Transcript 39. PERFORMING LINEAR TRANSFORMATION

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
Number
HOURS
s
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
Graph and find the linear
regression line for the
number of bacteria present
after 3.75 hours.
Number
HOURS
s
1.0
1.8
1.5 regression
2.4
Linear
2.0
3.1
2.5
4.3
3.0
5.8
Scatter plots
3.5
8.0
4.0
10.6
4.5
14.0
Residual plots
5.0
18.0
Hours = -4.2744 + 3.9433 (bacteria)
Predicted number of
bacteria after 3.75 hours
2.024 bacteria
IS THIS AN
ACCURATE
PREDICTION?
Linear Transformation
Applying a function such as
the logarithm or square root
to a quantitative variable is
called transforming or reexpressing the data
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
3
(length)
A. Scatterplots
B. Linear Model
Weight = 4.0658 + .o1467 (length)3
Correlation = .99