CHAPTER 4: EMPIRICAL RESULTS AND DISCUSSIONS OF QUANTITATIVE ANALYSIS
4.3. Logistic regression analysis
127
Table 4-24: Student Performance in Accounting 101 (Binomial Logistic Regression), FMS, CLMS, 2004 (Dependent Variable is Student’s Final Examination Pass/Fail Marks in Accounting 101)
Predictor variables Coefficients Stand. Error Z-value
Total matric points Equal or Above 36 0.51* 0.30 1.75
HG D in matric English I 0.51* 0.29 1.86
HG D in matric Maths 0.47* 0.26 1.75
HG D in matric Accounting 0.82** 0.40 2.05
Age -0.03** 0.02 -1.94
English as home first language 1.12* 0.70 1.61
English as home first language by matric Accounting Scores
-1.20* 0.75 -1.61
Constant 2.57 0.64 4.03
Log likelihood = - 271.91 Number of obs = 1651 Prob > chi2 = 0.0186
LR Chi-square statistic (7) = 16.83 Pseudo R2 = 3%
Source: Estimation
*Significant at 10 percent alpha level;
** Significant at 5 percent alpha level;
*** Significant at 1 percent alpha level.
Holding all other variables at certain value, the odds of getting a final examination pass mark in ACCT101 for a one-unit increase in HG symbol D in matric Accounting is exp(0.82) = 2.27. So in terms of percent change, holding all other variables at certain value, we will see 127 percent increase in the odds of getting a final examination pass mark for a one-unit increase in HG symbol D in matric Accounting. Holding all other variables at certain value, the odds of getting a final examination pass mark in ACCT101 for a one- unit increase in the age of the student is exp(0.03) = 1.03. So in terms of percent change, holding all other variables at certain value, we will see 3 percent decrease in the odds of getting a final examination pass mark for a one-unit increase in the age of the student. Holding all other variables at certain value, the odds of getting a final examination pass mark in ACCT101 for a one-unit increase in English as home first language is exp(1.12) = 3.06. So in terms of percent change, holding all other variables at certain value, we will see 206 percent increase in the odds of getting a final examination pass mark for a one-unit increase in English as home first language. Holding all other variables at certain value, the odds of getting a final
128 examination pass mark in ACCT101 for a one-unit increase in the interaction variable English as home first language by matric Accounting scores is exp(1.20) = 3.32. So in terms of percent change, holding all other variables at certain value, a 232 percent decrease in the odds of getting a final examination pass mark will be seen for a one-unit increase in the interaction variable English as home first language by matric Accounting.
Table 4-25: Student Performance in Accounting 101 (Binomial Logistic Regression), FMS, CLMS, 2008 (Dependent Variable is Student’s Final Examination Pass/Fail Marks in Accounting 101)
Predictor variables Coefficients Stand. Error Z-value
Total matric points Equal or Above 36 1.85** 0.59 1.93
HG D in matric Maths 1.56 0.79 0.87
Matric Maths 0.90 0.09 -1.11
ECON101 6.19*** 1.64 6.89
English as home first language 0.95 0.26 -0.18
Log likelihood = - 239.63 Number of obs = 1006 Prob > chi2 = 0.0000
LR Chi-square statistic (7) = 59.46 Pseudo R2 = 11%
Source: Estimation
*Significant at 10 percent alpha level;
** Significant at 5 percent alpha level;
*** Significant at 1 percent alpha level.
For the 2008 academic year, holding all other variables at certain value, the odds of getting a final examination pass mark in ACCT101 for a one-unit increase in ECON101 is exp(1.85) = 6.36. More explicitly in terms of percent change, holding all other variables at certain value, we will see a 536 percent increase in the odds of getting a final examination pass mark for a one-unit increase in ECON101. Holding all other variables at certain value, the odds of getting a final examination pass mark in ACCT101 for a one- unit increase in total matric points (or APS) equals or above 36 is exp(6.18) = 482.68. More explicitly in terms of percent change, holding all other variables at certain value, we will see a 48,168 percent increase in the odds of getting a final examination pass mark for a one-unit increase in total matric points equals or above 36.
