Question

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 is as follows. Use Table 2 and Table 4.

ANOVA df SS MS F Significance F
Regression 2 188,246.8 94,123.4 9.04E-07
Residual 17 45,457.32 2,673.96 Total 19 233,704.1 Coefficients Standard Error t Stat p-value Lower 95% Upper 95%
Intercept −301.62 549.7135 −0.5487 0.5903 −1,461.52 858.28
Poverty 53.1597 14.2198 3.7384 0.0016 23.16 83.16
Income 4.9472 8.2566 0.5992 0.5569 −12.47 22.37
a. Specify the sample regression equation. (Negative values should be indicated by a minus sign. Round your answers to 4 decimal places.)
11formula272.mml = + Poverty + Income
b-1. Choose the appropriate hypotheses to test whether the poverty rate and the crime rate are linearly related.
H0: β1 ≥ 0; HA: β1 < 0
H0: β1 ≤ 0; HA: β1 > 0
H0: β1 = 0; HA: β1 ≠ 0
b-2. At the 5% significance level, what is the conclusion to the test?
Reject H0; the poverty rate and the crime rate are linearly related.
Reject H0; the poverty rate and the crime rate are not linearly related.
Do not reject H0; we can conclude the poverty rate and the crime rate are linearly related.
Do not reject H0; we cannot conclude the poverty rate and the crime rate are linearly related.
c-1. Construct a 95% confidence interval for the slope coefficient of income. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)
Confidence interval to
c-2. Using the confidence interval, determine whether income influences the crime rate at the 5% significance level.
Income is significant in explaining the crime rate, since its slope coefficient does not significantly differ from zero.
Income is not significant in explaining the crime rate, since its slope coefficient significantly differs from zero.
Income is significant in explaining the crime rate, since its slope coefficient significantly differs from zero.
Income is not significant in explaining the crime rate, since its slope coefficient does not significantly differ from zero.
d-1. Choose the appropriate hypotheses to determine whether the poverty rate and income are jointly significant in explaining the crime rate.
H0: β1 = β2 = 0; HA: At least one β j < 0
H0: β1 = β2 = 0; HA: At least one β j > 0
H0: β1 = β2 = 0; HA: At least one β j ≠ 0
d-2. At the 5% significance level, are the poverty rate and income jointly significant in explaining the crime rate?
Yes, since the null hypothesis is rejected.
Yes, since the null hypothesis is not rejected.
No, since the null hypothesis is rejected.
No, since the null hypothesis is not rejected.

Answer 1

The poverty rate is linearly related to the crime rate, and jointly with income, they are significant in explaining crime rate variations among New England cities. However, income alone is not a significant predictor of crime rate at the 5% significance level. The sample regression formula is provided based on the given coefficients.

Step-by-step explanation:

Based on the regression results provided, we can determine several things about the relationship between poverty rate, median income, and crime rate:

• The sample regression equation would be written as CrimeRate = -301.62 + 53.1597(Poverty) + 4.9472(Income).
• To test the linear relationship between poverty rate and crime rate, the appropriate hypotheses are H0: β1 = 0 versus HA: β1 ≠ 0.
• Given the poverty rate t Stat of 3.7384 and a p-value of 0.0016, we reject H0 at the 5% significance level, concluding that the poverty rate and crime rate are linearly related.
• The 95% confidence interval for the slope coefficient of income is from -12.47 to 22.37.
• Since 0 is within the confidence interval, we conclude that income is not significant in explaining the crime rate at the 5% significance level.
• For joint significance of poverty rate and income, the null hypothesis is H0: β1 = β2 = 0 and the alternative is HA: At least one βj ≠ 0.
• Given the Significance F of 9.04E-07, we can say that the poverty rate and income are jointly significant in explaining the crime rate because we reject the null hypothesis at the 5% significance level.

Answer 2

Answer: You must give more points for questions that are this long

sincerely,

A Friend

Step-by-step explanation: