An elections officer wants to model voter turnout (y) in a ...

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Question 1

The model E(y) = β0 + β1x1 + β2x2 + β3x3 was used to relate E(y) to a single qualitative variable. How many levels does the qualitative variable have?

Question 2

An elections officer wants to model voter turnout (y) in a precinct as a function of the type of precinct.

Consider the model relating mean voter turnout, E(y), to precinct type:

E(y) = β₀ + β₁x₁ + β₂x₂, where x₁ = 1 if urban, 0 if not
x₂ = 1 if suburban, 0 if not
(Base level = rural)

The p-value for the test H₀: β₁ = β₂ = 0 is .14. Interpret the result.
◦ Reject H₀ at α = .10; the model is useful for predicting voter turnout.
◦ Reject the model since it only explains 14% of the variation.
◦ Do not reject H₀ at α = .10; there is no evidence of a difference between the mean voter turnouts for urban, suburban, and rural precincts.
◦ Reject H₀ at α = .01; there is evidence of a difference between the mean voter turnouts for urban, suburban, and rural precincts.

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Thanks for the timely response, appreciate it