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 | 11.7 | 31.6 | 24.5 | 14.3 | 7.5 | 27.7 | 16.2 | 20.1 |
y | 26 | 73 | 39 | 23 | 15 | 30 | 15 | 25 |
(a) Make a scatter diagram of the data.
Then visualize the line you think best fits the data.
(b) Use a calculator to verify that Σx = 153.6,
Σx2 = 3430.18, Σy = 246,
Σy2 = 10030 and Σxy = 5584.4.
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 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.Given our value of r, y should tend to remain constant as x increases.
X | Y | X * Y | |||
11.7 | 26 | 304.2 | 136.89 | 676 | |
31.6 | 73 | 2306.8 | 998.56 | 5329 | |
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 | |
Total | 153.6 | 246 | 5584.4 | 3430.18 | 10030 |
r = 0.791
Given our value of r, y should tend to increase as x increases.
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