129 A perusal of the results presented in Tables 4-26 and 4-27 reveals that in the 2004 academic year, the odds ratio in favour of getting a final examination pass mark in ACCT102 is exp(0.08) = 1.08 for a one-unit increase in total matric points (or APS), holding all other variables at certain value. More explicitly in terms of percent change, the coefficient for total matric points says that, holding all other variables at certain value, we will see 8 percent increase in the odds ratio of getting a final examination pass mark in ACCT102 for a one-unit increase in total matric points.
Table 4-26: Student Performance in Accounting 102 (Binomial Logistic Regression), FMS, CLMS, 2004 (Dependent Variable is Student’s Final Examination Pass/Fail Marks in Accounting 102)
Predictor variables Coefficients Stand. Error Z-value
Total matric points
0.08*** 0.04 2.37
Matric Maths scores -0.22** 0.11 -2.03
English as home first language -0.84** 0.42 -2.00
Age 0.08** 0.04 2.14
Gender -0.09 0.38 -0.25
ISTN 101 -0.00 0.02 -0.18
Constant -0.37 2.12 -0.17
Log likelihood = - 110.80958 Number of obs = 514
Prob > chi2 = 0.0502
LR Chi-square statistic (6) = 12.58 Pseudo R2 = 5.37%
Source: Estimation
* Significant at 10 percent alpha level;
** Significant at 5 percent alpha level;
*** Significant at 1 percent alpha level.
To get a final examination pass mark in ACCT102, the odds ratio is exp(0.22) = 1.25 for a one-unit increase in matric Maths score, holding all other variables at certain value. More explicitly in terms of percent change, the coefficient for matric Maths scores says that, holding all other variables at certain value, we will see 25 percent decrease in the odds ratio of getting a final examination pass mark in ACCT102 for a one- unit increase in matric Maths score. To get a final examination pass mark in ACCT102, the odds ratio is exp(0.84) = 2.32 for a one-unit increase in English as home first language, holding all other variables at certain value. In terms of percent change, the coefficient for English as home first language says that,
130 holding all other variables at certain value, we will see 132 percent decrease in the odds ratio of getting a final examination pass mark in ACCT102 for a one-unit increase in English as home first language.
Table 4-27: Student Performance in Accounting 102 (Binomial Logistic Regression), FMS, CLMS, 2008 (Dependent Variable is Student’s Final Examination Pass/Fail Marks in Accounting 102)
Predictor variables Coefficients Stand. Error Z-value
ACCT101 1.16*** 0.04 4.99
HG D in matric Maths 0.17*** 0.16 -2.29
Matric English I 1.27*** 0.13 2.24
Age 0.97 0.02 -0.94
Race 1.98 1.32 1.02
ECON 101 1.31 0.56 0.64
Log likelihood = - 86.895642 Number of obs = 513
Prob > chi2 = 0.0000
LR Chi-square statistic (6) = 54.76 Pseudo R2 = 24%
Source: Estimation
* Significant at 10 percent alpha level;
** Significant at 5 percent alpha level;
*** Significant at 1 percent alpha level.
To get a final examination pass mark in ACCT102, the odds ratio is exp(0.08) = 1.08 for a one-unit increase in the age of the student, holding all other variables at certain value. In terms of percent change, the coefficient for the age of the student indicates that, holding all other variables at certain value, we will see 8 percent increase in the odds ratio of getting a final examination pass mark in ACCT102 for a one-unit increase in the age of the student. None of the first-year module final examination marks was statistically significant to explain academic performance of students in ACCT101 and ACCT102.
