2. M11.E.4.2.1 Draw, find and/or write an equation for a line of best fit for a scatter plot.

3. Usually in math class, the points all fall on a line Real data is never perfect. We draw a “line of best fit”

4. The line of best fit is either a smooth curve or a straight line Never connect the dots.

5. The “line of best fit” splits the points and is tilted to get as close as possible to the most points there is one point a little above the line and one point a little below the line this point is farther above the line and this point is farther below the line The other 2 points are right on the line.

6. Which is the “line of best fit” for this data? This does split the points, but the points above the line are much closer than the points below the line There are 4 points above the line & only 2 points below the line This isn’t bad, but the line on C is closer to more points.

7. Sometimes there are a lot of data points

8. Pick two points on the line that are not data points. It is best if they are far apart and it is easy to find their coordinates (2, 16) (10.4, 46)

9. Find the slope: (we’ll need it to write the equation of the line) (2, 16) (10.4, 46) m = ------ Δy Δx

10. Now we’ll write the equation of the line using slope-intercept form : A line has a lot of values for y y is a variable It also has a lot of values for x x is a variable

11. Now we’ll write the equation of the line using slope-intercept form : y is a variable The line only has one slope x is a variable

12. Now we’ll write the equation of the line using slope-intercept form : y is a variable The line only has one slope x is a variable

13. Now we’ll write the equation of the line using slope-intercept form : y is a variable The line only crosses the y-axis at one place x is a variable

14. Now we’ll write the equation of the line using slope-intercept form : y is a variable The line only crosses the y-axis at one place x is a variable

15. Draw the line of best fit and write the equation.

16. You probably didn’t pick the same points – but we should get about the same slope. (.1, 5.8) (2.6,.6)

17. (.1, 5.8) (2.6,.6) m = ------ Δy Δx

19. M11.E.4.2.2 Make predictions using the equations or graphs of best-fit lines of scatter plots.

20. Use the equation. What will the distance be when the time is 19 s? The y values are distances The x values are times y = 3.6(19) + 9 y = 68.4 + 9 y = 77.4 m It’s not on the graph! Your 1 st graph

21. Draw the line of the best fit, write the equation of the line, and predict the age of a business owner that earns $160,000.

22. Draw the line of the best fit, write the equation of the line, and predict the age of a business owner that earns $160,000 (16,52000) (56,128000) m = -------------------- = --------- = 1900 128000-52000 76000 56-16 40 y = 1900x + 22 y = 1900 x + 22000