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Published byCarlos Farrell Modified over 3 years ago

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Re-expressing Data Straightening a curved scatterplot

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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 = But then, when you plot the residuals, you get this. Uh-oh, now what do we do???

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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…

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Using logarithms to straighten out a scatter plot If the data looks exponential… Xlog(Y) If the data looks logarithmic… log(X)Y If the data doesnt straighten out with either of these… log(X)log(Y)

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The Ladder of Powers Other functions might work too… 2Square the data values, or y 2 1The original data values 1/2The square root of the data values 0Not the zero power, but the logarithm of either x or y or both -1/2The reciprocal square root of y The reciprocal of y.

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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… Lets try an example…

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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? YearPop. (millions)

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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? Distance (ft)Candlepower

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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? Year$ (millions)

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