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 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)

Age (days) Length of tail (mm) – Fitting a Line to Data

 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 s s s s s s s s s s s s 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 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.

 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

HOMEWORK Page 296 #10 – 24 even