# 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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### Rescale measures of association for meta-analysis (e.g., log-transformed independent variables)

I am carrying out a meta-analysis of studies evaluating the association between blood levels of specific environmental pollutants and health outcomes (binary). Some studies reported OR/RR/HR for ...
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### log transform left data in r

I am having trouble finding the transformation operation for left/negatively skewed data. The catch? All of my values are between 0 and 1. As such, trying the standard log10 transformation command ...
1 vote
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### Rejection sampling method in tail of truncated exponential distribution (answered)

See edit below as question has been answered. I want to sample from an exponential distribution with parameter $\lambda>0$ truncated in the tail between $a>0$ and $b>0$, such that $b>a$, ...
186 views

### Back Transforming log-log Model for Prediction

I have a model that is log-log and I would like to make raw predictions of $Y$ with it: $\ln(Y) = B_0 + B_1\ln(X)$ All answers and articles I have found concerning back transforming for prediction ...
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### How to do log subtract (just like logsumexp) with probabilities? [closed]

To subtract a small probability from another, this answer has constraint on log probabilities l1 > l2: Subtracting very small probabilities - How to compute? but I need a function that works for ...
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### Interpreting log transformed variables in a regression [duplicate]

I am very confused about the interpretation of log transformed variables in a regression. For example, I have a log-level model with a B0=4.95 and B1=-1.07. So my model would be log(y)=4.95 - 1.07X. ...
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### Is the exponent of the MAD (Median Absolute Deviation) of log transformed Data measuring the relative distance from median in the untransformed data?

I want to confirm whether taking the Exponent of the MAD of Log Transformed Data gives me a measure of relative distance from median of the original untransformed data. So say I have a MAD of 0.2 for ...
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1 vote
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### How to interpret a regression table with logged DVs?

I'm writing a research paper and am using R for my quantitative analysis. I'm using OLS regression and have needed to perform a log transformation on my dependent variables for linearity however I don'...
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1 vote
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### Can we find a variance formula in terms of the log of the density? ($f(t) = e^{u(t)}$, need variance in terms of $u$)

Given a density $f(t)$, say over $t\in \mathbb{R}^n$ absolutely continuous with Lebesgue measure. Write $u(t) = \log(f(t))$ taking values in $[-\infty, \infty)$ so $f = \exp(u)$. Can we find a general ...
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### plotting log-transformed data, but running statistics on raw data?

I intend to compare differences between means of eight groups. The differences between some of the means are only visible when I plot (in a box plot) the log-transformed data. However, I am unsure as ...
1 vote
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### Simple example of Log-Sum-Exp trick for continuous case

I am trying to confirm my understanding of how to apply the [Log-Sum-Exp trick to recover a posterior distribution from a log-posterior distribution. I want to consider a simple example from a model I ...
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### Recovering normalized posterior distribution from log-posterior

For a Bayesian estimation problem that I am working on, where I update the log-posterior (many times based on data) instead of the posterior itself using Bayes rule. I find the following (rather ...
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1 vote
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### Can log2 be substituted with ln in logDice association measure?

I am currently doing collocational analysis in the Russian National Corpus, to be precise the Russian national news subcorpus, to see what is the most significant collocates of the lemma "gay&...
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### Is there a statistical reason why I have diagonal lines in log2FC correlation plots?

I have created a de novo RNA-seq assembly using Trinity with samples from 4 treatment groups and then ran a DEG analysis on each pairwise combination of the 4 groups. Then, I looked at how DEGs that ...
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### Optimal Conditional Distribution for Minimising Information-Theoretic Expression

Consider two countable sets $\mathcal{X}$ and $\mathcal{Y}$. I aim to find the conditional distribution $P_{Y|X}$ that minimizes the following expression for any $x \in \mathcal{X}$ \sum_y P_{Y|X}(y|...
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### Adapting two-sample $t$-test of a ratio for log transformation

I have some data, belonging to paired groups $A,B$. From each group I get a non-negative statistic $d^A,d^B$ which is averaged on all samples in group. My interest is in the ratio $\frac{d^A}{d^B}$, i....
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### Log transformation uses

I am trying to understand how the migration of a male member affects the number of hours spent by left-behind women in various agricultural and non-agricultural activities. I used a simple OLS model ...
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### Standard error calculation of intercept in logarithmic line equation?

