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?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.2: Arithmetic Sequences

Problem 67E

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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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