“Numbers are like people… torture

them long enough and they’ll tell

you anything...”

Linear transformation

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

Activity 1

HOURSNumbe

rs1.0 1.81.5 2.42.0 3.12.5 4.33.0 5.83.5 8.04.0 10.64.5 14.05.0 18.0

Graph and find the linear regression line for the

number of bacteria present after 3.75 hours.

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

HOURSNumbe

rs

1.0 1.8

1.5 2.4

2.0 3.1

2.5 4.3

3.0 5.8

3.5 8.0

4.0 10.6

4.5 14.0

5.0 18.0

Applying a function such as the logarithm or

square root to a quantitative variable is

called transforming or re-expressing the data

Linear Transformation

Properties of Logarithm

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

However, our focus will be on:

power and

logarithmic transformation

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

salmon

A. Scatterplots

B. Linear Model

Weight = -299.0423 + 25.2024 (length)

Correlation = .95

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

A. Scatterplots

B. Linear Model

Weight = 4.0658 + .o1467 (length)3

Correlation = .99