8.35 Murders and poverty; Part II. Exercise 8.25 presents regression output from a model for predicting annual murders per million from the percentage living in poverty based on a random sample of 20 metropolitan areas. The model output is also provided below: Estimate Std. Error t value P-value 29.901 7.789 3.839 0.001 2.559 0.390 6.562 0.000 (Intercept) - poverty% 8 = 5.512 R^2 = 70.52% Radj = 68.89% What are the hypotheses for evaluating whether the poverty percentage is a significant predictor of the murder rate? State the conclusion of the hypothesis test from part (a) in the context of the data. Calculate a 95% confidence interval for the slope of the poverty percentage and interpret it in the context of the data.
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First, we need to state the null and alternative hypotheses for evaluating whether poverty percentage is a significant predictor of murder rate. H0: β1 = 0 (Poverty percentage has no effect on murder rate) Ha: β1 ≠ 0 (Poverty percentage has a significant effect Show more…
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4. Section 14.3, A sociologist believe that the crime rate in an area is significantly influenced by the area's poverty rate and median income. Specifically, she hypothesizes crime will increase with poverty and decrease with income. She collects data on crime rate (crimes per 100,000 residents), the poverty rate (%), and the median income (in $1,000) from 41 New England cities. A portion of the regression result is shown below. Table 1: Coefficients Standard error t stat p-value Intercept -301.62 549.71 -0.55 0.5864 Poverty 53.16 14.22 3.74 0.0006 Income 4.95 8.26 0.6 0.5526 (a) Are the signs as expected on the slope coefficients? (b) Interpret the slope coefficient for poverty. (c) What is the sample regression equation? Predict the crime rate in an area with poverty rate of 20% and a median income of $50,000.
Madhur L.
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.
Lucas F.
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. [You may find it useful to reference the t table.] ANOVA df SS MS F Significance F Regression 2 2,517.3 1,258.7 0.29 0.749 Residual 17 72,837.53 4,284.56 Total 19 75,354.8 Coefficients Standard Error t Stat p-value Intercept 716.6835 86.0322 8.330 0.000 Poverty 3.3717 4.7573 0.7090 0.488 Income 3.6612 14.3119 0.2560 0.801 -1. Construct a 95% confidence interval for the slope coefficient of income. (Negative values should be indicated by a minus sign. Round "tα/2,df" value to 3 decimal places, and final answers to 2 decimal places.)
Supreeta N.
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