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 2 294.3 147.2 9.73E-01 Residual 17 91,413.94 5,377.29 Total 19 91,708.30 Coefficients Standard Error t Stat p-value Lower 95% Upper 95% Intercept 760.09 93.0941 8.1648 0.0000 563.68 956.50 Poverty −0.0245 5.8042 −0.0042 0.9967 −12.27 12.22 Income 3.2598 14.1819 0.2299 0.8209 −26.66 33.18 a. Specify the sample regression equation. (Negative values should be indicated by a minus sign. Report your answers to 4 decimal places.) Crimeˆ Crime ^ = + 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 hypothesis test? Do not reject H0Picture we cannot conclude the poverty rate and the crime rate are linearly related. Reject H0Picture the poverty rate and the crime rate are linearly related. Do not reject H0Picture we can conclude the poverty rate and the crime rate are linearly related. Reject H0Picture the poverty rate and the crime rate are not 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

Answer #1

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 2 294.3 147.2 9.73E-01 Residual 17
91,413.94 5,377.29 Total 19 91,708.30 Coefficients Standard Error t
Stat p-value Lower...

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...

For a sample of 27 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). He finds that SSE = 4,102,577 and SST =
7,622,089.
a. Calculate the standard error of the estimate.
(Round your answer to 4 decimal places.)
***The answer is not 405.0964

For a sample of 31 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). He finds that SSE = 4,184,806 and SST = 7,721,398. a.
Calculate the standard error of the estimate. (Round your answer to
4 decimal places.) b-1. What proportion of the sample variation in
crime rate is explained by the variability in the explanatory
variables?...

Data were gathered from a simple random sample of cities. The
variables are Violent Crime (crimes per 100,000 population),
Police Officer Wage (mean $/hr), and Graduation Rate (%). Use the
accompanying regression table to answer the following questions
consider the coefficient of Graduation Rate. Complete parts a
through e.
Dependent variable is: Violent Crime
R squared=38.1 R squared (adjusted)=40.3 s=129.6 with 37
degrees of freedom
Variable
Coeff
SE (Coeff)
t-ratio
P-value
Intercept
1388.65
183
.9
7.55
<
0.0001
Police Officer...

Use the Excel output in the below table to do (1) through (6)
for each ofβ0, β1,
β2, and β3.
y = β0 +
β1x1 +
β2x2 +
β3x3 + ε
df = n – (k + 1) = 16 – (3 + 1) = 12
Excel output for the hospital labor needs case (sample size:
n = 16)
Coefficients
Standard
Error
t Stat
p-value
Lower 95%
Upper 95%
Intercept
1946.8020
504.1819
3.8613
0.0023
848.2840
3045.3201
XRay (x1)
0.0386...

Use the Excel output in the below table to do (1) through (6)
for each ofβ0, β1,
β2, and β3.
y = β0 +
β1x1 +
β2x2 +
β3x3 + ε
df = n – (k + 1) = 16 – (3 + 1) = 12
Excel output for the hospital labor needs case (sample size:
n = 16)
Coefficients
Standard
Error
t Stat
p-value
Lower 95%
Upper 95%
Intercept
1946.8020
504.1819
3.8613
0.0023
848.2840
3045.3201
XRay (x1)
0.0386...

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