The Line of Best Fit

Class Goals - By the end of the period, you will understand and be able to…

  • Find a linear equation that approximates a set of data points.
  • Determine whether there is a positive, negative, or no correlation in a set of real data.
  • Apply the line of best fit for Interpolation and Extrapolation.

Example #1

  1. Plot the points on the graph.
  2. Then, find the equation of the line that best fits the following points.
  3. Graph line through the points.

TI-30 Instructions

  1. Prepare Calculator Settings
  2. mode
  3. Make sure the entire Left Column is highlighted
  4. Edit Lists
  5. Data
  6. Put x-coordinates under L1
  7. Put y-coordinates under L2
  8. Find the Equation for the Line of Best Fit
  9. 2ndStat
  10. #2
  11. Make sure your xDATA has L1 and your yDATA has L2.
  12. Scroll Down to CALC and hit enter
  13. Scroll down and look for a = and b=.
  14. The calculator knows y = mx + b as y = ax + b.
  15. Plug a in for slope.
  16. Plug b in for y-intercept.

TI-83 (or better) Instructions

  1. Turning On Diagnostic Settings
  2. 2nd#0 (to go to the Catalog)
  3. Scroll Down to “DiagnosticOn”
  4. Enter
  5. Enter
  6. Edit Lists
  7. Stat
  8. Enter
  9. Put x-coordinates under L1
  10. Put y-coordinates under L2
  11. Graph
  12. Find the Equation for the Line of Best Fit
  13. Stat
  14.  (Right Arrow Key – to move to CALC)
  15. #4
  16. Enter

Linear Regression Activity

Height (inches) vs. Shoe Size

Your Height (in inches):Your Shoe Size:

  1. Equation of the Line that best fits the data:
  1. Describe Correlation:
  1. Plug your shoe size into the equation. How close is it to your height?
  1. Estimate the shoe size of someone who is 61 inches tall.
  1. Estimate the shoe size of someone who is 81 inches tall.
  1. Estimate the shoe size of someone who is 41 inches tall.
  1. Estimate the height of someone who wears a size 8 shoe.
  1. Estimate the height of someone who wears a size 15 shoe.
  1. Estimate the height of someone who wears a size 5 shoe.

Quick Vocabulary

InterpolationExtrapolation

Practice Problems – Draw a scatter plot of the data. Get the equation of the line that best fits the data.

1.

  1. Line of Best Fit:
  1. What is the value of y, when x = 6.2?
  2. What is the value of y, when x = 1.3?
  3. What is the value of x, when y = 6.2?
  4. What is the value of x, when y = 1.3?

2.

  1. Line of Best Fit:
  2. What is the value of y, when x = 5?
  3. What is the value of y, when x = -5?
  4. What is the value of x, when y = 10?
  5. What is the value of x, when y = 1.5?

More Applications

Using the information above, answer the questions.

Age, x / 1 / 2 / 3 / 5 / 8 / 13 / 18 / 21
Height (in inches), y / 24 / 29 / 36 / 44 / 54 / 64 / 72 / 72
  1. On the coordinate plane, create a scatter plot of your data.

  1. Find the equation of the line of best fit for the data.
  1. Graph your line with your data. Label your axes.
  1. How tall should this person have been when he/she was 10?
  1. How tall should this person have been when he/she was 50?
  1. How old should this person have been when he/she was 48 inches tall?
  1. How old should this person have been when he/she was 88 inches tall?
  1. Are your answers for parts (d) and (f) reasonable?
  1. Are your answers for parts (e) and (g) reasonable?
  1. Briefly explain the difference between parts (h) and (i).