For the 2008 academic year, holding all other variables at certain value, the odds of getting a final examination pass mark in ACCT102 for a one-unit increase in ACCT101 is exp(1.16) = 3.19. So in terms of percent change, holding all other variables at certain value, we will see 219 percent increase in the odds of getting a final examination pass mark for a one-unit increase in ACCT101. Holding all other variables at
131 certain value, the odds of getting a final examination pass mark in ACCT102 for a one-unit increase in Matric English I is exp(1.27) = 3.56. In terms of percent change, holding all other variables at certain value, we will see 256 percent increase in the odds of getting a final examination pass mark for a one-unit increase in Matric English I. Holding all other variables at certain value, the odds of getting a final examination pass mark in ACCT102 for a one-unit increase in the race of the student (white students = 1) is exp(1.98) = 7.24. So in terms of percent change, holding all other variables at certain value, we will see 624 percent increase in the odds of getting a final examination pass mark for a one-unit increase in the number of white students. Holding all other variables at certain value, the odds of getting a final examination pass mark in ACCT102 for a one-unit increase in the age of the student is exp(0.98) = 2.66. In terms of percent change, holding all other variables at certain value, we will see 166 percent increase in the odds of getting a final examination pass mark for a one-unit increase in the age of the student.
A perusal of results presented in Tables 4-28 and 4-29 indicate that in the 2004 academic year, holding all other variables at certain value, we will see 54 percent decrease in the odds ratio of getting a final examination pass mark in ECON101 for a one-unit increase in the HG symbol D in matric Maths score since exp(0.43) = 1.54. Holding all other variables at certain value, we will see 40 percent increase in the odds ratio of getting a final examination pass mark in ECON101 for a one-unit increase in the HG symbol D in matric Business Economics score since exp(0.34) = 1.40. Holding all other variables at certain value, we will see 3 percent increase in the odds ratio of getting a final examination pass mark in ECON101 for a one-unit increase in the age of the student since exp(0.03) = 1.03. Holding all other variables at certain value, we will see 256 percent increase in the odds ratio of getting a final examination pass mark in ECON101 for a one-unit increase in the quantitative method module MATHS134 since exp(1.27) = 3.56.
Although some of the other variables had coefficients with the expected signs, none proved to be significant at the 1, 5, or 10 percent level.
132
Table 4-28: Student Performance in Economics 101 (Binomial Logistic Regression), FMS, CLMS, 2004 (Dependent Variable is Student’s Final Examination Pass/Fail Marks in Economics 101)
Predictor variables Coefficients Stand. Error Z-value
Total matric points equal or above 36 -0.11 0.13 -0.86
HG D in matric Maths -0.43*** 0.16 -2.73
HG D in matric economics -0.04 0.41 -0.10
HG D in matric English I -0.04 0.15 -0.28
HG D in matric business economics 0.34* 0.21 1.63
Non-black with matric Maths scores 0.22 0.33 0.68
Age 0.03*** 0.01 4.09
Gender -0.17 0.12 -1.44
English as home first language -0.61 0.69 -0.88
English as home first language with matric Economics scores
0.34 0.68 0.50
English as home first language with matric Maths scores
0.54 0.39 0.21
ISTN 101 0.41 0.20 1.39
MATHS134 1.27* 0.79 1.61
Constant -1.09 0.97 -1.13
Log likelihood = - 874.392 Number of obs = 1651
Prob > chi2= 0.0004
LR Chi-square statistic (13) = 37.37 Pseudo R2 = 2.1%
Source: Estimation
*Significant at 10 percent alpha level;
** Significant at 5 percent alpha level;
*** Significant at 1 percent alpha level.
133 For the 2008 academic year, holding all other variables at certain value, we will see 95 percent increase in the odds ratio of getting a final examination pass mark in ECON101 for a one-unit increase in the race of the student (White students = 1) since exp(0.67) = 1.95. Holding all other variables at certain value, we will see 5412 percent increase in the odds ratio of getting a final examination pass mark in ECON101 for a one- unit increase in ACCT101 since exp(4.01) = 55.12.
