Question

An association was formed by students to protest labor exploitation in the apparel industry. There were 18 student​ "sit-ins" for a​ "sweat-free campus" organized at several universities. Data were collected for the duration​ (in days) of each​ sit-in, as well as the number of student arrests. The data for 5​ sit-ins in which there was at least one arrest and the results of a simple linear regression are found below. Let y be the number of arrests and x be the duration. Complete parts a through d.

​Sit-In	University	Duration ​(days)	Number of Arrests
12	University 1	4	55
14	University 2	11	11
15	University 3	22	14
17	University 4	44	16
18	University 5	11	12

Unstandardized   Coefficients Standardized Coefficients Model B    Std. Error Beta t Sig. 1 ​ (Constant) 1.826 14.699 0.124 0.909      DURATION 8.239 5.332 0.666 1.545 0.220

a. Write the equation of a​ straight-line model relating y to x.

Choose the correct answer below.

A. y=β1x

B. y=β1x2+β0

C.y=β0+β1x+ε

D.y=β1x+ε

b. Use the results of the linear regression to find the least squares prediction equation.

y=______+( ______)x

​(Type an integer or decimal rounded to three decimal places as​ needed.)

c. Give a practical interpretation of the​ y-intercept of the least squares line. If a practical interpretation is not​ possible, explain why.

Choose the correct answer below.

A.For each additional one day​ duration, the number of arrests is estimated to change by the value of the​ y-intercept.

B.For each additional​ arrest, the duration is estimated to change by the value of the slope.

C.Since a​ sit-in with duration 0 is outside the range of the sample​ data, the​ y-intercept has no practical interpretation.

D.Since a​ sit-in with 0 arrests is outside the range of the sample​ data, the​ y-intercept has no practical interpretation.

d. Give a practical interpretation of the slope of the least squares line. Over what range is the interpretation​ meaningful?

What is the best interpretation of the​ slope?

A. Since a​ sit-in with duration 0 is outside the range of the sample​ data, the slope has no practical interpretation.

B.For each additional one day​ duration, the number of arrests is estimated to increase by the value of the slope.

C.Since a​ sit-in with 0 arrests is outside the range of the sample​ data, the slope has no practical interpretation.

D.For each additional​ arrest, the duration is estimated to change by the value of the slope. Over what range is the interpretation​ meaningful?

A.The interpretation is valid only for​ sit-ins with the number of arrests within the range of the sample data.

B.The interpretation is valid for all​ sit-ins with the number of arrests greater than 0.

C.The interpretation is valid for all​ sit-ins with durations greater than 0.

D.The interpretation is valid only for​ sit-ins with durations within the range of the sample data.

Click to select your answer(s).

Answer 1