Question

Listed below are numbers of enrolled students (in thousands) and numbers of campus burglaries for randomly selected large colleges in a recent year.

Enrollment	32	31	53	28	27	36	42	30	34	46
Burglaries	103	103	86	57	32	131	157	20	27	161

The best-fit line based on this data is:

burglaries = 3.47 enrollment - 36.77

with r² = 0.315

Answer the following questions:

How much of the variation in burglaries can be accounted for by the best-fit line?                            [ Select ]                       ["0.315%", "3.47%", "31.5%", "36.77%"]      

The regression equation predicts the number of campus burglaries to                            [ Select ]                       ["increase", "decrease", "not change"]         by                            [ Select ]                       ["0.315", "3.47", "36.77"]         for each additional one thousand students on campus.

Predict the number of campus burglaries when enrollment is 40 (thousands of students):

Predicted burglaries_{enrollment=40} =                            [ Select ]                       ["102.03", "167.59", "175.57", "1474.27"]      

Answer 1

The best-fit line based on this data is:

burglaries = 3.47 enrollment - 36.77

with r2 = 0.315

Answer the following questions:

31.5% of the variation in burglaries can be accounted for by the best-fit line

The regression equation predicts the number of campus burglaries to increase by 3.47 for each additional one thousand students on campus.

Predict the number of campus burglaries when enrollment is 40 (thousands of students):

Predicted burglaries enrollment= 3.47*40- 36.77 = 102.03