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 f
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.
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SUMMARY OUTPUT |
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Regression Statistics |
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Multiple R |
0.597512 |
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R Square |
0.357021 |
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Adjusted R Square |
0.303439 |
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Standard Error |
7.724526 |
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Observations |
40 |
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ANOVA |
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df |
SS |
MS |
F |
Significance F |
|
Regression |
3 |
1192.732 |
397.5774 |
6.663125 |
0.001076925 |
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Residual |
36 |
2148.059 |
59.6683 |
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Total |
39 |
3340.791 |
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|
|
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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;
- Derive the regression model
- Assess the independent variables significance at 5% level (develop hypothesis if necessary in the analysis)?
- Discuss minimum of 3 assumption in OLS regression.
Step by step
Solved in 5 steps
