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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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