In: Math
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.

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.