Q.2 Regression

A researcher believes that exam grades are a function of time spent studying, hours of sleep and attendance rate. To investigate this, she takes a sample of 30 students and collects the following data:

X1 = Total time spent studying for a particular exam (in hours)

X2 = Total hours of sleep the week before the exam

X3 = The student's attendance rate over the session (in percentage)

The researcher also collects the exam results (in percentage) of the 30 students of the exam and generates regression analysis output, partially shown below:

ANOVA
	df	SS	MS	F
Regression	3	6442	2147.3	25.274
Residual	26	2209	84.96
Total	29	8651
R Square	0.745
	Coefficients	Standard Error	t Stat
Intercept	8.342	3.734	2.234
Study	1.991	0.498	3.998
Sleep	-0.031	0.211	-0.015
Attendance	0.189	0.078	2.423

Answer the following questions based on the provided information.

a) Complete the following multiple regression equation (2 marks):

Estimated Y =

b) Interpret the meaning of the coefficient of determination (4 marks)

c) Interpret the meaning of the slope coefficients for Study and Sleep (4 marks).

d) Write down another potential independent variable that could be included in the analysis (2 mark).

e) Predict the results for a student who studied for 19 hours, got 55 hours of sleep and attended class 85% of the time. (2 marks)

f) Is the overall model significant at the 5% level of significance. What does this finding mean? (no need to show the hypothesis testing steps, only provide the interpretation required) (4 marks)

g) which regression coefficients are significant at the 5% level of significance. What does this finding mean? (no need to show the hypothesis testing steps, only provide the interpretation required) (4 marks)