Scatter Plots and
The Line of Best Fit - Using A Graphing Calculator
In
scientific research we may gather data and notice that when the data is plotted,
there seems to be a linear relationship between the variables. The data may
not be exactly linear but may appear close to lying on a line. A graph of
such data is called a Scatter Plot.
Our job then becomes one of finding the equation of the
line that best describes the relationship between the variables.
Consider the table below which shows the relationship between the year in
which the Olympics was held, and the winning times for the 100 m sprint.
| Year |
Time |
Year |
Time |
| 1900 |
11.0 |
1956 |
10.5 |
| 1904 |
11.0 |
1960 |
10.2 |
| 1908 |
10.8 |
1964 |
10.0 |
| 1912 |
10.8 |
1968 |
9.95 |
| 1920 |
10.8 |
1972 |
10.14 |
| 1924 |
10.6 |
1976 |
10.06 |
| 1928 |
10.8 |
1980 |
10.25 |
| 1932 |
10.3 |
1984 |
9.99 |
| 1936 |
10.3 |
1988 |
9.92 |
| 1948 |
10.3 |
1992 |
9.96 |
| 1952 |
10.4 |
1996 |
9.84 |
Practice Questions-
Use a graphing calculator to draw a scatter plot, determine the equation of
the line of best fit, and determine the correlation coefficient for the given
data. Set your WINDOW appropriately.
| 1. |
2. |
3. |
4. |
||||||||||||
| x |
y |
x |
y |
x |
y |
x |
y |
||||||||
| 2 |
7 |
1 |
7 |
1 |
1 |
3 |
0 |
||||||||
| 4 |
13 |
4 |
1 |
4 |
1 |
5 |
1 |
||||||||
| 6 |
19 |
6 |
- 3 |
4 |
4 |
7 |
2 |
||||||||
| 7 |
22 |
7 |
- 5 |
1 |
4 |
9 |
4 |
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