# 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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### How to improve upon my composite index from right skewed data in R

Do you have any advice for creating an index from right skewed-data with several extreme outliers in R. I am new to creating indexes for analysis and could use some advice on how to do it in R. So ...
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### Can a “proportionality” metric designed for compositional data analysis be used for non-compositional representations of the data?

I have been diving deep into compositional data analysis. Here is a great thread containing a conversation with Thomas Quinn, who is pushing this type of research in microbiology, about some ...
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### Reasoning for tranforming linear model to log-level

I have a multiple linear regression model and found that my error terms are not normally distributed. When looking at the histogram of the dependent variable, it looks like below. I am not sure how ...
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### How to deal with indeterminate values in a linear regression?

I have some experimental data over the time. I need to fit this data to two models in their linearized forms: Model 1: $\ln (a-y)=\ln a-b\ t$ Model 2: $\dfrac{t}{y}=\dfrac{1}{k\ d}+\dfrac{t}{c}$ My ...
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### Should I use log transformation for my multiple regression? [duplicate]

My response variable is a bank interest rate, and I have as explanatory variables: a concentration index, the non-payment rate and the basic interest rate of the economy: ...
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### Confidence intervals for a log transformed dependent variable

I have a basic OLS regression equation with the dependent variable ($Y$) log transformed and a binary independent variable ($X$). In order to correctly interpret coefficient $\beta$ for the $X$ ...
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### why arima uses differencing transform not the log transform to make data stationary?

I am currently working on time series project and i am naive. I would like to ask, there exist strict stationary, differencing stationarity. If i understood correct the first order differencing ...
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### Different forms of Stirling's approximation

I have Stirling's approximation in the form: Please could someone explain how this is equivalent to the form: log(n!) = nlog(n) - n for large n?
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### When is Log-Cosh Loss used?

I have seen people speaking of the Log-Cosh Loss that is 2 times differentiable and mimic the Mean Absolute Error goers 0. It is therefore useful for algorithm that need hessian. Hence I'm not sure ...
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### What would a suitable justification be to use 'log(exports)' as a dependent variable instead of solely 'exports'? [duplicate]

I am doing a diff-in-diff analysis, looking at whether a regulation had an impact on British pollution-intensive exports. Initially I used 'total exports of pollution-intensive goods' as my dependent ...
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### Summation of Log Probabilities

I am trying to implement the following: where the right part returns a probability between 0 and 1. Regarding the product, the authors of the respective paper note: Due to numerical precision ...
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### log likelihood function causes huge differences with similar inputs

I am not sure whether there is a solution to this problem, but here goes. My problem is that in my function, I am taking log of a matrix and then taking its mean, and doing this for two very similar ...
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### log-log plot and straight line fit

I think this is a silly question, but I'm using a very simple data to be fit using a power law equation. If I use a non linear fit (log-log line), I got some parameters that don't correspond if I ...
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### what is the distribution of the log of a normal distribution? [duplicate]

if you exponentiate a normal distribution, Y=exp{X} where X is a normally distributed random variable (RV), then Y is log-normally distributed. What is the ...
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### Augmented Dickey-Fuller test interpretation before and after log transform the data

I have apply the stationarity test to a stock's adjusted price by using the Augmented Dickey Fuller Test with the program R. That is the output from ...
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### Why to use log while calculating probability of an email being spam?

I worked on a basic spam email project (Naive Bayes classifier with Laplace smoothing). In source code, to calculate probabilities of spam or ham, log of the final result is being used. Why is it ...
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### How to interpret different shapes of a log-log graph?

I have a number vs size plot for two species. I'm trying to figure out through some basic plotting what shapes it could take-up. I suspected some sort of hump shaped curve where size peaks at ...
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### Regression: Is it bad practice to use log difference as approximation for % difference when changes are large?

I'm running a vector autoregression model with quarterly IPOs as one of the variables. Since the number of IPOs isn't stationary, I took the log first difference to make it stationary. However, I ...
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### Why is the expected gradient of a density not parallel to the expected gradient of the log density?

I'm confused by a seemingly counter-intuitive property of the interaction between distributions, log transforms, expectations and gradients. Suppose I have some distribution over random variable $x$ ...
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### log values in coxph model?

I have a data frame of gene expression values (sequencing). When I do CPM-normalization without doing log2, I get much "better" (lower) p-values compared to when I do log2-CPM. What is the ...