If the scatter is curved, we can straighten it Then use a linear model Types of transformations for x, y, or both: 1.Square 2.Square root 3.Log 4.Negative Reciprocal 5.Reciprocal Chapter 10: Re-expressing Data

The relationship between fuel efficiency (in miles per gallon) and weight (in pounds) for late model cars looks fairly linear at first:

A look at the residuals plot shows a problem:

We can re-express fuel efficiency as gallons per hundred miles (a reciprocal) and eliminate the bend in the original scatterplot:

A look at the residuals plot for the new model seems more reasonable:

Goals of Re-expression Goal 1: Make the distribution of a variable more symmetric.

Goal 2: Make the spread of several groups more alike, even if their centers differ.

Goal 3: Make the form of a scatterplot more linear and evenly spread.

Note: If the data has no 0 or negatives, log is very useful.

Why Not Use Curves of best fit? Slope and y-int of lines are easier to understand!

Chapter 10 Assignment #1 – 17 Odd