Question 6 (7 marks)

Department of Education was analysing the average mathematics test score in the schools in Victoria. It noticed that there were dramatic differences in scores among the schools. In the attempt to improve the scores of all the schools, department attempted to determine the factors that account for the differences. Accordingly, they took a random sample of 40 schools across the state and for each determined the mean test score last year, the percentage of teachers in the schools who have at least one university degree in mathematics, the mean age and the mean annual income of the mathematics teachers.

The following is regression output from Excel.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.597512
R Square	0.357021
Adjusted R Square	0.303439
Standard Error	7.724526
Observations	40
ANOVA
	df	SS	MS	F	Significance F
Regression	3	1192.732	397.5774	6.663125	0.001076925
Residual	36	2148.059	59.6683
Total	39	3340.791
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	35.67762	7.278849	4.901547	2.03E-05	20.91542769
Math-Degree	A	0.069846	3.543263	0.001115	0.105828013
Age	B	0.185213	1.321886	0.194545	-0.130798844
Income ('000)	C	0.152819	0.872253	0.388851	-0.176634459

You are required to;

(a) Derive the regression model.

(b) Assess the independent variables significance at 5% level (develop hypothesis if necessary in the analysis)?

(c) Discuss minimum of 3 assumption in OLS regression.