Question 134655: The following table shows the length of winning long jumps in the Olympic Games.
Year 1900 1904 1908 1912
Length (in feet) 7.86 8.03 8.18 8.31
Show that the data are not linear?
Find the equation of the regression line that gives length as a function of time. Round the regression line parameters to three decimal places. Be sure to identify your variables.
Explain in practical terms the meaning of the slope of the regression line.
What does your equation predict for the Olympic Games in 2004? Is this reasonable?
The winning long jump in the 1920 Olympic Games was 7.82 feet. How does this value compare with the value predicted by the regression line model?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The following table shows the length of winning long jumps in the Olympic Games.
Year 1900 1904 1908 1912
Length (in feet) 7.86 8.03 8.18 8.31
Show that the data are not linear?
To be linear there must be a constant slope.
slope from 1900 to 1904 = (8.03-7.86)/4 = 0.27/4 = 0.0675
slope from 1904 to 1908 = (8.18-8.03)/4 = 0.15/4
They are not the same so data is not strictly linear.
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Find the equation of the regression line that gives length as a function of time. Round the regression line parameters to three decimal places. Be sure to identify your variables.
Using TI Linear Regression equation function I get:
length = 0.038(year after 1900) + 7.87
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Explain in practical terms the meaning of the slope of the regression line.
For each addition year after 1900 the length will increase 0.038 ft.
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What does your equation predict for the Olympic Games in 2004? Is this reasonable?
2004 is 104 years after 1900
l(2004) = 0.038(104)+7.87 = 11.77 ft.
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The winning long jump in the 1920 Olympic Games was 7.82 feet. How does this value compare with the value predicted by the regression line model?
1920 is 20 years after 1900
Predicted length = l(1920) = 0.038(20)+7.82 = 8.62 feet
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Cheers,
Stan H.
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