1. Fitting a Line to Data CCSS.Math.Content.8.SP.A.2 CCSS.Math.Content.8.SP.A.2 Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.

2. Lesson Preview Purpose of Drawing Lines of Best Fit Caution: Correlation and Causation Using the Eye to Find the Line of Best Fit – Practice Calculating the Equation an “Eyeballed” Line Using a Computer to Calculate a Line of Best Fit Honors: Using Means to Find the Line of Best Fit Conclusion Quiz

3. Purpose of Drawing Lines of Best Fit When two things (varibles) are related, we can collect data on them, and use a line to describe that relationship.  Ex: Age & Height or Income & Education When we are unsure if two variables are related, graphing them could help us judge if there is a relationship.

4. Purpose of Drawing Lines of Best Fit When two things (varibles) are related, we can collect data on them, and use a line to describe that relationship.  Ex: Age & Height or Income & Education When we are unsure if two variables are related, graphing them could help us judge if there is a relationship. A line of best fit (or "trend" line) is a straight line that best represents the data on a scatter plot. This line may pass through some of the points, none of the points, or all of the points. Our Example: Crystal finally saved up enough money to buy a car, $10,000. Now she gets to shop for the used car and wonders what kind of mileage she can expect in her price range. She found some data online showing the price of a used car and the Odometer reading (the part of the car that tracks miles). She decides to do some math to estimate the mileage for a 10,000 price. Independent variable x Dependent variable y

5. Caution: Correlation and Causation Does it make sense to find a relationship between the two things? If so, then proceed with graphing and finding your line! Example: A Pirate Shortage Caused Global Warming (www.buzzfeed.com)

6. Using the Eye to Find the Line of Best Fit – Practice

8. Calculating the Equation an “Eyeballed” Line (60,000, 12,000) (30,852, 15.590) Y 2 – Y 1 / X 2 – X 1 = m (15,590 - 12,000) / (30,862 - 60,000) = 3,590 / -29,138 = -0.1232 = m slope y = - 0.1232x + b 12,000 = - 0.1232 (60,000) + b 12,000 = - 7392.4 + b b = 19,392 y = -0.1232x + 19,392 10,000 = -0.1232x + 19,392 -9,392 = -0.1232x x = 76,233.76 miles

9. Using a Computer to Calculate a Line of Best Fit

10. Calculating the Equation an “Eyeballed” Line y = - 0.0984x + 18458 10,000 = -0.0984x + 18,458 -8,458 = -0.0984x x = 85,955 miles

11. Honors: Using Means to Find the Line of Best Fit

13. Conclusion By eye we calculated 76,233 miles for $10,000. By computer we calculated 85,955 miles. A difference of 9,722 miles. Estimate when circumstances allow. Using a computer to do this is easy! No substitute for a human brain when interpreting results!

14. Quiz

15. Birth year Life expectancy in years 193059.7 194062.9 195068.2 196069.7 197070.8 198073.7 199075.4 200077

16. Quiz SpeedFuel Efficiency 3240 6427 7724 4237 8222 5736 7228

17. Thanks for working so hard! Created by Miranda Nogaki Middle School Math and Science Teacher KoolLearning.com