Do larger universities tend to have more property crime? University crime statistics are affected by a variety of factors. The surrounding community, accessibility given to outside visitors, and many other factors influence crime rate. Let x be a variable that represents student enrollment (in thousands) on a university campus, and let y be a variable that represents the number of burglaries in a year on the university campus. A random sample of n = 8 universities in California gave the following information about enrollments and annual burglary incidents.
x | 12.5 | 30.0 | 24.5 | 14.3 | 7.5 | 27.7 | 16.2 | 20.1 |
y | 27 | 74 | 39 | 23 | 15 | 30 | 15 | 25 |
(b) Use a calculator to verify that Σx = 152.8,
Σx2 = 3350.98, Σy = 248,
Σy2 = 10230 and Σxy = 5530.9.
Compute r. (Round to 3 decimal places.)
As x increases, does the value of r imply that
y should tend to increase or decrease? Explain your
answer.
Given our value of r, y should tend to remain constant as x increases. Given our value of r, y should tend to decrease as x increases. Given our value of r, y should tend to increase as x increases. Given our value of r, we can not draw any conclusions for the behavior of y as x increases.
Solution :
X | Y | XY | X^2 | Y^2 |
12.5 | 27 | 337.5 | 156.25 | 729 |
30 | 74 | 2220 | 900 | 5476 |
24.5 | 39 | 955.5 | 600.25 | 1521 |
14.3 | 23 | 328.9 | 204.49 | 529 |
7.5 | 15 | 112.5 | 56.25 | 225 |
27.7 | 30 | 831 | 767.29 | 900 |
16.2 | 15 | 243 | 262.44 | 225 |
20.1 | 25 | 502.5 | 404.01 | 625 |
n | 8 |
sum(XY) | 5530.90 |
sum(X) | 152.80 |
sum(Y) | 248.00 |
sum(X^2) | 3350.98 |
sum(Y^2) | 10230.00 |
Numerator | 6352.80 |
Denominator | 8388.24 |
r | 0.7573 |
r square | 0.5736 |
Xbar(mean) | 19.1000 |
Ybar(mean) | 31.0000 |
SD(X) | 8.3913 |
SD(Y) | 19.0146 |
b | 1.8361 |
a | -4.0689 |
r = 0.757
Given our value of r, y should tend to increase as x increases.
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