For a sample of 20 New England cities a sociologist studies

For a sample of 20 New England cities, a sociologist studies the crime rate in each city (crimes per 100,000 residents) as a function of its poverty rate (in %) and its median income (in $1,000s). A portion of the regression results are as follows. Use Table 2 and Table 4.

Specify the sample regression equation. (Negative values should be indicated by a minus sign. Report your answers to 4 decimal places.)

Choose the appropriate hypotheses to test whether the poverty rate and the crime rate are linearly related.

Choose the appropriate hypotheses to determine whether the poverty rate and income are jointly significant in explaining the crime rate.

At the 5% significance level, are the poverty rate and income jointly significant in explaining the crime rate?

Solution

A. Crime = 301.62 + 53.1597 Poverty + 4.9472 Income

B1. H₀: ₁ = 0; H_A: ₁ 0 . Option (2)

B2. Since p-value is less than the significance level i.e. 0.05, hence we cannot accept the null hypothesis and conclude that poverty & crime rate are linearly related. Option (1)

D1. .H₀: ₁ = ₂ = 0; H_A: At least one _j < 0 . Option (1).

D2. No, since the null hypothesis is rejected. Option (3).