Table 4-29: Student Performance in Economics 101 (Binomial Logistic Regression), FMS, CLMS, 2008 (Dependent Variable is Student’s Final Examination Pass/Fail Marks in Economics 101)
Predictor variables Coefficients Stand. Error Z-value
Total matric points 0.99 0.01 -0.34
ACCT101 4.02*** 1.19 4.70
Matric English I 1.02 0.03 0.65
English as home first language 1.16 0.22 0.81
Race 0.67* 0.16 -1.74
Log likelihood = - 438.5311 Number of obs = 716
Prob > chi2= 0.0001
LR Chi-square statistic (13) = 26.37 Pseudo R2 = 3%
Source: Estimation
*Significant at 10 percent alpha level;
** Significant at 5 percent alpha level;
*** Significant at 1 percent alpha level.
A perusal of results presented in Tables 4-30 and 4-31 indicate that in the 2004 academic year, holding the age and race of the student, non-black by matric Maths scores, and English as home first language at certain value, we will see a marginal one percent increase in the odds ratio of getting a final examination pass mark in ECON102 for a one-unit increase in ECON101 since exp(0.01) = 1.01. Holding ECON101, age of the student, non-black by matric Maths scores, and English as home first language at certain value, we will see 200 percent increase in the odds ratio of getting a final examination pass mark in ECON102 for a one-unit increase in the race of the student (white=1) since exp(1.10) = 3.00. Holding all other variables at certain value, we will see 2 percent increase in the odds ratio of getting a final examination pass mark in ECON102 for a one-unit increase in the age of the student since exp(0.02) = 1.02.
134
Table 4-30: Student Performance in Economics 102 (Binomial Logistic Regression), FMS, CLMS, 2004 (Dependent Variable is Student’s Final Examination Pass/Fail Marks in Economics 102)
Predictor variables Coefficients Stand. Error Z-value
ECON101 0.01* 0.01 1.92
Race 1.10*** 0.37 2.95
Age 0.02** 0.01 2.18
Non-black by matric Maths scores -0.44** 0.23 -1.93
English as home first language -0.97*** 0.34 -2.87
Constant 0.43 0.37 1.14
Log likelihood = - 673.43 Number of obs = 1436 Prob > chi2= 0.0003
LR Chi-square statistic (5) = 23.58 Pseudo R2 = 2%
Source: Estimation
*Significant at 10 percent alpha level;
** Significant at 5 percent alpha level;
*** Significant at 1 percent alpha level.
Holding all other variables at certain value, we will see 55 percent decrease in the odds ratio of getting a final examination pass mark in ECON102 for a one-unit increase in the interaction variable non-black students by matric Maths since exp(0.44) = 1.55. Holding ECON101, age and race of the student, and non- black by matric Maths scores at certain value, we will see 164 percent decrease in the odds ratio of getting a final examination pass mark in ECON102 for a one-unit increase in English as home first language since exp(0.97) = 2.64.
Table 4-31: Student Performance in Economics 102 (Binomial Logistic Regression), FMS, CLMS, 2008 (Dependent Variable is Student’s Final Examination Pass/Fail Marks in Economics 102)
Predictor variables Coefficients Stand. Error Z-value
ECON101 1.15*** 0.01 11.66
ACCT102 1.06*** 0.01 4.96
HG D in matric English I 0.69* 0.15 -1.64
Race 1.38 0.41 1.10
English as home first language 0.63** 0.14 -2.96
Log likelihood = - 319.2593 Number of obs = 905
Prob > chi2= 0.0000
LR Chi-square statistic (5) = 432.07 Pseudo R2 = 40.36%
Source: Estimation
*Significant at 10 percent alpha level;
** Significant at 5 percent alpha level;
*** Significant at 1 percent alpha level.
135 For the 2008 academic year, holding all other variables at certain value, we will see 216 percent increase in the odds ratio of getting a final examination pass mark in ECON102 for a one-unit increase in ECON101 since exp(1.15) = 3.16. Holding all other variables at certain value, we will see 101 percent increase in the odds ratio of getting a final examination pass mark in ECON102 for a one-unit increase in the HG in Matric English since exp(0.70) = 2.01. Holding all other variables at certain value, we will see 90 percent increase in the odds ratio of getting a final examination pass mark in ECON102 for a one-unit increase in English as home first language since exp(0.64) = 1.90. Holding all other variables at certain value, we will see 189 percent increase in the odds ratio of getting a final examination pass mark in ECON102 for a one-unit increase in ACCT102 since exp(1.06) = 2.89.