Consider the second OLS results for a Lgpa model in which international student, ATAR, Exam night study time, study time, exam night study time squared and a constant.
Number of jobs = 924
F (6, 924) = 81.21
Prob > F = 0.000
R squared = 0.2103
Adjusted R squared = 0.2088
Lgpa Coefficient / standard error = t p-value
International student 0.165 / 0.035 = 4.71 0.000
ATAR 0.072 / 0.072 = 6.00 0.000
Exam night time study 0.014 / 0.014 = 2.80 0.024
Study time 0.413 / 0.413 = 3.30 0.018
Exam night time study2 -0.012 / -0.012 = -12.0 0.000
Constant 0.120 / 0.120 = 0.96 0.254
a) Write the mathematical model.
Lgpa = + B1 International student + B2 ATAR + B3 Exam night time study + B4 Study time + B5 Exam night time study2 + error t
b) What might be the theoretical reasons for including the squared terms in tenure and experience?
The squared terms are to make them have two curves (non-linear functional form), to include both the positive and negative curve. For example, a curved graph line with Lgpa of the Y axis and night time study on the X axis, that represents the diminishing marginal return to scale. Where the non-linear impact on lgpa has a negative coefficient. From the change in relationship, the data can tell us that the more night study someone does can have an negative impact on grades after a certain point, as the student would be tired.
c) Carefully interpret the estimated coefficient on the international student dummy. Do you reject the null hypothesis that the true parameter on international student is equal to zero?
The international student coefficient is a qualitative variable, meaning it is relative – binary. First, the significance level is 1%, second the sign is positive and third international students earn 16% more, reject as of P-value.
d) How strong is the evidence that night time study has nonlinear effects on Lgpa? Show a graph of the implied relationship between night time study and Lgpa.
Night time study is squared to capture the non-linear effects on Lgpa. The graph would have Lgpa on the Y axis and night time study on the X axis, showing a convex curve.
e) Consider a starts studying on the exam night. By the end of the first hour, how much will the expected GPA have grown? Carefully explain your calculations.
As it is near the start of the curve, each hour study would plus the corresponding coefficient number: 0.014 to the GPA.
f) Interpret F-test results.
The F-test represents the overall validity of the model.
H0: B1 = B2 = B3 = B4 = B5 = 0
H1: At least one coefficient is unequal to zero.
As we reject the null hypothesis of f-test, at least one of the variables (coefficients) is statistically significant, so the model has statistical validity.