1 / 16

Continuing the Line of Best Fit

dieter
Télécharger la présentation

Continuing the Line of Best Fit

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. A completely black dog was strolling down Main street during a total blackout affecting the entire town. Not a single streetlight had been on for hours. As the dog crosses the center of the road a Buick Skylark with 2 broken headlights speeds towards it, but manages to swerve out of the way just in time. How could the driver see the dog to swerve in time?

  2. Continuing the Line of Best Fit • as a Predictor • Interpolation • Extrapolation • Residuals Why does this look like a good Line of Best Fit?

  3. Line of Best Fit (Regression Line)Purpose • When scatter plots show what appears to be linear regression, we use a straight line to show the overall pattern of the data. • We can predict values from this mathematical model (y = mx+b) • Take your time to identify what x and y represent for each question

  4. Review of y = mx+b • m represents = ________________________ • The slope of a regression line is only a predicted rate of change, rather than therate of change. • b represents = ________________________

  5. Prediction • Interpolation – estimating predicted values between known values GOOD! • Extrapolation – estimating predicted values outside of known values BAD!!

  6. Practice problem A group of 10 students was selected at random and asked for their high school GPA and their freshmen GPA in college the next year. • Is there a linear relationship between the high school GPA and the freshmen GPA? • What is the predicted college freshmen GPA, if we know that the high school GPA of a student is 3.4? • Is this prediction “interpolation” or “extrapolation”? Why?

  7. Residuals • The distance between the points of a scatter plot and the Line of Best Fit. • A positive residual always falls above the line. A negative residual always falls below the line. • Examining the residuals helps assess how well the line describes the data Does a linear model (y = mx+b) describe the data? Residuals = Observed values – Predicted values

  8. The distance in redrepresents the residual value for each data point. • The residuals above would be positive. • The residuals below would be negative.

  9. From your packet: 9.3 Problem set #1 Line of Best Fit:

  10. Residual Plot – helps to see if a linear model (y = mx + b) is appropriate y Things to look for in a residual plot: • No pattern: “snow” • Even distribution above and below the x axis x

  11. 9.3 Problem Set #2

  12. 9.3 Problem Set #3

  13. Do #4 – 6 with your partners!

  14. 9.3 Problem Set #4

  15. 9.3 Problem Set #5

  16. 9.3 Problem Set #6

More Related