 3024662 353608 7321739 306067 6458518 118327 2976872 2006-2007 163809 3147252 344521 7041312 310620 6218457 125460 3111280 2007-2008 172978 3195731 344853 6871795 312759 5858484 134246 3070023 2008-2009 183443 3305391 347840 6745016 313911 5515123 142432 2951889 2009-2010 195852 3409823 347840 6922624 313911 5214045 142432 2886090 2010-2011 211225 3599663 359039 7048493 312710 4968302 146789 2835025 2011-2012 229724 3873445 366045 7100950 311970 4926401 150133 2755210 2012-2013 244478 4148356 381432 7202767 315405 4869839 150915 2675320 Note. “T” is the number of teachers; “S” is the number of students.
(Data from the website of Ministry of Education and Training (Vietnam) http://www.moet.gov.vn)
Results
Before using T-GM(1,1) and T-GM(1,n) to predict the number of teachers and students
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for admission in Vietnam, the data are tested based on Eq. (2-1). In this case m = 10, class ratio obtained (0)(k)[0.83,1.20]. The results of testing data showed that the data consistent with two prediction models (Results of testing data are shown in the Table 5-3).
Table 5-3
Results of testing data
Preschool Teachers (0)(k) 0.97 0.97 0.98 0.95 0.94 0.94 0.93 0.92 0.94 Students (0)(k) 0.94 0.91 0.96 0.98 0.97 0.97 0.95 0.93 0.93 Primary Teachers (0)(k) 1.01 1.02 1.03 1.00 0.99 1.00 0.97 0.98 0.96 Students (0)(k) 1.07 1.06 1.04 1.02 1.02 0.97 0.98 0.99 0.99 Lower
Secondary
Teachers (0)(k) 0.95 0.96 0.99 0.99 1.00 1.00 1.00 1.00 0.99 Students (0)(k) 0.99 1.03 1.04 1.06 1.06 1.06 1.05 1.01 1.01 Upper
Secondary
Teachers (0)(k) 0.93 0.90 0.94 0.93 0.94 1.00 0.97 0.98 0.99 Students (0)(k) 0.93 0.94 0.96 1.01 1.04 1.02 1.02 1.03 1.03
Table 5-4
The predicted results and the accuracy of the T-GM(1,1) model
Unit: Person Year Preschool Primary Lower Secondary Upper Secondary
T S T S T S T S
2003-2004 150335 2588837 362627 8350191 280943 6612099 98714 2616207 2004-2005 147618 2793914 345881 7313716 303412 6692077 115262 3021324 2005-2006 156906 2925826 348417 7263028 305104 6399295 119820 2989212 2006-2007 166779 3063965 350971 7212691 306805 6119321 124558 2957441 2007-2008 177272 3208627 353544 7162703 308516 5851597 129483 2926007 2008-2009 188426 3360119 356135 7113061 310236 5595586 134602 2894908 2009-2010 200282 3518763 358746 7063763 311966 5350775 139925 2864139 2010-2011 212884 3684897 361376 7014807 313705 5116675 145457 2833697 2011-2012 226279 3858876 364025 6966190 315454 4892817 151209 2803579 2012-2013 240516 4041068 366694 6917910 317213 4678753 157188 2773781 2013-2014 255650 4231863 369382 6869965 318982 4474055 163403 2744300 2014-2015 271735 4431665 372090 6822352 320761 4278312 169864 2715132 MAPE(%) 2.04 1.79 2.05 2.72 0.95 1.46 2.67 2.60 Note. “T” is the number of teachers; “S” is the number of students.
The prediction results and the accuracy of the T-GM(1,1) model are shown in the Table
The prediction results and the accuracy of the T-GM(1,1) model are shown in the Table