For a sample of 41 New England cities, a sociologist studies the crime rate in e

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). A portion of the regression results are shown in the following table.

Calculate the standard error of the estimate. (Round your answer to 2 decimal places.)

What proportion of the sample variation 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

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). A portion of the regression results are shown in the following table.

Explanation / Answer

Ans:

a)Standard error of estimate=sqrt(Mean squareresidual)=sqrt(174,327.3 )=417.52

b-1)

Proportion of the sample variation in crime rate is explained by the variability in the explanatory variables,R2

R2=SS(regression)/SS residual)

=3,500,526 /7,684,380=0.4555

45.55%

b-2)

proportion is unexplained variability=1-0.4555=0.5445

54.45%

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