Transforming to Achieve Linearity (C10 BVD) AP Statistics Review Transforming to Achieve Linearity (C10 BVD)

Answer: Straighten it! Or: Use a curved regression model like QuadReg, PwrReg If not specified, choose to Straighten. How do I model the relationship between data if the scatterplot isn’t “straight”?

How to Straighten a Curve If shape is: levels off Try: square the y-list If shape is: possibly half a parabola or a parabola Try: square root the y-list If shape is: all positive y’s, curved Try: take log of y’s (or ln) Others to try: -1/sqrt(y), -1/y, log x, log x and log y These are listed roughly in order of “power”: If a re-expression bends the curve more, go the other way, if it bends it too far the other direction, go back up the list. Some version of log re-expression often works. It can take a few (or several) tries to find a good “straightener”. As you gain experience, you will become faster. How to Straighten a Curve

Once straightened, you can do LinReg and do all the analysis as before, but when you write the equation, remember your re-expression. For example, if your y-list became log(y), then your equation is log(y)-hat = mx+b When using the equation, you may have to “undo” a log, etc. to get actual predicted y’s. Writing the Equation