2. 5.4 – Fitting a Line to Data

3.  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

4.  Usually, there is no single line that passes through all data points  BEST-FITTING LINE – the line that fits best to the data

5.  Example 1 You 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) 514 215 93 78 121 103 312 69

6. Age (days) Length of tail (mm) 514 215 93 78 121 103 312 69 5.4 – Fitting a Line to Data

7.  Example 2 The 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 YearWinning Time 194811.9 s 195211.5 s 195611.5 s 196011.0 s 196411.4 s 196811.0 s 197211.1 s 197611.1 s 198011.1 s 198411.0 s 198810.5 s 199210.8 s 199610.9 s

8.  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

9.  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

10.  Example 3 The 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.

11.  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

12.  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)

13.  Graphing Calculator Activity

14. HOMEWORK Page 296 #10 – 24 even