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 11.7 28.4 24.5 14.3 7.5 27.7 16.2 20.1 y 23 69 39 23 15 30 15 25 (a) Make a scatter diagram of the data. Get Flash Player Flash Player version 10 or higher is required for this question. You can get Flash Player free from Adobe's website. Then visualize the line you think best fits the data. (b) Use a calculator to verify that Σx = 150.4, Σx2 = 3238.18, Σy = 239, Σy2 = 9315 and Σxy = 5202.1. 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 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

a)

b)

X	Y	XY	X²	Y²
11.7	23	269.1	136.89	529
28.4	69	1959.6	806.56	4761
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

	X	Y	XY	X²	Y²
total sum	150.400	239.000	5202.10	3238.180	9315.0

      
SSxx =    Σx² - (Σx)²/n =   410.660
SSxy=   Σxy - (Σx*Σy)/n =   708.900
SSyy =    Σy²-(Σy)²/n =   2174.875

correlation coefficient ,    r = Sxy/√(Sx.Sy) =   0.750

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