MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Here are the gold medal times for the women’s 100-meter freestyle (swimming) in every other Summer Olympics:
|
Gold Medal Times in the Women's 100-Meter Freestyle Swimming for Every Other Summer Olympics |
|
|
Year |
Time (seconds) |
|
1912 |
81.5 |
|
1924 |
73.6 |
|
1932 |
67.9 |
|
1952 |
66.6 |
|
1960 |
62.4 |
|
1968 |
61.0 |
|
1976 |
55.65 |
|
1984 |
55.92 |
|
1992 |
54.64 |
|
2000 |
53.8 |
|
2008 |
53.4 |
- Draw a
scatter plot of the data.
- Describe the relationship between the variables in the graph.
There is a negative relationship between Year and Time. Therefore, when the year starts increasing, the Gold Medal Times in the Women's 100-Meter Freestyle Swimming for Every Other Summer Olympics starts decreasing. When the year starts decreasing, the Gold Medal Times in the Women's 100-Meter Freestyle Swimming for Every Other Summer Olympics starts increasing.
- Find the
correlation coefficient .
Mean of x = 1964.364
Mean of y = 62.401
∑(X−X⎯⎯⎯)(Y−Y⎯⎯⎯)=−2806.684
∑X-X¯2=10062.545
∑(Y−Y⎯⎯⎯)2=842.830
value of correlation coefficients is -0.9638
- Find the least-squares regression line.
- Find the estimated gold medal time for 1924 and for 1976. Are these estimates reliable? Are they reasonable?
- Why are your answers in Question 5 different than the times given in the table?
- Find the estimated gold medal time for 2022 and for 2200. Are these estimates reliable? Are they reasonable?
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