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	10.5	30.6	24.5	14.3	7.5	27.7	16.2	20.1
y	25	70	39	23	15	30	15	25

(a) Make a scatter diagram of the data.

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Then visualize the line you think best fits the data.

(b) Use a calculator to verify that Σx = 151.4, Σx² = 3341.34, Σy = 242, Σy² = 9550 and Σxy = 5377.9.

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.

(a) Given our value of r, we can not draw any conclusions for the behavior of y as x increases.

(b) Given our value of r, y should tend to decrease as x increases.

(c) Given our value of r, y should tend to remain constant as x increases.

(d) Given our value of r, y should tend to increase as x increases.

Answer 1

a.

b.

X Values
∑ = 151.4
Mean = 18.925
∑(X - M_x)² = SS_x = 476.095

Y Values
∑ = 242
Mean = 30.25
∑(Y - M_y)² = SS_y = 2229.5

X and Y Combined
N = 8
∑(X - M_x)(Y - M_y) = 798.05

R Calculation
r = ∑((X - M_y)(Y - M_x)) / √((SS_x)(SS_y))

r = 798.05 / √((476.095)(2229.5)) = 0.775

As r value is positive so y will increase with increase in x

So answer here is

(d) Given our value of r, y should tend to increase as x increases.