Fox Module 13: Dummy variable regression HW
(The attached PDF file has better formatting.)
Homework assignment: auto insurance rating territories
An insurer examines claim frequencies for 15 territories: 5 urban, 5 suburban, and 5 rural.
Urban | Sub-urban | Rural |
Territory | Claim Frequency | Territory | Claim Frequency | Territory | Claim Frequency |
1 | 14.30% | 6 | 10.88% | 11 | 9.59% |
2 | 11.00% | 7 | 16.58% | 12 | 8.54% |
3 | 20.90% | 8 | 12.72% | 13 | 10.32% |
4 | 16.85% | 9 | 9.40% | 14 | 10.01% |
5 | 12.85% | 10 | 12.92% | 15 | 9.24% |
A. How many dummy variables does this regression use?
B. What are the values of the dummy variables for urban, sub-urban, and rural? Assume rural is the base territory, with dummy variables equal to zero.
C. Use Excel or other statistical software to run the regression. What are the values of á, â1, and â2? (Fox uses ã1 and ã2 instead of â1 and â2 for dummy variables.) Explain what each of the coefficients means.
Jacob: Fox uses both ã1 and ã2 as well as â1 and â2.
Rachel: We do this is the territory number has a quantitative value. But the territory numbers here are just indicators; they have no quantitative meaning. The regression equation is
Frequency = á + â1 × D1 + â2 × D2
In Fox’s notation, this is Frequency = á + ã1 × D1 + ã2 × D2