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 29.4 24.5 14.3 7.5 27.7 16.2 20.1 y 27 71 39 23 15 30 15 25 (a) Make a scatter diagram of the data. Then visualize the line you think best fits the data.

(b) Use a calculator to verify that Σ(x) = 154.2, Σ(x2) = 3369.34, Σ(y) = 245, Σ(y2) = 9795 and Σ(x y) = 5452.3. Compute r.

Answer 1

a) Scatter Plot:

b) From the given data

S.No	X	Y	X^2	Y^2	XY
1	14.5	27	210.25	729	391.5
2	29.4	71	864.36	5041	2087.4
3	24.5	39	600.25	1521	955.5
4	14.3	23	204.49	529	328.9
5	7.5	15	56.25	225	112.5
6	27.7	30	767.29	900	831
7	16.2	15	262.44	225	243
8	20.1	25	404.01	625	502.5
Total =	154.2	245	3369.34	9795	5452.3

Karl Pearson correlation Coefficient is rxy = 0.7651