Questions tagged [logarithm]
The logarithm of a number is the power to which the base must be raised to get the number.
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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 ...
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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?
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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
<...
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Interpreting log-log regression with log(1+x) as independent variable
Is interpreting log-log regression with log(1+x) as independent variable the same as having log(x) as independent variable? 1% increase in x results in beta% change in y?
What is x has both negative ...
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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?
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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) ...
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How to interpret logarithmically transformed coefficients in linear regression?
My situation is:
I have 1 continuous dependent and 1 continuous predictor variable that I've logarithmically transformed to normalise their residuals for simple linear regression.
I would ...
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Reporting regression statistics after logarithmic transformation
I'm a bit troubled about how to report linear regression statistics after log transformation of the dependent variable.
I suppose I should report the transformed coefficient, but would they be easily ...
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Natural log approximation
I've got an equation that contains
$$x^p - 1$$
$x$ is any positive number (such as 2) and $p$ is a small positive number close to 0 (such as 0.001).
For some reason (that I may have known in High ...
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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.
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Interpretation of marginal effects in Logit Model with log$\times$independent variable
I am totally confused by statistics and I would be glad if you could help me.
I have a difficulties to interpret marginal effects in logit model, if my independent variable is log transformed.
I ...
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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 ...
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How to interpret log-log regression coefficients for other than 1 or 10 percent change?
I have read many threads here on how to interpret coefficients in a regression where the predictor and the dependent variable are log-transformed. Most give an answer for a one or ten percent change. ...
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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. ...
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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 ...
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