1. “Numbers are like people… torture them long enough and they’ll tell you anything...” Linear transformation

2. On this chapter, we will learn... Explain what is meant by transforming data Discuss the advantages of transforming linear data Tell where y=log (x) fits into the hierarchy of power transformation Explain the ladder of power transformation Explain how linear growth differs form exponential growth

3. Activity 1 HOURS Number s 1.01.8 1.52.4 2.03.1 2.54.3 3.05.8 3.58.0 4.010.6 4.514.0 5.018.0 Graph and find the linear regression line for the number of bacteria present after 3.75 hours.

4. Hours = -4.2744 + 3.9433 (bacteria) Predicted number of bacteria after 3.75 hours 2.024 bacteria IS THIS AN ACCURATE PREDICTION? Linear regression Scatter plots Residual plots HOURS Number s 1.01.8 1.52.4 2.03.1 2.54.3 3.05.8 3.58.0 4.010.6 4.514.0 5.018.0

5. Applying a function such as the logarithm or square root to a quantitative variable is called transforming or re- expressing the data Linear Transformation

6. Properties of Logarithm

7. First steps in transforming In unit of measurement: Celsius to Fahrenheit (in temperature) Miles to Kilometers (in distance) Pounds to Kilograms (in weight) Linear transformation

8. However, our focus will be on: power and logarithmic transformation

9. Punch these in... Average weight and length of harvested salmon

10. A. Scatterplots B. Linear Model Weight = -299.0423 + 25.2024 (length) Correlation =.95

11. Now let’s transform the model by taking the cube of the lengths and then graph the weight versus length with this transformation Weight = a x (length) 3

12. A. Scatterplots B. Linear Model Weight = 4.0658 +.o1467 (length) 3 Correlation =.99