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	12.7	29.6	24.5	14.3	7.5	27.7	16.2	20.1
y	23	75	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 = 152.6, Σx² = 3332.18, Σy = 245, Σy² = 10179 and Σxy = 5485.5.

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 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 increase as x increases.

Answer 1

	X	Y	X * Y	X2	Y2
	12.7	23	292.1	161.29	529
	29.6	75	2220	876.16	5625
	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	152.6	245	5485.5	3332.18	10179

Part a)

Part b)

r = 0.765

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