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 = 4,166,091 and SST = 7,712,159. 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? (Round your answer to 4 decimal places.) b-2. What proportion is unexplained? (Round your answer to 4 decimal places.)

Answer 1

Solution

Part (a)

Standard error of the estimate

= sqrt(MSE)

= sqrt{SSE/df)}

= sqrt{4166091/(29 – 1 – 2)}

= sqrt(160234.2692)

= 400.2927 ANSWER

Part (b)

Proportion explained

= SSRegression/SST

= (SST - SSE)/SST

= (7712159 – 4166091)/7712159

= 1 – 0.5402

= 0.4598 ANSWER 2

Part (c)

Answer 2 =>

Unexplained proportion = 0.5402 ANSWER 3

DONE