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Re-expressing Data

Re-expressing Data. Straightening a curved scatterplot. Suppose this happens to you…. You make a scatter plot on your calculator and plot the LSRL. It looks like a pretty good fit, and r = 0.997. But then, when you plot the residuals, you get this. Uh-oh, now what do we do???.

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Re-expressing Data

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  1. Re-expressing Data Straightening a curved scatterplot

  2. Suppose this happens to you… You make a scatter plot on your calculator and plot the LSRL. It looks like a pretty good fit, and r = 0.997. But then, when you plot the residuals, you get this. Uh-oh, now what do we do???

  3. What do you do when a linear model is NOT appropriate? We transform our data values using mathematical functions to see if they fit better than a straight line. You can take the logarithm of the x values, take the logarithm of the y values, take reciprocals, take square roots, etc. To keep you organized, your textbook gives some guidelines…

  4. Using logarithms to straighten out a scatter plot

  5. The Ladder of PowersOther functions might work too…

  6. Remember… • Finding a good functional model is a guess-and-check process. • There is no such thing as a perfect model. • You are looking for one that is simply good enough… • Let’s try an example…

  7. Linearize the data and make a model for world population… • Enter this data in L1 and L2 and plot the points. What do you notice? • Now try making L3 by using log(L2). • Plot L1 and L3 and now make the LSRL. • What is the predicted population for 2010?

  8. Linearize the data and make a model for light intensity… • Enter this data in L1 and L2 and plot the points. What do you notice? • Now try making L3 by using a function of L2. What should we use? • Plot L1 and L3 and now make the LSRL. • What is the predicted intensity for 12 feet?

  9. Linearize the data and make a model for mortgage amounts at Republic National Bank… • Enter this data in L1 and L2 and plot the points. What do you notice? • Now try making L3 by using a function of L2. What should we use? • Plot L1 and L3 and now make the LSRL. • What is the predicted mortgage level for 1990?

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