5.4 – Fitting a Line to Data

Today we will be learning about:◦ Finding a linear equation that approximated a set

of data points

◦ Determining whether there is a positive or negative correlation or no correlation is a set of real-life data

Usually, there is no single line that passes through all data points

BEST-FITTING LINE – the line that fits best to the data

Example 1You are studying the way a tadpole turns into a frog. You collect data to make a table that shows the ages and the lengths of the tails of 8 tadpoles. Draw a line that corresponds closely to the data. Write an equation of the line.

Age (days)

Length of tail (mm)

5 14

2 15

9 3

7 8

12 1

10 3

3 12

6 9

Age (days)

Length of tail (mm)

5 14

2 15

9 3

7 8

12 1

10 3

3 12

6 9

Example 2The winning Olympic times for the women’s 100 meter run from 1948 to 1996 are shown in the table. Draw a line that corresponds closely to these times. Write an equation of your line.

Olympic Year Winning Time

1948 11.9 s

1952 11.5 s

1956 11.5 s

1960 11.0 s

1964 11.4 s

1968 11.0 s

1972 11.1 s

1976 11.1 s

1980 11.1 s

1984 11.0 s

1988 10.5 s

1992 10.8 s

1996 10.9 s

A correlation (r) is a number between -1 and 1 that indicates how well a straight line can represent the data.

When the points on a scatter plot can be approximated by a line with a positive slope, x and y have a POSITIVE CORRELATION

When the points can be approximated by a line with negative slope, x and y have a NEGATIVE CORRELATION.

When the points cannot be approximated by a straight line, there is RELATIVELY NO CORRELATION

Example 3The Hernandez family spent 6 hours traveling by car.

The two graphs show the gallons of gas that remain in the gas tank and the miles driven for each of the 6 hours. Which is which? Explain.

Describe the correlation of each set of data.

There are many technologies available to help graph many data points and to find the best fitting line.

Today we will work with graphing calculators

Example 4◦ Use a graphing calculator to find the best-fitting

line for the data.◦ (38, 62), (28, 46), (56, 102), (56, 88), (24, 36),

(77, 113), (40, 69), (46, 60)

Graphing Calculator Activity

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