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.]ANOVAdfSSMSFSignificance FRegression23,949.51,974.80.280.756Residual17118,203.966,953.17 Total19122,153.4 CoefficientsStandardErrort Statp-valueIntercept726.7716120.78226.0170.000Poverty4.79016.40310.74800.465Income-2.837218.4228−0.15400.879 Choose the appropriate hypotheses to test whether the poverty rate and the crime rate are linearly related.multiple choice 1H0: β1 ≥ 0; HA: β1 < 0H0: β1 = 0; HA: β1 ≠ 0H0: β1 ≤ 0; HA: β1 > 0b-2. At the 5% significance level, what is the conclusion to the test?multiple choice 2Do not reject H0we cannot conclude that the poverty rate and the crime rate are linearly related.Reject H0we can conclude that the poverty rate and the crime rate are linearly related.Do not reject H0we can conclude that the poverty rate and the crime rate are linearly related.Reject H0we cannot conclude that 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 "tα/2,df" value to 3 decimal places, and final answers to 2 decimal places.)c-2. Using the confidence interval, determine whether income influences the crime rate at the 5% significance level.multiple choice 3Income 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 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 does not significantly differ from zero.

b-1) The null and alternative hypotheses are H0: β1 = 0; HA: β1 ≠ 0 b-2) Since the p-value is…

Answered: b-2. At the 5% significance level, what…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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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 as follows. [You may find it useful to reference the t table.]

ANOVA	df	SS	MS	F	Significance F
Regression	2	3,949.5	1,974.8	0.28	0.756
Residual	17	118,203.96	6,953.17
Total	19	122,153.4

	Coefficients	Standard Error	t Stat	p-value
Intercept	726.7716	120.7822	6.017	0.000
Poverty	4.7901	6.4031	0.7480	0.465
Income	-2.8372	18.4228	−0.1540	0.879

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

multiple choice 1

H₀: β₁ ≥ 0; H_A: β₁ < 0
H₀: β₁ = 0; H_A: β₁ ≠ 0
H₀: β₁ ≤ 0; H_A: β₁ > 0

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

multiple choice 2

Do not reject H₀we cannot conclude that the poverty rate and the crime rate are linearly related.
Reject H₀we can conclude that the poverty rate and the crime rate are linearly related.
Do not reject H₀we can conclude that the poverty rate and the crime rate are linearly related.
Reject H₀we cannot conclude that 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 "t_α/2,df" value to 3 decimal places, and final answers to 2 decimal places.)

c-2. Using the confidence interval, determine whether income influences the crime rate at the 5% significance level.

multiple choice 3

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 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 does not significantly differ from zero.

Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.

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