Questions tagged [logarithm]
The logarithm of a number is the power to which the base must be raised to get the number.
689
questions
243
votes
4
answers
374k
views
When (and why) should you take the log of a distribution (of numbers)?
Say I have some historical data e.g., past stock prices, airline ticket price fluctuations, past financial data of the company...
Now someone (or some formula) comes along and says "let's take/use ...
- 14.8k
226
votes
8
answers
540k
views
In linear regression, when is it appropriate to use the log of an independent variable instead of the actual values?
Am I looking for a better behaved distribution for the independent variable in question, or to reduce the effect of outliers, or something else?
- 2,421
86
votes
6
answers
145k
views
Why is it that natural log changes are percentage changes? What is about logs that makes this so?
Can somebody explain how the properties of logs make it so you can do log linear regressions where the coefficients are interpreted as percentage changes?
- 1,067
64
votes
3
answers
80k
views
Interpretation of log transformed predictor and/or response
I'm wondering if it makes a difference in interpretation whether only the dependent, both the dependent and independent, or only the independent variables are log transformed.
Consider the case of
<...
- 3,147
44
votes
4
answers
21k
views
Why are log probabilities useful?
Probabilities of a random variable's observations are in the range $[0,1]$, whereas log probabilities transform them to the log scale. What then is the corresponding range of log probabilities, i.e. ...
- 4,025
34
votes
4
answers
77k
views
Expected value of a natural logarithm
I know $E(aX+b) = aE(X)+b$ with $a,b $ constants, so given $E(X)$, it's easy to solve. I also know that you can't apply that when its a nonlinear function, like in this case $E(1/X) \neq 1/E(X)$, and ...
- 341
32
votes
6
answers
20k
views
In statistics, should I assume $\log$ to mean $\log_{10}$ or the natural logarithm $\ln$?
I'm studying statistics and often come across formulae containing the log and I'm always confused if I should interpret that as the standard meaning of ...
30
votes
6
answers
11k
views
What are alternatives to broken axes?
Users are often tempted to break axis values to present data of different orders of magnitude on the same graph (see here). While this may be convenient it's not always the preferred way of displaying ...
- 3,788
28
votes
1
answer
49k
views
Expected value and variance of log(a)
I have a random variable $X(a) = \log(a)$ where a is normal distributed $\mathcal N(\mu,\sigma^2)$. What can I say about $E(X)$ and $Var(X)$? An approximation would be helpful too.
- 435
26
votes
2
answers
32k
views
Why log-transforming the data before performing principal component analysis?
Im following a tutorial here: http://www.r-bloggers.com/computing-and-visualizing-pca-in-r/ to gain a better understanding of PCA.
The tutorial uses the Iris dataset and applies a log transform prior ...
24
votes
2
answers
75k
views
How to transform negative values to logarithms?
I would like to know how to transform negative values to log(), since I have heteroskedastic data. I've read that log(x+1) ...
- 541
23
votes
2
answers
24k
views
Are log difference time series models better than growth rates?
Often I see authors estimate a "log difference" model, e.g.
$\log (y_t)-\log(y_{t-1}) = \log(y_t/y_{t-1}) = \alpha + \beta x_t$
I agree this is appropriate to relate $x_t$ to a percentage change in $...
- 231
22
votes
5
answers
6k
views
What is the intuitive meaning of having a linear relationship between the logs of two variables?
I have two variables which don't show much correlation when plotted against each other as is, but a very clear linear relationship when I plot the logs of each variable agains the other.
So I would ...
- 1,381
21
votes
1
answer
48k
views
do logs modify the correlation between two variables?
I am applying logs to two very skewed variables and then doing the correlation.
Before logs the correlation is 0.49 and after logs it is 0.9. I thought the logs only change the scale. How is this ...
- 537
20
votes
1
answer
14k
views
Log probability vs product of probabilities
According to this wikipedia article, one can represent the product of probabilities x⋅y as -log(x) - log(y) making the ...
- 365