For a sample of 20 New England cities, a sociologist studies the crime rate in e

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 $1,000). A portion of the regression results is as follows. Use Table 2 and Table 4 ANOVA Regression 2 188,246.8 94,123.4 Residual 17 Total df SS 9.04E-07 45,457.32 2,673.96 19 233,704.1 Coefficients Standard Error t Stat p-value Lower 95% Upper 95% ntercept -301.62 Poverty 53.1597 Income 549.7135 -0.5487 0.5903 -1,461.52 858.28 83.16 22.37 14.2198 8.2566 23.16 0.5992 0.5569-12.47 3.7384 0.0016 4.9472 a. Specify the sample regression equation. (Negative values should be indicated by a minus sign. Round your answers to 4 decimal places.) 301.6253.1597 Poverty 4.9472 Income b-1. Choose the appropriate hypotheses to test whether the poverty rate and the crime rate are linearly b-2. At the 5% significance level, what is the conclusion to the test? Reject Ho; the poverty rate and the cn me rate are linearly related. O Reject Ho, the poverty rate and the crime rate are not linearly related. Do not reject Ho; we can conclude the poverty rate and the crime rate are linearly related. Do not reject Ho; we cannot conclude the poverty rate and the crime rate are linearly relaterd 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 12.47 to 22.37 c-2 Using the confidence interval, determine whether income influences the crime rate at the 5% ficance level Income is not 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. Income is significant in explaining the crime rate, since its slope coefficient significantly differs from zero. O Income is 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: 1-2:0; HA: At least one j#0 0H0: 1-2:0; HA: At least one 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 O Yes, since the null hypothesis is not rejected. No, since the null hypothesis is rejected. No, since the null hypothesis is not rejected.

Explanation / Answer

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 $1,000). A portion of the regression results is as follows. Use Table 2 and Table 4 ANOVA Regression 2 188,246.8 94,123.4 Residual 17 Total df SS 9.04E-07 45,457.32 2,673.96 19 233,704.1 Coefficients Standard Error t Stat p-value Lower 95% Upper 95% ntercept -301.62 Poverty 53.1597 Income 549.7135 -0.5487 0.5903 -1,461.52 858.28 83.16 22.37 14.2198 8.2566 23.16 0.5992 0.5569-12.47 3.7384 0.0016 4.9472 a. Specify the sample regression equation. (Negative values should be indicated by a minus sign. Round your answers to 4 decimal places.) 301.6253.1597 Poverty 4.9472 Income b-1. Choose the appropriate hypotheses to test whether the poverty rate and the crime rate are linearly b-2. At the 5% significance level, what is the conclusion to the test? Reject Ho; the poverty rate and the cn me rate are linearly related. O Reject Ho, the poverty rate and the crime rate are not linearly related. Do not reject Ho; we can conclude the poverty rate and the crime rate are linearly related. Do not reject Ho; we cannot conclude the poverty rate and the crime rate are linearly relaterd 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 12.47 to 22.37 c-2 Using the confidence interval, determine whether income influences the crime rate at the 5% ficance level Income is not 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. Income is significant in explaining the crime rate, since its slope coefficient significantly differs from zero. O Income is 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: 1-2:0; HA: At least one j#0 0H0: 1-2:0; HA: At least one 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 O Yes, since the null hypothesis is not rejected. No, since the null hypothesis is rejected. No, since the null hypothesis is not rejected.

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