1. Line of Best Fit 3.3 A

2. Goal
Understand how to create a line of best fit by hand AND on the graphing calculator.

3. Real Life vs. Math Class
A linear equation, and planned examples will create a perfect line.
In real life, there are often “linear relationships”, but the data does not create a perfect line.
Our goal is to find a line that reasonably fits the data.
Called the “line of best fit”

4. Linear, but not a line
This is called a Scatter Plot.

5. By hand or Calculator
By hand is an estimate, but the calculator will give an exact line of best fit.

6. By Hand
Draw a line that evenly splits up the points so that half are above the line and half are below.
*The # of points on the line does not matter.
We are finding y=mx+b, so we need m and b.
2. To find slope, pick two points on the line (they will probably not be points in the original data set). Plug them into 𝑆𝑙𝑜𝑝𝑒= 𝑦 2 − 𝑦 1 𝑥 2 − 𝑥 1 .
3. Pick a 3rd point on the line, and plug it in for x and y in y=mx+b. Solve for b.

7. Example A photo studio is offering year book photos.
Find the equation for the line of best fit.
# of pics 44 31 24 15
Price ($)
19.00
16.00
13.00
10.00

8. Step 1: plot the points
Price
# of pics

9. Step 2: Draw the line

10. Step 3: Find the Slope Points on the line: (15,10) and (44,19)

11. Step 4: Find the y-intercept
Plug slope into the equation.
𝑦=0.27𝑥+𝑏
Pick another point on the line. I will use (35,16).
Plug into x and y.
16= 𝑏
16=9.45+𝑏
𝑏=6.55

12. Step 5: Plug m and b into the equation
𝑦=0.27𝑥+6.55

13. On calculator Called Linear Regression Stat – edit – enter
𝐿 1 =𝑥 𝑣𝑎𝑙𝑢𝑒𝑠 𝑎𝑛𝑑 𝐿 2 =𝑦 𝑣𝑎𝑙𝑢𝑒𝑠
2. Enter values from chart (be careful!)
Stat – calc – LinReg – enter
2nd – 1 - , - 2nd – 2 - , - vars – y vars – enter – enter.

14. Partner Problem Make a scatter plot of the data.
Hours without Sleep 8 12 16 20
# of Homework Errors 6 10 14
Make a scatter plot of the data.
Draw a line of best fit.
Find an equation of the line.
Use you equation to estimate how many errors a student would make if they did not sleep for 45 hours.

15. Homework!