Question

1. In one of the Boston city parks, there has been a problem with muggings in the summer months. A police cadre took a random sample of 10 days (out of a 90-day summer) and compiled the following data. For each day, x represents the number of police officers on duty and y represents the number of reported muggings on that day.

x	10	15	16	1	4	6	18	12	14	7
y	5	2	1	9	7	8	1	5	3	6

a. Propose a straight-line model to relate the number of police officers on duty on a day to the number of reported muggings on that day.
b. Draw a scatter plot of the data. Does it appear that a straight-line model will be an appropriate fit to the data?

c. Fit the model to the data using the method of least squares and give the least squares prediction equation.

d. Interpret the slope of the least squares line

e. Predict the number of muggings for 20 police officers on duty.

Answer 1

a)

x represents the number of police officers on duty and y represents the number of reported muggings on that day

b. Draw a scatter plot of the data. Does it appear that a straight-line model will be an appropriate fit to the data?

yes it appears to be straight line model fit for this data.

c. Fit the model to the data using the method of least squares and give the least squares prediction equation.

Least square linear regression equation: y = -0.4932x + 9.7798

d) slope:

slope of the regression equation would be -0.4932x

e. Predict the number of muggings for 20 police officers on duty.

y = -0.4932x + 9.7798

x = 20

y = -0.4932*(20) + 9.7798

y = -0.0842