please see attached my regression models i need help with the interpreting quest

Question

please see attached my regression models i need help with the interpreting questions below

(a) 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.

(b) 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 exam performance.

Explanation / Answer

(a)

Based on the regression output obtained in Step 4.

The overall Model is not adequate. We have adjusted R square=0.060024291 and R square is also around 6%. It means variation explained by independent variables (Gender, Citizenship etc.) in dependent variable (Examination performanece) is only 6%. Thus there will are missing 94% variation causing factors, thus it is difficult to use this model for prediction.

Now comming to the part of statistical significance of the coefficients of the model. We have p-value for variable gender statististically not significant (0.072332>0.05) at 0.05 level of significance. Thus Examination performance in Males and Females does not differ significantly, keeping other variables role contant.

The variable Degree type plays a significant role in examination performance of the students. The P-value in case of Degree type variable is less than 0.05.

Now comming to the part of Citizenship of students.

We have three type of citizenships in the model.

1. Australian

2. East Asian

3. Others.

In the Model, the Others (Citizenship) has been considard as reference category. Australian citizenship plays statistically significant role as compared to other citizenship in examination performance, as p-value is 0.0329<0.05. It means a student having Australian citizenship differes in examination performance as compared to Other citizenship. But East Asian citizenship doesnot play a significant role in comparison with Other citizenship in examination performance, because p-value in case of East Asian citizenship is greater than 0.05 (0.12>0.05). Thus there is no difference in examination performance of East Asian citizenship and Others citizenship.

(b)

When we have only Gender variable in the regression model. It plays a significant role. In step 1, we can see the p-value of Gender variable is <0.05 (Level of significance). It means, male and female students examination performance differs.

But, as we add degree type variable in the model (Second step), the Gender variable becomes not significant. This is because of lot of variation in degree type varaible which adjusts both the genders (males and females) at equal examination performance. The variation in degree type variable is evident from its highly significant p-value (which is <0.01).

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