Presentation on theme: "Straightening a curved scatterplot"— Presentation transcript:
1Straightening a curved scatterplot Re-expressing DataStraightening a curved scatterplot
2Suppose 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???
3What 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…
4Using logarithms to straighten out a scatter plot If the data looks exponential…Xlog(Y)If the data looks logarithmic…log(X)YIf the data doesn’t straighten out with either of these…
5The Ladder of Powers Other functions might work too… 2Square the data values, or y21The original data values1/2The square root of the data valuesNot the zero power, but the logarithm of either x or y or both-1/2The reciprocal square root of y-1The reciprocal of y.
6Remember…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…
7Linearize 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)1950251919552755196030201965333419703691197540661980443019854825199052551995566220006057
8Linearize 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)Candlepower2531.2584.3833.61021.1159.5205.3253.4
9Linearize 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)19701.219722.519742.919763.119785.819808.3198210.8198414.7198621.8198829.7