Using Linear Functions to Model Real-World Data

Caution: TEMATH's tools will occasionally write results into this Report window. The results will be written on the last line in the window. When this happens, you will need to scroll back to your position in the instructions. You may want to print a copy of the instructions in this Report window before you begin.

Table Men[22,2] contains the Men's Long Jump Olympics Gold Medal Performances for the years 1896 to 1992.

Select Show Data Table from the Work menu.
The data will be displayed. The distances are measured in inches.
Close the Data Table window.
Select Plot from the Graph menu.

Carefully examine the plot of the data. Note that there are breaks in the data for the years 1912 to 1920 and 1936 to 1948. What happened in these years? Also, note the stellar performance by Bob Beamon in the 1968 Olympics in the mile high city of Mexico City.

Does the data appear to have a linear trend? If so, let's find the least squares line fit to the data.

Select Least Squares - Line from the Tools menu.

The least squares line will be drawn in the Graph window and its equation will be written into the first row of the Work window.

Interpret the meaning of the slope (0.706763) of this line. What does it suggest will happen between each Olympics (every four years)?

Table Women[22,2] contains the Women's Long Jump Olympics Gold Medal Performances for the years 1948 to 1992.

Data for women

Select the table Women[22,2] in the Work window.
Select Overlay Plot from the Graph menu.
Examine the plot of the Women's data and compare it to the men's data.
Select Least Squares - Line from the Tools menu.
The least squares line will be drawn in the Graph window and its equation will be written into the first row of the Work window.

Interpret the meaning of the slope (1.17024) of this line. What does it suggest will happen between each Olympics (every four years)?

Compare the women's trend line to the men's trend line. What do the trend lines appear to be predicting for the future?

Let's investigate the future predictions (the ever dangerous extrapolations) of these trend lines.

Click in the Domain & Range window and change the plotting domain and range to 1890t2200 and 0s600.
Select Plot All from the Graph menu.

Interpret these graphs.

To find the point where the two lines intersect,

Click the Curve Intersection tool on the Tool Palette.
Click in the Graph window near the point where the two lines intersect.
The coordinates of the point of intersection will be written into this Report window at the bottom.

What do these trend lines predict will happen in the 2108 Olympics?

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