Enkh-amgalan

1. The Study of the Relationship among
Academic Performance, Family Income
and Student`s Distance from Home to
Campus
Speakers: B. Enkh-Amgalan, Mongolia
B. Javzandulam, Mongolia
Ning Ye Zi Peng, China
July 6, 2018

2. Contents
•Hypothesis
•Literature review
•Dataset
•Methods
•Result
•Conclusion

3. Hypothesis
Students live nearby the school and
who have more family income
intends to get higher marks on
course.

4. Dataset
We used data collected from New Mongol Institute of
Technology.
Description
Final grade GPA of 31 first year students in
2017
Distance Collected using google street map
Family income Taken from questionnaire when
they enrolled

5. Outcome variable
Graded point average GPA.
Independent variables
Distance. measure capturing the distance, in km,
between a student’s permanent residence and her
or his institution.
Family income. Our income measure
distinguishes between students who are low,
medium, or high-income dependent students.

6. Methods
We have only one year of cross sectional data, so
using the LINEAR REGRESSION technique to
evaluate the hypothesis of this paper is the most
appropriate methodology.
The regression equation as:
k=2

7. We want to choose the estimates
of a and b so as to minimize the sum of
squared errors of prediction.

8. Equations for calculation regression
equation

9. Results
№ First Name Letter Grade DISTANCE Family income
Y X1 X2 X1*Y X2*Y X1*X2
1 Түмэн-Үйлс 4.5 6.7 2.0 30.2 9.0 13.4
2 Хонгорзул 4.5 0.75 2.0 3.4 9.1 1.5
3 Анударь 5.0 18.3 3.0 91.5 15.0 54.9
4 Энхсайхан 1.1 6.3 3.0 6.9 3.3 18.9
5 Тамир 4.9 4.5 3.0 22.1 14.8 13.5
6 Нандин- 2.9 1.3 2.0 3.8 5.8 2.6
7 Басбаатар 4.8 1.2 2.0 5.8 9.7 2.4
8 Заяа 4.7 0.6 2.0 2.8 9.4 1.2
9 Золбадрах 4.7 1.1 3.0 5.1 14.0 3.3
10 Баасанцэрэн 5.0 18 2.0 89.6 10.0 36.0
11 Цэрэннямаа 1.8 11.2 2.0 19.9 3.6 22.4
12 Ариунзаяа 4.1 8.8 1.0 35.9 4.1 8.8
13 Сугармаа 5.0 0.3 2.0 1.5 10.0 0.6
14 Мөнх-Эрдэнэ 4.6 7.4 1.0 33.7 4.6 7.4
15 Уянга 5.0 0.7 2.0 3.5 10.0 1.4
16 Уранбилэг 5.0 0.5 2.0 2.5 10.0 1.0
17 Сүндэръяа 4.3 3.8 2.0 16.4 8.7 7.6
18 Соёлмаа 5.0 2.9 3.0 14.4 14.9 8.7
19 Билгүүн 2.0 6 3.0 12.3 6.1 18.0
20 Номуун 4.8 6.4 2.0 30.7 9.6 12.8
21 Хантөгөлдөр 4.7 1.6 1.0 7.6 4.7 1.6
22 Дөлгөөн 4.4 10 1.0 44.1 4.4 10.0
23 Болортуяа 4.8 1.9 1.0 9.1 4.8 1.9
30 Юндэндорж 4.1 4.8 2.0 19.8 8.3 9.6
31 Бямбажав 3.0 6.7 2.0 19.9 6.0 13.4
Y X1 X2 X1*Y X2*Y X1*X2
130.1 157.1 62.0 636.2 254.5 320.9 Sum
31.0 31.0 31.0 31.0 31.0 31.0 Number of attribute
4.2 5.1 2.0 20.5 8.2 10.4 Mean value
1.4 0.9 0.7 5.3 3.9 2.2 Std Deviation
576.0 151.0 138.0 USS

10. We can collect the data into a matrix like this:
y X1 X2
Y 576.0 -22.8 -5.6
X1 151.0 6.8
X2 138.0
Y`=4.06-0.15X1+0.03X2
Therefore, our regression equation is:
Y`=4.06-0.15*distance+0.03*income

11. Visual Representations of the
Regression
0
1
2
3
4
5
6
1 2 3 4 5
Actual GPA vs Predicted GPA

12. R-square (R2)
№ First Name Letter DISTA Family Predicted
Y X1 X2 Y`
1 Түмэн-Үйлс 4.5 6.7 2.0 3.0 1.5
2 Хонгорзул 4.5 0.75 2.0 3.9 0.6
3 Анударь 5.0 18.3 3.0 1.2 3.8
4 Энхсайхан 1.1 6.3 3.0 3.0 -1.9
Resid
30 Юндэндорж 4.1 4.8 2.0 3.3 0.9
31 Бямбажав 3.0 6.7 2.0 3.0 0.0
Y X1 X2 Y` Residual error
Mean 4.20 5.07 2.00 3.24 0.96
Variance 1.00 20.20 0.50 0.50 1.26
USS 577.93 339.61 67.46

13. Testing the Significance of R2
error
Mean 4.20 5.07 2.00 3.24 0.96 0.96 0.77
Variance 1.00 20.20 0.50 0.50 1.26 0.50 0.50
USS 577.93 339.61 67.46
error Rsquared F
7 2.00 3.24 0.96 0.96 0.77 0.88 101.46
0 0.50 0.50 1.26 0.50 0.50 0.71 33.80
339.61 67.46
error Rsquared F
4.20 5.07 2.00 3.24 0.96 0.96 0.77 0.88
1.00 20.20 0.50 0.50 1.26 0.50 0.50 0.71
577.93 339.61 67.46

14. Relationship of GPA, Family Income and Student`s
Distance

15. Conclusion
•Family income has positive influence on
GPA
•Distance has negative influence on GPA

16. Thanks for your kind
considerations!!!