1. 4.1 Transformations

2. Why do we transform? Purpose of transforming is to achieve linearity
Once linear, can use LSRL to make predictions
transforming/re-expressing—when applying a function such as logarithm or square root to a quantitative variable

3. Rockfish Tournament
Organizing a fish tournament where prizes are rewarded to the heaviest fish caught
Know fish will be measured and released
Know using delicate scale while fish is floppy around is not accurate
Easier to measure length—need a way to convert length to weight

4. Rockfish Tournament
Length (L1)
Weight (L2)
5.2 2
28.2
318
8.5 8
29.6
371
11.5 21
30.8
455
14.3 38
32.0
504
16.8 69
33.0
518
19.2
117
34.0
537
21.3
148
34.9
651
23.3
190
36.4
719
25.0
264
37.1
726
26.7
293
37.7
810

5. Rockfish Tournament Make a scatterplot—what is the pattern? R=
Make residual plot  What do you see?

6. Rockfish Tournament
Use the model and cube all the length measurements in table and recreate scatterplot (L3, L2)
L3 = (L1)^3

7. Rockfish Tournament What is LSRL on transformed points? What is r? r2?
So _______of the variation in the weight of Atlantic Ocean rockfish is predicted by the LSRL given length3.

8. Rockfish Tournament
Now make original scatterplot (L1, L2) with new LSRL equation (make x^3)
Now what would be the weight of a fish 36 centimeters?

9. Pg 265 #2 a) Make a scatterplot of data. Describe what you see
Length (cm)
Period (s)
16.5
0.777
17.5
0.839
19.5
0.912
22.5
0.878
28.5
1.004
31.5
1.087
34.5
1.129
37.5
1.111
43.5
1.290
46.5
1.371
106.5
2.115
b) Find LSRL. Is it a good model for the data?
c) Pendulum should be proportional to the square root of the length
d) What is the equation of LSRL? How well does it fit transformed data? Justify using residual plot and r2.
e) Predict the period of an 80 cm pendulum

10. HW: pg 266 #3