CA EC F06 O’Brien
CA 9th ed Lial
College Algebra
Linear Regression Extra Credit Problems
1.
Given below is a table of the gold medal distances in the long jump (measured in meters) for 1896
through 1996. Note that the 1916, 1940, and 1944 Olympics were skipped due to wars.
Olympic Number
1
Distance (meters)
6.35
2
7.18
3
7.34
4
7.48
5
7.60
7
7.15
8
7.44
9
7.73
10
7.64
11
8.06
14
7.82
15
7.75
16
7.83
17
8.12
18
8.07
19
8.90
20
8.24
21
8.35
22
8.54
23
8.54
24
8.72
25
8.67
26
8.50
Source: World Almanac, 2000
a)
Enter the data and make a scatterplot using a grapher (use ZoomStat to view). Record a quick
sketch of the scatterplot.
b)
Fit a linear regression equation to the data. Record the equation and then use it to predict the
distance of the long jump at the 2004 games in Athens (the 28th Olympics). Multiply the metric
distance by 3.18 to obtain the distance in feet.
1
CA EC F06 O’Brien
CA 9th ed Lial
2)
A college algebra professor wanted to see the linear correlation between student scores on the first
exam and the overall course grades. Below is a table of these values.
First Exam
Course Grade
54
60
64
68
51
69
98
93
73
80
95
91
99
90
66
70
60
69
73
68
60
66
52
66
75
83
101
95
55
59
79
77
71
67
78
74
90
87
99
78
62
67
73
67
63
76
54
65
69
75
67
80
52
57
82
82
89
89
75
76
90
83
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CA EC F06 O’Brien
CA 9th ed Lial
a)
Enter the data and make a scatterplot using a grapher (use ZoomStat to view). Record a quick
sketch of the scatterplot.
b)
Find a linear regression equation. Record the equation and then use it to predict a student's course
grade given that he/she earned an 81% on the first exam.
c)
Find the correlation coefficient.
d)
Based on the value of the correlation coefficient, is the score on the first exam a good predictor of
the final course grade? Why or why not?
A statistics professor was interested in the relationship between students' college GPAs and the
number of hours worked per week on a part-time job. She expected that there would be a high
negative linear correlation. Below is the data that she collected from a random sample of college
students who held part-time jobs.
Hours Worked
GPA
3)
16
2.9
7
3.5
10
2.5
33
1.8
20
3.0
22
2.2
15
2.8
12
3.4
19
2.7
13
3.1
25
2.1
23
2.6
5
3.3
19
3.1
23
2.4
26
2.4
18
3.3
10
3.4
32
2.0
18
2.9
22
2.5
15
3.3
20
2.3
22
2.6
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CA EC F06 O’Brien
CA 9th ed Lial
a)
Enter the data and make a scatterplot using a grapher (use ZoomStat to view). Record a quick
sketch of the scatterplot.
b)
Find the linear regression equation. Record the equation and then use it to predict the GPA of a
student who works 23 hours per week.
c)
Find the correlation coefficient.
d)
Based on the value of the correlation coefficient, was the professor's expectation regarding a high
negative correlation correct? Why or why not?
A marathon runner was able to remember his times for 1 mile, 5 miles, 10 miles, 15 miles,
20 miles, 25 miles, and his final 26.2 mile time. However, he would like to know what his
10K (6.2 miles) time was. Since he had run fairly consistently throughout the entire race, he
thought the linear correlation coefficient should be close to 1. The data table below gives the times
for the miles mentioned above.
Miles
Time (minutes)
4)
a)
1
6.20
5
31.95
10
64.53
15
98.17
20
133.63
25
170.65
26.2
179.03
Enter the data and make a scatterplot using a grapher (use ZoomStat to view). Record a quick
sketch of the scatterplot.
b)
Find the linear regression equation. Record the equation and then use it to estimate his 10K time.
Note the times above are given in total elapsed minutes rounded to the nearest hundredth. Convert
the 10K time to minutes and seconds.
c)
Find the correlation coefficient.
d)
Based on the correlation coefficient, was the runner correct in his assumption that he ran fairly
consistently throughout the race? Why or why not?
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