(a) For this data, find the value of the Pearson's product-moment correlation coefficient, r. Eduardo looked in a sports science text book. He found that the following information about r was appropriate for athletic performance. Value of 17 Description of the correlation 0 ≤ırı<0.4 weak 0.4 ≤iri < 0.8 moderate 0.8 ≤r ≤ 1 strong (b) Comment on your answer to part (a), using the information that Eduardo found. (c) Write down the equation of the regression line of t on x, in the form t = ax + b. A 57-year-old male also ran in the 5000 m race. (d) Use the equation of the regression line to estimate the time he took to complete the 5000 m race.
(a) For this data, find the value of the Pearson's product-moment correlation coefficient, r. Eduardo looked in a sports science text book. He found that the following information about r was appropriate for athletic performance. Value of 17 Description of the correlation 0 ≤ırı<0.4 weak 0.4 ≤iri < 0.8 moderate 0.8 ≤r ≤ 1 strong (b) Comment on your answer to part (a), using the information that Eduardo found. (c) Write down the equation of the regression line of t on x, in the form t = ax + b. A 57-year-old male also ran in the 5000 m race. (d) Use the equation of the regression line to estimate the time he took to complete the 5000 m race.
ChapterP: Prerequisites
SectionP.6: The Rectangular Coordinate System And Graphs
Problem 2ECP
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Transcribed Image Text:(a) For this data, find the value of the Pearson's product-moment correlation coefficient, r.
Eduardo looked in a sports science text book. He found that the following information about r
was appropriate for athletic performance.
Value of Iri
0≤ırı<0.4
0.4≤ir <0.8
0.8 ≤r ≤ 1
Description of the correlation
weak
moderate
strong
(b) Comment on your answer to part (a), using the information that Eduardo found.
(c)
Write down the equation of the regression line of t on x, in the form t = ax + b.
A 57-year-old male also ran in the 5000 m race.
(d)
Use the equation of the regression line to estimate the time he took to complete the
5000 m race.
Transcribed Image Text:Eduardo believes that there is a linear relationship between the age of a male runner and the
time it takes them to run 5000 metres.
To test this, he recorded the age, x years, and the time, t minutes, for eight males in a single
5000 m race. His results are presented in the following table and scatter diagram.
x, years
t, minutes
Time
18
29.4
45
40
35
30
25
0
24 28
29.2
10
31.1 33.6 32.2
F8
L.
20
•
36 40 46 52 62
33.1
35.2 40.4
30
·
40
Age
●
A
50
●
60
70
X
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