AP Statistics Section 4.1 ATransforming 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 length3 (x),

in L3 vs. weight (y) in L2. Is the scatterplot linear? ____

1

3

Highlight L3 ENTERL1 ^ 3 ENTER

yes

Calculate the LSL on the transformed points (length3, weight) and determine r2.

995.

)h.015(lengt4.066 weightPredicted2

3

r

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

)5.31(015.066.4 3weightpredicted

904.472weight

Now we’ll look at the residual plot.