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 shown in the accompanying table. Use Table 2 and Table 4. ANOVA df SS MS F Significance F Regression 2 5,081.3 2,540.7 0.5368 5.94E-01 Residual 17 80,460.13 4,732.95 Total 19 85,541.40 Coefficients Standard Error t Stat p-value Lower 95% Upper 95% Intercept 723.66 91.7833 7.8844 0.0000 530.01 917.30 Poverty 2.2587 5.0381 0.4483 0.6596 -8.37 12.89 Income 11.8452 12.8168 0.9242 0.3683 -15.20 38.89 a. Specify the sample regression equation. (Negative values should be indicated by a minus sign. Report your answers to 4 decimal places.) Crime = 723.6600 + 2.2587 Poverty + 11.8452 Income b-1. Choose the appropriate hypotheses to test whether the poverty rate and the crime rate are linearly related. H0: ?1 = 0; HA: ?1 ? 0 b-2. At the 5% significance level, what is the conclusion to the hypothesis test? 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 -8.37 to 12.89 c-2. Using the confidence interval, determine whether income is significant in explaining the crime rate at the 5% significance level. 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: ?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. 

          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 shown in the accompanying table. Use Table 2 and Table 4.

ANOVA df SS MS F Significance F
Regression 2 5,081.3 2,540.7 0.5368 5.94E-01
Residual 17 80,460.13 4,732.95
Total 19 85,541.40

Coefficients Standard Error t Stat p-value Lower 95% Upper 95%
Intercept 723.66 91.7833 7.8844 0.0000 530.01 917.30
Poverty 2.2587 5.0381 0.4483 0.6596 -8.37 12.89
Income 11.8452 12.8168 0.9242 0.3683 -15.20 38.89

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

Crime = 723.6600 + 2.2587 Poverty + 11.8452 Income

b-1. Choose the appropriate hypotheses to test whether the poverty rate and the crime rate are linearly related.

H0: ?1 = 0; HA: ?1 ? 0

b-2. At the 5% significance level, what is the conclusion to the hypothesis test?

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 -8.37 to 12.89

c-2. Using the confidence interval, determine whether income is significant in explaining the crime rate at the 5% significance level.

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: ?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.
Show more…
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 shown in the accompanying table. Use Table 2 and Table 4. ANOVA df SS MS F Significance F Regression 2 5,081.3 2,540.7 0.5368 5.94E-01 Residual 17 80,460.13 4,732.95 Total 19 85,541.40 Coefficients Standard Error t Stat p-value Lower 95% Upper 95% Intercept 723.66 91.7833 7.8844 0.0000 530.01 917.30 Poverty 2.2587 5.0381 0.4483 0.6596 -8.37 12.89 Income 11.8452 12.8168 0.9242 0.3683 -15.20 38.89 a. Specify the sample regression equation. (Negative values should be indicated by a minus sign. Report your answers to 4 decimal places.) Crime = 723.6600 + 2.2587 Poverty + 11.8452 Income b-1. Choose the appropriate hypotheses to test whether the poverty rate and the crime rate are linearly related. H0: ?1 = 0; HA: ?1 ? 0 b-2. At the 5% significance level, what is the conclusion to the hypothesis test? 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 -8.37 to 12.89 c-2. Using the confidence interval, determine whether income is significant in explaining the crime rate at the 5% significance level. 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: ?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.

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Elementary Statistics a Step by Step Approach
Elementary Statistics a Step by Step Approach
Allan G. Bluman 9th Edition
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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 shown in the accompanying table. Use Table 2 and Table 4. ANOVA df SS MS F Significance F Regression 2 5,081.3 2,540.7 5.94E-01 Residual 17 80,460.13 4,732.95 Total 19 85,541.40 Coefficients Standard Error t Stat p-value Lower 95% Upper 95% Intercept 723.66 91.7833 7.8844 0.0000 530.01 917.30 Poverty 2.2587 5.0381 0.4483 0.6596 -8.37 12.89 Income 11.8452 12.8168 0.9242 0.3683 -15.20 38.89 a. Specify the sample regression equation. (Negative values should be indicated by a minus sign. Report your answers to 4 decimal places.) Crime = 723.6600 + 2.2587 Poverty + 11.8452 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 b-2. At the 5% significance level, what is the conclusion to the hypothesis test? 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 -8.37 to 12.89 c-2. Using the confidence interval, determine whether income is significant in explaining the crime rate at the 5% significance level. 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 Βj ≠ 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.
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Transcript

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00:01 So here i'm going to focus on the two parts of the problem that it seems that you've been marked incorrect on, specifically starting with c1, where you are asked for a 95 % confidence interval, 95 % ci, for the slope of the coefficient of income.
00:23 So this is something that you're actually already given in the display.
00:28 If we look at the bottom of that table, you can see that we have coefficients, standard error, t, stat, key value, lower 95%, and upper 95%.
00:45 So the lower 95 % and upper 95 % values are actually going to be the upper and lower bounds of the confidence interval.
00:57 So one second here.
00:59 Essentially, the question, what it's getting at isn't really doing any calculations on your own.
01:06 Instead, the focus is on how do you interpret the out.
01:10 Put that you're getting from the software...
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