1. A high school teacher is interested in the extent to which truancy (or school absenteeism) is related to and predicts misbehavior. For a sample of 8 students, she compares the number of absences during the semester and the number of times the students received a disciplinary slip for misbehaving in class. Here are the data:
Absences
Disciplinary slips
0
4
1
4
0
2
5
7
3
3
4
11
1
0
2
5
a. Measure and test the strength of the relationship between absenteeism and incidents of misbehavior.
b. Derive and interpret an equation that predicts the number of disciplinary slips based on absences.
c. To what extent does the number of absences account for differences in the number of disciplinary slips?
2. A research center wants to determine whether a state’s unemployment rate can be used to predict the number of human trafficking cases in the same state. Ten states with similar human trafficking laws were selected, and the results are reported below:
State
Percent unemployment
Human Trafficking Cases
A
2.5
14
B
6.9
25
C
2.1
5
D
6.5
21
E
3.6
18
F
4.4
8
G
5.9
18
H
7.6
5
I
1.5
6
K
4.0
10
a. What are the median, and mean values for gun trafficking cases?
b. What is the association between unemployment and human trafficking cases in these 10 states? Is the association significant?
c. Calculate the regression coefficient using unemployment as the independent variable.
d. If a state reported 2.7% unemployment in 2014, what would you predict the number of human trafficking cases to be?
3. A psychiatrist wondered how much a night’s sleep could affect a person’s alertness and reaction time. She collected a random sample of people and asked them (X ) how many hours of sleep they got the night before and then used a simple test to determine (Y ) their reaction time in seconds. The following results were obtained:
Hours of sleep
Reaction time
5.0
13
10.5
8
4.0
15
6.0
12
7.5
11
6.5
13
2.5
21
6.0
10
4.5
17
8.0
11
a. Draw a scatter plot of the data.
b. Calculate the regression slope and Y-intercept.
c. Draw the regression line on the scatter plot.
d. Predict the number of seconds it would take for someone who got 8.5 hours of sleep to react.
e. Find the coefficients of determination and nondetermination. What do they mean?
f. Construct an analysis of variance table and perform an F test on the significance of the regression.
