Question

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5. Listed in the table below are the robbery and aggravated assault rates (occurrences per 100,000)...

5. Listed in the table below are the robbery and aggravated assault rates (occurrences per 100,000) for the 12 most populated U.S. cities in 2006:

City

Robbery (x)

Aggravated Assault (y)

New York

288

330

Los Angeles

370

377

Chicago

555

610

Houston

548

562

Phoenix

288

398

Philadelphia

749

720

Las Vegas

409

508

San Antonio

180

389

San Diego

171

301

Dallas

554

584

San Jose

112

248

Honolulu

105

169

a. Calculate the standard error of the estimate.

b. Estimate the strength of the linear relationship between x and y.

Solutions

Expert Solution

a)

SSE =Syy-(Sxy)2/Sxx= 22,977.1253
error Variance σ2 = s2 =SSE/(n-2) = 2297.7125
standard error of estimate = se =√s2 = 47.9345

b)

correlation coefficient r= Sxy/(√Sxx*Syy)               = 0.9605

as correlation coefficient is positive and closer to 1, this tells us that there is a strong positive   linear relationship between x and y.

milcah answered 7 months ago
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