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Line of Best Fit3.3 A
Goal
• Understand how to create a line of best fit by hand AND on the graphing calculator.
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”
Linear, but not a line
This is called a Scatter Plot.
By hand or Calculator
By hand is an estimate, but the calculator will give an exact line of best fit.
By Hand
1. 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 .3. Pick a 3rd point on the line, and plug it in for x and y in y=mx+b. Solve for b.
Example
• A photo studio is offering year book photos.
• Find the equation for the line of best fit.
# of pics 44 31 24 15Price ($) 19.00 16.00 13.00 10.00
Step 1: plot the pointsPrice
# of pics
Step 2: Draw the line
Step 3: Find the Slope
• Points on the line: (15,10) and (44,19)
Slope=
Step 4: Find the y-intercept
• Plug slope into the equation.
• Pick another point on the line. I will use (35,16).
• Plug into x and y.
Step 5: Plug m and b into the equation
On calculator
Called Linear Regression
1. Stat – edit – enter
2. Enter values from chart (be careful!)3. Stat – calc – LinReg – enter4. 2nd – 1 - , - 2nd – 2 - , - vars – y vars – enter –
enter.
Partner ProblemHours without Sleep
8 8 12 12 16 16 20 20
# of Homework Errors
8 6 6 10 8 14 14 12
1.Make a scatter plot of the data.2.Draw a line of best fit.3.Find an equation of the line.4.Use you equation to estimate how many
errors a student would make if they did not sleep for 45 hours.
Homework!
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