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Chapter 10 Re-expressing Data: Get it Straight!!

Chapter 10 Re-expressing Data: Get it Straight!!. *Straightening Relationships *Goals of Re-Expression *Ladder of Powers. Straightening Relationships. To use a linear model, the scatterplot must be straight enough Check scatterplot AND residual plot

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Chapter 10 Re-expressing Data: Get it Straight!!

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  1. Chapter 10Re-expressing Data: Get it Straight!! *Straightening Relationships *Goals of Re-Expression *Ladder of Powers

  2. Straightening Relationships • To use a linear model, the scatterplot must be straight enough • Check scatterplot AND residual plot • We have the ability to straighten data so that we can use a linear model for scatterplots that do not satisfy the straight enough condition

  3. MPG and Weight

  4. A Hummer weighs about 6000 pounds. What is the predicted MPG?

  5. MPG vs Gallons/100 Miles Change 25 mpg into gallons/100 miles

  6. Scatterplot: gal/100 miles and weight

  7. Revisit the Hummer What is the predicted fuel efficiency for a Hummer? (6000 lbs) The new model predicts that a 6000 lbs Hummer would get 9.7 gallons/100 miles Convert that back into MPG

  8. Not Sold?? You regularly use re-expression What units do you use to talk about how fast you went on a bike? What units do you use to talk about how fast you run?

  9. Goals of Re-Expressing • 1) Make the distribution of a variable more symmetric • easier to compare centers • if its unimodal you could perhaps use the Normal Model

  10. Goals • Make the spread of several groups more alike • groups with similar spreads are easier to compare • centers may be different

  11. Goals • Make the form of a scatterplot more nearly linear • linear models are easier to describe

  12. Goals • Make the scatter in a scatterplot spread out evenly rather than following a fan shape • having an even scatter is a condition of many methods in Stats (we will see later)

  13. Ladder of Powers Use to systematically re-express data The farther you move from 1 (original data) the greater the effect on the data Certain re-expressions work better for different types of data

  14. Ladder of Powers

  15. Plan B: Attack of the Logs Try taking the logs of BOTH the x values and the y values.

  16. Example Let’s try to predict the shutter speed based off the f/stop of a cameras lens. Enter data

  17. What Can Go Wrong? • Don’t expect your model to be perfect • Don’t choose a model based on R2 alone • always check the residual plot • Watch out for scatterplots that change direction • Watch out for negative values • Rescale years • Don’t stray too far from the ladder

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