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	10.7	30.8	24.5	14.3	7.5	27.7	16.2	20.1
y	26	78	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.)

This answer has not been graded yet.

(b)

Use a calculator to verify that Σ(x) = 151.8, Σ(x²) = 3357.86, Σ(y) = 251, Σ(y²) = 10785 and Σ(x y) = 5654.0.

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 remain constant 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 decrease as x increases.Given our value of r, y should tend to increase as x increases.

Answer 1

Solution:

a) Scatter plot of the date is given below:

b) Using calculator I have made a table which is given below:

From the above table it is verified that Σ(x) = 151.8, Σ(x^{​​​​​​2}) = 3357.86, Σ(y) = 251, Σ(y^{​​​​​​2}) = 10785 and Σ(x y) = 5654.0.

The value of r is given by the formula,

r = 0.756.

If value of r is positive, it means that there is positive correlation between independent variable x and dependent variable y. It implies that as the value of x increases the value of y also increases.

If value of r is negative, it means that there is negative correlation between independent variable x and dependent variable y. It implies that as the value of x increases the value of y decreases.

If value of r is zero, it means that there is no correlation between independent variable x and dependent variable y. It implies that we can not draw any conclusion for the behavior of y as x increases.

For the given data, r = 0.756 which is positive. It implies that as x increases y should tend to increase.

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