You plan to develop regression models to investigate the factors that influence

Question

You plan to develop regression models to investigate the factors that influence students’ final mark performance. However, you are not sure how to handle the country of citizenship variable. After further discussion and based on international standardised tests, you and your project officer believe that East Asian students tend to have stronger maths background, and decide to create three categories: Australian, East Asian and others, to re-code this variable.

You also agree that East Asian students should include those from China, Japan, Korea, Taiwan and South East Asian countries, and that students from New Zealand are not classified as Australian. You conduct a stepwise regression according to the following procedure:

LINK TO DATA: https://drive.google.com/open?id=0ByzEe_CmXUf1Q2ZTLVhHTThuQzg

Step 1: Gender only

Step 2: Gender and Degree Type

Step 3: Gender, Degree Type and Country of Citizenship

Step 4: Gender, Degree Type, Country of Citizenship and Lecture Attendance

(a) Present the regression output for each of the four steps. (4 marks)

(b) Based on the regression output obtained in Step 4, answer the following questions:

• Comment on the overall adequacy of the model.

• For each of the four independent variables, interpret the regression coefficients and comment on their statistical significance. (5 marks)

(c) Describe the changes to the regression coefficient of Gender and its statistical significance when Degree Type is added to the model in Step 2. Considering also the result in Question 2 in Task 1, discuss if there is any gender difference in test performance. (3 marks)

LINK TO DATA: https://drive.google.com/open?id=0ByzEe_CmXUf1Q2ZTLVhHTThuQzg

Explanation / Answer

a) already done in excel file

b)

R^2 = 0.117 , which is very low , hence this model is not adequate

if p-value < 0.05

then the variable is significant , here Gender and Country (Australia=1) is not significant

Degree type (Single=1) , Country (East Asia=1) and Lecture Attendance is significant

the coefficients (b) can interpreted as if we change one variable by one unit while other variables remains constant, then dependent variable (y) change by b units

for example

if Lecture attendance increase by 1 unit then y increases by 0.7154751327 units

c)

when Gender was only independent variable , then p-value = 0.03957 < 0.05 , hence it was significant

but when Degree type is added , p-value of Gender become 0.11694 > 0.05 , hence insignificant

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