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 29.0 24.5 14.3 7.5 27.7 16.2 20.1 y 24 75 39 23 15 30 15 25 (a) Make a scatter diagram of the data. Selection Tool Line Ray Segment Circle Vertical Parabola Horizontal Parabola Point No Solution Help 123456789101112131415161718192021222324252627282930313251015202530354045505560657075 Clear Graph Delete Layer Fill WebAssign Graphing Tool Graph LayersToggle Open/Closed After you add an object to the graph you can use Graph Layers to view and edit its properties. Then visualize the line you think best fits the data. (b) Use a calculator to verify that Σx = 150.0, Σx2 = 3250.22, Σy = 246, Σy2 = 10226 and Σxy = 5405.2. 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 increase 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 remain constant as x increases. Given our value of r, y should tend to decrease as x increases.

Answer 1

a ) the scatter diagram is give as

x	y	x2	y2	xy
10.7	24	114.49	576	256.8
29	75	841	5625	2175
24.5	39	600.25	1521	955.5
14.3	23	204.49	529	328.9
7.5	15	56.25	225	112.5
27.7	30	767.29	900	831
16.2	15	262.44	225	243
20.1	25	404.01	625	502.5
150	246	3250.22	10226	5405.2

Σx = 150.0, Σx2 = 3250.22, Σy = 246, Σy2 = 10226 and Σxy = 5405.2.

using minitab>stat>basic stat>Regression

we have

Correlation: x, y

Pearson correlation of x and y (r) = 0.734
P-Value = 0.038

since there is a strong positive linear relationship between x and y so
Given our value of r, y should tend to increase as x increases