AP Statistics Section 4.1 A Transforming to Achieve Linearity

In Chapter 3, we learned how to analyze relationships between two quantitative variables that showed a linear pattern. When two- variable data shows a nonlinear relationship, we must develop new techniques for finding an appropriate model.

The process of changing the data mathematically to find a linear model is called ___________ or ____________ the data. transforming re-expressing

The transformations we will study are __________ and ______ transformations. These transformations change the scale of measurement that was used when the data was collected. logarithmic power

Example 1: Consider the average length and weight at different ages for Atlantic rockfish.

Use your calculator to draw a scatterplot of the data for length (x), in L1 and weight (y), in L2. Is it linear? ____ Is there a pattern? _____ Since there is a pattern, let’s try to “straighten” the data. no yes

Since length is __ dimensional and weight (which depends on volume) is __ dimensional, let’s graph length 3 (x), in L3 vs. weight (y) in L2. Is the scatterplot linear? ____ Highlight L3 ENTER L1 ^ 3 ENTER yes

Calculate the LSL on the transformed points (length 3, weight) and determine r 2.

Predict the weight of an Atlantic Rockfish that is 31.5cm long.

Now we’ll look at the residual plot.