The lengths (in feet) of the winning men\'s discus throws in a regularly-held co
ID: 2911982 • Letter: T
Question
The lengths (in feet) of the winning men's discus throws in a regularly-held competition are given by the following ordered pairs. (1920, 135.5) (1956, 173.8) (1984, 207.4) (1924, 140.2) (1960, 183.1) (1988, 214.7) (1928, 144.2) (1964, 189.0) (1992, 202.6) (1932, 151.2) (1968, 201.4) (1996, 216.6) (1936, 154.5) (1972, 200.2) (2000, 216.2) (1948, 162.1) (1976, 210.4) (2004, 218.2) (1952, 169.4) (1980, 207.6) (2008, 214.7) (a) Sketch a scatter plot of the data. Let y represent the length of the winning discus throw (in feet) and let t = 20 represent 1920. (b) Use a straightedge to sketch the best-fitting line through the points and find an equation of the line. (Round the slope and y-intercept to the nearest whole number.) (c) Use the regression feature of a graphing utility to find the least squares regression line that fits the data. (Round the slope and y-intercept to two decimal places.)
Explanation / Answer
a) Scatter plot easy peasy.
Just plot each point on the graph and then join then one after the other.
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b) Connect the firts and last point together
(20,135.5) and (108,214.7)
Slope = (214.7 - 135.5) / (108 - 20) = 0.9
And now
y = 0.9t + C
Using point (20,135.5), we can find constant C :
135.5 = 0.9*20 + C
So, C = 117.5
So, y = 0.9t + 117.5 ----> ANS
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c)
I did this....
xuru.org --> go to this url
Click on "Regression Tools" ----> Linear regression
Now, enter the coordinates thus :
(20, 135.5)
(56, 173.8)
(84, 207.4)
(24, 140.2)
(60, 183.1)
(88, 214.7)
(28, 144.2)
(64, 189.0)
(92, 202.6)
(32, 151.2)
(68, 201.4)
(96, 216.6)
(36, 154.5)
(72, 200.2)
(100, 216.2)
(48, 162.1)
(76, 210.4)
(104, 218.2)
(52, 169.4)
(80, 207.6)
(108, 214.7)
Then hit "Calculate"
And it gave me....
y = 1.007876574 x + 119.7174912
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