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!