In a study of differences in levels of community demand for firefighters, the following sample regression was obtained, based on 46 towns in Bavaria, Germany:

where
y = number of full-time firefighters per capita
x₁ = maximum base salary of firefighters, in thousands of euro
x₂ = percentage of population
x₃ = estimated per capita income, in thousands of euro
x₄ = population density
x₅ = amount of intergovernmental grants per capita, in thousands of euro
x₆ = number of miles from the regional city
x₇ = percentage of the population that is male and between 12 and 21 years of age
The numbers in parentheses under the coefficients are the estimated coefficient standard errors.
a. Find and interpret a 99% confidence interval for β₅.
b. Test, against a two-sided alternative, the null hypothesis that β₄ is 0, and interpret your result.
c. Test, against a two-sided alternative, the null hypothesis that β₇ is 0, and interpret your result.

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ŷ = -0.00178 -0.00035x₁0.00002x2 + 0.00036x3 (0.00014) +0.52569x4 (0.68648) R² = 0.3572 (0.00010) (0.000016) + 0.05146x5 0.00009x6 +0.00743x7 (0.01367) (0.00004) (0.00348) -