For a sample of 41 New England cities, a sociologist studies the crime rate in e
ID: 3380801 • Letter: F
Question
For a sample of 41 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). The regression results are shown.
Calculate the standard error of the estimate. (Round your answer to 2 decimal places.)
What proportion of the variability in crime rate is explained by the variability in the explanatory variables? (Round your answer to 4 decimal places.)
Explained proportion
What proportion is unexplained? (Round your answer to 4 decimal places.)
Unexplained proportion
ANOVA df SS MS F Significance F Regression 2 3,536,461 1,768,230.5 11.08998 3.3E-04 Residual 26 4,145,543 159,444.0 Total 28 7,682,004Explanation / Answer
For a sample of 41 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). The regression results are shown.
ANOVA
df
SS
MS
F
Significance F
Regression
2
3,536,461
1,768,230.5
11.08998
3.3E-04
Residual
26
4,145,543
159,444.0
Total
28
7,682,004
a.
Calculate the standard error of the estimate. (Round your answer to 2 decimal places.)
=sqrt(MSE) =sqrt(159444) = 399.30
b-1.
What proportion of the variability in crime rate is explained by the variability in the explanatory variables? (Round your answer to 4 decimal places.)
Explained proportion=SSR/SST
= 3536461/7682004 = 0.4604
b-2.
What proportion is unexplained? (Round your answer to 4 decimal places.)
Unexplained proportion =1- explained proportion
= 1-0.4604
= 0.5396
ANOVA
df
SS
MS
F
Significance F
Regression
2
3,536,461
1,768,230.5
11.08998
3.3E-04
Residual
26
4,145,543
159,444.0
Total
28
7,682,004
a.
Calculate the standard error of the estimate. (Round your answer to 2 decimal places.)
=sqrt(MSE) =sqrt(159444) = 399.30
b-1.
What proportion of the variability in crime rate is explained by the variability in the explanatory variables? (Round your answer to 4 decimal places.)
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