Line of Best Fit 3.3 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 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.

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

Step 1: plot the points Price # of pics

Step 2: Draw the line

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

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=0.27 35 +𝑏 16=9.45+𝑏 𝑏=6.55

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

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.

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.

Homework!