3. Logarithmic Transformations
To solve logs, you can use the log and ln buttons on your calculator. But
when x is in a log, you must rewrite it or “undo” or invert it.
You can rewrite the logs in exponential form:
logb x = y → by = x
log x = 2 102 = x = 100
(when there is no base, the log is in base 10)
ln x = y → ey = x
ln x = 3 e3 = x
4. Logarithmic Transformations
When you use logs to transform data to make a linear graph, you have two
options:
1. Use the log or natural log of the y variable (response variable) – log
transformation & exponential models. The graph will be the
explanatory variable x on the x-axis, and the natural log of the response
variable ln y or log y on the y-axis.
2. Use the log of both variables – power models using log transformations.
The x-axis is the log or natural log of the explanatory variable log x or
ln x, and the y-axis is the log or natural log of the response variable log
y or ln y.
5. Logarithmic Transformations
Reading & Interpreting option 1 - Log transformations on the response
variable y.
Pg. 773-775
If a variable grows exponentially, its logarithm grows linearly.
6. Logarithmic Transformations
Option 2 - Power Models with 2 log transformations
If a power model describes the relationship between two variables, a
scatterplot of the logarithms of both variables should produce a linear
pattern.
Pg. 778-779
7. Logarithmic Transformations
We can use our graphing calculators to model log transformations and
determine whether a log transformation is needed on just y or both x and y
to achieve linearity.
Enter the values of the explanatory data in L1 and the values of the response
variable in L2
Define L3 as the log of L1
Define L4 as the log of L2
To determine which model to use, graph a
plot of L1 vs L4, then graph a plot of L3 vs L4
We will use whichever is more linear.
Run Linear Regression – LinReg(a + bx) L3, L4, Y1
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