1. No category

A.P. Statistics. - Linear Regression t-tests
Name ________________________________________
1. A random sample of teachers were asked to measure the distance from their home to school and the average
time it takes for them to drive to school over a week’s time.. The data is below. It is believed that the time
that teachers take to drive to school varies linearly and positively with distance.
Teacher 1
Distance 5.3
Time
2
2.4
20.3 8.2
3
8.1
4
5.2
5
6
7
12.4 15.2 8.2
8
9
10
11.1 16.2 5.2
11
12
13
10.0 16.7 2.9
11.4 17.3 25.9 24.8 9.3
15.5 23.9 9.6
23.9 17.1 3.8
Enter the data on your calculator and plot the points.
a. Find the equation of the least squares line. ______________________________________
b. Interpret the slope of this line in English. ___________________________________________________
________________________________________________________________________________________
c. Find r. ________. Interpret it within the context of this problem.
___________________________________________________________________________________
d. Find r 2 ________. Interpret it within the context of this problem.
___________________________________________________________________________________
! e. Given your answer in d) what is another reason for why the time would vary as much (or as little) as it does.?
f. Formulate null and alternative hypotheses about the slope of the true regression line and perform the test
g. Write your conclusion in English.
h. Find and interpret and 95% confidence interval on the slope.
www.MasterMathMentor.com
Stu Schwartz
2. A random sample of 15 students had their blood pressure taken before and after a pop quiz. The quiz was
then graded. The experimenter believed that the students who had a greater increase in BP would have a
lower grade. Following is the data. Enter it into your calculator.
Student
Initial BP
1
120
2
132
3
144
4
102
5
140
6
120
7
125
8
145
9
127
10
105
11
110
12
128
13
124
14
126
15
112
Final BP
145
137
129
133
140
138
130
127
132
129
112
118
140
127
119
Grade
66
82
93
69
75
72
88
95
62
77
90
55
81
72
70
a. Find the equation of the least squares line. ______________________________________
b. Interpret the slope of this line in English. ___________________________________________________
________________________________________________________________________________________
c. Find r. ________. Interpret it within the context of this problem.
___________________________________________________________________________________
d. Find r 2 ________. Interpret it within the context of this problem.
___________________________________________________________________________________
! e. Given your answer in d) what is another reason for why the grade would vary as much (or as little) as it
does.?
f. Formulate null and alternative hypotheses about the slope of the true regression line and perform the test
g. Write your conclusion in English.
h. Find and interpret and 95% confidence interval on the slope.
www.MasterMathMentor.com
Stu Schwartz