Question

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	14.5	30.2	24.5	14.3	7.5	27.7	16.2	20.1
y	25	69	39	23	15	30	15	25

(a)

Make a scatter diagram of the data. Then visualize the line you think best fits the data. (Submit a file with a maximum size of 1 MB.)

(b)

Use a calculator to verify that Σ(x) = 155.0, Σ(x²) = 3417.02, Σ(y) = 241, Σ(y²) = 9411 and Σ(x y) = 5419.7.

Compute r. (Enter a number. 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 remain constant 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.

Answer 1

b. The value of r is 0.795
(The calculations are provided below)

Given our value of r, y should tend to increase as x increases because the value of r is positive.

Thank you.