Question

For a sample of 29 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 = 4,133,564 and SST = 7,676,478.

a. Calculate the standard error of the estimate.

b-1. What proportion of the sample variation in crime rate is explained by the variability in the explanatory variables?

b-2. What proportion is unexplained?

Answer 1

Answer:

Given,

a)

Given,

To determine the Standard error of estimate

Standard error of estimate = sqrt(SSE/(n-2))

substitute values

= sqrt(4,133,564 / (29 - 2))

= sqrt(4,133,564 / (27))

= sqrt(153094.963)

Standard error of estimate = 391.274

b)

Explained variation

= 1 - SSE/SST

substitute values

= 1 - 4,133,564/7,676,478

= 1 - 0.5385

Explained variation = 0.462

c)

Unexplained variation = 1 - 0.462

= 0.538