Sports The ordered pairs below give the winning times (in seconds) of the women’s 100 -meter freestyle in the Olympics from 1984 through 2012. 1984 , 55.92 2000 , 53.83 1988 , 54.93 2004 , 53.84 1992 , 54.64 2008 , 53.12 1996 , 54.50 2012 , 53.00 (a) Sketch a scatter plot of the data. Let y represent the winning time (in seconds) and let t = 84 represent 1984. (b) Sketch the line that you think best approximates the data and find an equation of the line. (c) Use the r e g r e s s i o n feature of a graphing utility to find the equation of the least squares regression line that fits the data. (d) Compare the linear model you found in part (b) with the linear model you found in part (c).
Sports The ordered pairs below give the winning times (in seconds) of the women’s 100 -meter freestyle in the Olympics from 1984 through 2012. 1984 , 55.92 2000 , 53.83 1988 , 54.93 2004 , 53.84 1992 , 54.64 2008 , 53.12 1996 , 54.50 2012 , 53.00 (a) Sketch a scatter plot of the data. Let y represent the winning time (in seconds) and let t = 84 represent 1984. (b) Sketch the line that you think best approximates the data and find an equation of the line. (c) Use the r e g r e s s i o n feature of a graphing utility to find the equation of the least squares regression line that fits the data. (d) Compare the linear model you found in part (b) with the linear model you found in part (c).
Solution Summary: The author explains how to graph the winning time of the women in the Olympics (in seconds) from 1984 to 2012.
Sports The ordered pairs below give the winning times (in seconds) of the women’s
100
-meter
freestyle in the Olympics from 1984 through 2012.
1984
,
55.92
2000
,
53.83
1988
,
54.93
2004
,
53.84
1992
,
54.64
2008
,
53.12
1996
,
54.50
2012
,
53.00
(a) Sketch a scatter plot of the data. Let
y
represent the winning time (in seconds) and let
t
=
84
represent 1984.
(b) Sketch the line that you think best approximates the data and find an equation of the line.
(c) Use the
r
e
g
r
e
s
s
i
o
n
feature of a graphing utility to find the equation of the least squares regression line that fits the data.
(d) Compare the linear model you found in part (b) with the linear model you found in part (c).
Definition Definition Representation of the direction and degree of correlation in graphical form. The grouping of points that are plotted makes it a scatter diagram. A line can be drawn showing the relationship based on the direction of points and their distance from each other.
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