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Using Statistical Regression to Investigate 
Track and Field Records


Activity Description Activity Guide


Part 1: The Women's 800-meter Run (1950-1985)

1.      Below is a table showing the world record for the women’s 800-meter run at different points in history.

Year

Time(sec)

1955

125

1960

124

1965

121

1970

120

1975

117

1980

113

2.      Enter the data values from the table into lists on your calculator.  

3.      Using the calculator's statistical plotting features graph the data.  You may need to set an appropriate viewing window for your calculator.

4.      What characteristics does the scatterplot have?   Does a linear function ‘fit’ the data points?

5.      Find the linear regression equation for the data points.  

6.      Graph the regression equation on the same axis as the scatterplot.  

7.      Does this regression equation ‘fit’ the data well?  Are all the points close to the regression line?

8.      Use the trace feature to find the regression equation’s estimate of the world record in 1977.  Is this estimate close to the actual world record of 117.5 seconds set by Svetla Zlateva on 8/24/1973?

9.      What would be a good estimate, based on the regression equation, for the world record next year?

10.   What would be the world record in the year 2224 based on the regression equation?  Does this make sense?  Why?

11.  Add the following data to your lists.  Once added, sort your data so that the years are in ascending order.  Make sure that the times are also sorted to retain the proper (year, time) relationship.

Year

Time(sec)

1940

136

1945

135

1950

133

1985

113

1990

113

1995

113

2000

113

12.  Recalculate the linear regression equation for this amended set of data.  Graph the new regression equation.  Does the regression equation fit this set of data points well?

13.  Find the quartic regression equation  for this set of data.  Graph the quartic regression equation on the same axis as the linear regression equation.

14.  Does the quartic regression equation model the data better than the linear regression equation?  Justify your answer.

15.  Are there years where the linear regression equation approximates the data better than the quartic regression equation?  When?

16.  If you were to pick one of these two equations to predict the world record time in the year 2002, which one would you choose?  Justify your answer.

17.  Find the estimated world record time in the year 2002 for each regression equation.  Do both estimates make sense?  Explain your answer.

18.  Zoom out one time and look at the equations.  Would either equation work well for estimating world record times in the distant future?  Why?  

Part 2: Beating the Calculator 

19.  Below are some general forms of different classes of functions.  Which class of functions could be transformed to most resembles the world record data?  Why? 

y = ex

y = e-x

y = sin(x)

y = sin (-x)

y = ln(x)

y = -ln(x)

 

 

 

20.   Using your response from task 19, build an equation to model the data.  Utilize shifting, scaling, and other techniques of transforming equations.

21.  Graph your model along with the quartic regression equation and the linear regression equation.  Describe the strengths and weaknesses of your model compared to the other two models.  Comment on the appropriateness of this model.

22.  What happens to your model when estimating world records in the distant future?  Does your model estimate future world records that are physically possible?

23.  Graph the equation y = -5ln(x-1940) on the same axis as the other regression equations.  How does this equation compare to the other three regression equations?  What are some strengths and weaknesses of this equation?

24.  What happens to this model when estimating world records in the distant future?  Does this model estimate future world records that are physically possible? Comment on the appropriateness of this model.

Part 3: The Men's Pole Vault

25.  Below is a table showing the world records for the men’s pole vault at different points in history.  Place the table in your calculator.

Year

Distance(cm)

1925

425

1927

427

1929

430

1931

430

1933

437

1935

439

1937

454

1939

454

1941

472

1943

477

26.  Generate a scatterplot from the data.  What are some characteristics of the scatterplot?

27.  Using the scatterplot predict the world record in the year 1956.  How did you arrive at that prediction?

28.  Find a regression equation that models this data.  You can use an equation from the calculator or construct one of your own.  Justify why you chose this equation.

29.  Use the equation from task 28 to estimate the world record in 1956.  Does this estimation closely match your prediction from task 27?  Which one do you believe is more reliable?  Why?

30.  In 1956 the world record was still 477cm.  How would your current scatterplot look if it were extended to the year 1956?  Why?

31.  In 1956 Cornelius Warmerdam still held the world record.  In 1957 Robert Gutowski broke the world record by vaulting 478cm.  Which person was the better pole-vaulter?  Why?

     32.  Go to the website:          

Look at all the information concerning Warmerdam and Gutowski.  Does any of this information change your mind about which person may have been the better pole-vaulter?  Why?

33.  Add the following data to your lists.  Once added, sort your data so that the years are in ascending order.  Make sure that the heights are also sorted to retain the proper (year, height) relationship. .  

1957

478

1959

478

1961

483

1963

520

1965

528

1967

538

1969

544

1971

549

1973

563

1975

565

1977

570

1979

570

1981

581

1983

583

1985

594

1987

603

1989

606

1991

611

1993

613

1995

614

1997

614

1999

614

 

34.  Look at the amended scatterplot.  Describe some the characteristics of this scatterplot.

35.   Return to the website listed above.  If you were going to construct an equation to predict future world record, would you include all the data points included in this website?  Which data points would you choose?  Justify your answer.

36.   Restrict your scatterplot to only those data points you chose in task 35.  Construct a regression equation that fits this data set.  You can use a calculator regression equation or construct one of your own.  Why did you choose this equation?  What are some strengths and weaknesses of this equation?

37.  Using your equation from task 36, predict the world record next year.  Predict the world record 10 years from now.  Do these predictions make sense physically? 

Extension:  

Interpreting the Spread of AIDS in the US
In this activity students are given data on the number of AIDS cases in the US and are asked to graph, interpret, and analyze the data.




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Last modified on August 15, 2001.