For a sample of 41 New England cities a sociologist studies

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	7,682,004

Solution

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.)