“Numbers are like people… torture them long enough and they’ll tell you anything...” Linear...
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Transcript of “Numbers are like people… torture them long enough and they’ll tell you anything...” Linear...
![Page 1: “Numbers are like people… torture them long enough and they’ll tell you anything...” Linear transformation.](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649f275503460f94c3e8b7/html5/thumbnails/1.jpg)
“Numbers are like people… torture
them long enough and they’ll tell
you anything...”
Linear transformation
![Page 2: “Numbers are like people… torture them long enough and they’ll tell you anything...” Linear transformation.](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649f275503460f94c3e8b7/html5/thumbnails/2.jpg)
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
![Page 3: “Numbers are like people… torture them long enough and they’ll tell you anything...” Linear transformation.](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649f275503460f94c3e8b7/html5/thumbnails/3.jpg)
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.
![Page 4: “Numbers are like people… torture them long enough and they’ll tell you anything...” Linear transformation.](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649f275503460f94c3e8b7/html5/thumbnails/4.jpg)
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
![Page 5: “Numbers are like people… torture them long enough and they’ll tell you anything...” Linear transformation.](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649f275503460f94c3e8b7/html5/thumbnails/5.jpg)
Applying a function such as the logarithm or
square root to a quantitative variable is
called transforming or re-expressing the data
Linear Transformation
![Page 6: “Numbers are like people… torture them long enough and they’ll tell you anything...” Linear transformation.](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649f275503460f94c3e8b7/html5/thumbnails/6.jpg)
Properties of Logarithm
![Page 7: “Numbers are like people… torture them long enough and they’ll tell you anything...” Linear transformation.](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649f275503460f94c3e8b7/html5/thumbnails/7.jpg)
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
![Page 8: “Numbers are like people… torture them long enough and they’ll tell you anything...” Linear transformation.](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649f275503460f94c3e8b7/html5/thumbnails/8.jpg)
However, our focus will be on:
power and
logarithmic transformation
![Page 9: “Numbers are like people… torture them long enough and they’ll tell you anything...” Linear transformation.](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649f275503460f94c3e8b7/html5/thumbnails/9.jpg)
Punch these in...Average weight and length of harvested
salmon
![Page 10: “Numbers are like people… torture them long enough and they’ll tell you anything...” Linear transformation.](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649f275503460f94c3e8b7/html5/thumbnails/10.jpg)
A. Scatterplots
B. Linear Model
Weight = -299.0423 + 25.2024 (length)
Correlation = .95
![Page 11: “Numbers are like people… torture them long enough and they’ll tell you anything...” Linear transformation.](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649f275503460f94c3e8b7/html5/thumbnails/11.jpg)
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
![Page 12: “Numbers are like people… torture them long enough and they’ll tell you anything...” Linear transformation.](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649f275503460f94c3e8b7/html5/thumbnails/12.jpg)
A. Scatterplots
B. Linear Model
Weight = 4.0658 + .o1467 (length)3
Correlation = .99