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 twovariable 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 ___________
transforming or
re-expressing the data.
____________
The transformations we will study
are __________
power
logarithmic and ______
transformations. These
transformations change the scale
of measurement that was used
when the data was collected.
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?
____
no Is there a pattern? _____
yes Since there is a
pattern, let’s try to “straighten” the data.
Since length is __
1 dimensional and
weight (which depends on volume) is
3 (x),
__
dimensional,
let’s
graph
length
3
in L3 vs. weight (y) in L2. Is the
scatterplot linear? ____
yes
Highlight L3 ENTER
L1 ^ 3 ENTER
Calculate the LSL on the transformed
points (length3, weight) and determine r2.
Predicted weight  4.066  .015(length )
3
r  .995
2
Predict the weight of an Atlantic
Rockfish that is 31.5cm long.
predicted weight  4.066  .015(31.5 )
3
weight  472.904
Now we’ll look at the residual plot.