5.4 – Fitting a Line to Data Today we will be learning about: ◦ Finding a linear equation that...
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Transcript of 5.4 – Fitting a Line to Data Today we will be learning about: ◦ Finding a linear equation that...
![Page 1: 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.](https://reader036.fdocuments.in/reader036/viewer/2022062517/56649ed05503460f94bdf3d0/html5/thumbnails/1.jpg)
5.4 – Fitting a Line to Data
![Page 2: 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.](https://reader036.fdocuments.in/reader036/viewer/2022062517/56649ed05503460f94bdf3d0/html5/thumbnails/2.jpg)
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
![Page 3: 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.](https://reader036.fdocuments.in/reader036/viewer/2022062517/56649ed05503460f94bdf3d0/html5/thumbnails/3.jpg)
Usually, there is no single line that passes through all data points
BEST-FITTING LINE – the line that fits best to the data
![Page 4: 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.](https://reader036.fdocuments.in/reader036/viewer/2022062517/56649ed05503460f94bdf3d0/html5/thumbnails/4.jpg)
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
![Page 5: 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.](https://reader036.fdocuments.in/reader036/viewer/2022062517/56649ed05503460f94bdf3d0/html5/thumbnails/5.jpg)
Age (days)
Length of tail (mm)
5 14
2 15
9 3
7 8
12 1
10 3
3 12
6 9
![Page 6: 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.](https://reader036.fdocuments.in/reader036/viewer/2022062517/56649ed05503460f94bdf3d0/html5/thumbnails/6.jpg)
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
![Page 7: 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.](https://reader036.fdocuments.in/reader036/viewer/2022062517/56649ed05503460f94bdf3d0/html5/thumbnails/7.jpg)
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
![Page 8: 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.](https://reader036.fdocuments.in/reader036/viewer/2022062517/56649ed05503460f94bdf3d0/html5/thumbnails/8.jpg)
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
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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.
![Page 10: 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.](https://reader036.fdocuments.in/reader036/viewer/2022062517/56649ed05503460f94bdf3d0/html5/thumbnails/10.jpg)
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
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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)
![Page 12: 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.](https://reader036.fdocuments.in/reader036/viewer/2022062517/56649ed05503460f94bdf3d0/html5/thumbnails/12.jpg)
Graphing Calculator Activity
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HOMEWORKPage 296
#10 – 24 even