I have a line equation log(y) = mlog(x) + log(c) for which I have plotted log(x) vs log(y) scatter plot using the given x and y values then performed linear regression to get best fit line. Using ...
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### How to construct confidence intervals for difference of means in logs

I have estimated an OLS model and a Negative binomial model of ln housing search (ln S) per unit (for instance, the average number of visitors per house or bidders per house) as a function of ...
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### Detrending and data transformation to logarithm can be done together?

I want to get the effect of bitcoin price changes on foreign currency price. The third variable is inflation, which is an explanatory variable. Should variables be detrended before regressing? Is it ...
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### Do you need to exponentiate an inverse hyperbolic sine

I have the following model: Yi = β1 + εi whereby Y is the inverse hyperbolic sine of the proportion of i county that is under the poverty threshold and β1 is a binary treatment variable. If I end up ...
1 vote
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### Deriving the Exact Percentage Change Formula in Logarithmic Models

I have been studying the relationship between logarithmic changes and percentage changes in the context of regression analysis. I understand that when working with small changes, the change in the ...
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### Conversion of log-transformed SD

In a meta-analysis of some research work, there are many situations in which the literature reported the mean values and their corresponding standard deviations in log-transformed forms. The question ...
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### Deriving log-likelihood contribution involving fixed effects (panel model)

I would appreciate some help with the following problem: We have the following panel model: $y_{it} = h(x_{it}\beta + c_i) + \epsilon_{it}, \quad t=1,\ldots,T, \quad i=1,\ldots,N$ where \begin{align*}...
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### Why use log per-million count when analyzing corpora?

This might be such a trivial question for you, but please bare with me as I don't have background in statistics. So I am curious about corpus linguistics, and especially in this case how corpora is ...
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### An interesting observation regarding the log transformation of data

I stumbled upon something interesting while attempting to do a log transformation for some data (with zeros) today. It seems that there must be a good reason for this that I'm just not seeing. I'm ...
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### Can the Log of PR AUC curve plot be any useful?

I was doing some tests regarding my PR curve for 2 different models (first image), and I got the idea of ploting the log of those curves (second image) to see if there were any insights that I could ...
1 vote
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### Applying Tangent Lines to Log-Scaled Data for Outlier Detection: Seeking Statistical Theories and Models

I've analyzed the view counts for a YouTube channel's videos (just for example), sorting them by views (on the left) and drawing a tangent line to approximate the central trend on a logarithmic scale (...
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### Diffrence in logs vs. a % changes in econometrics: why is the dif log approvimation almost always used when the exact quantity is easily available?

I have observed that in econometrics work people almost always use the difference in logs rather than the actual percentage change. This makes no sense to me. I understand that the difference in logs ...
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1 vote
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### Optimal method for estimating geometric mean ratio using Bayesian log transformed data

I'm working on a Bayesian analysis with a categorical variable involving two groups (A vs B). I'm seeking advice on the best method to compute the geometric mean ratio (GMR) together with the highest ...
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1 vote
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### Creating a confidence interval for the natural log of the proportion of successes [duplicate]

In a random sample of n subjects with n being very large, let X be the number of successes. Now I want to create the confidence interval for the natural log of the proportion of successes. Can I ...
61 views

### Log transformation leading to extremely negative R-squared and extremle values for MSE

I have a set of data and I am using this code on it: ...
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### Dealing with 0's in loglog regression by using indicator functions I(x > 0)?

Assume we want to estimate the following model $y = e^{\beta_0} * x_1^{\beta_1} * x_2{\beta_3}$ which we can linearize into $\log(y) = \beta_0 + \beta_1 * \log x_1 + \beta_2 * \log x_2$ Assume that ...
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### loglog regression with 0's in IV's

Assume we have 2 predictors $X_1$ and $X_2$ and an outcome $Y$ that we wish to model with the following function $y = e^{\beta_0} * X_1 ^{\beta_1} * X_2^{\beta_2}$ Also assume that we have some priors ...
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### R: boundary (singular) fit: see help('isSingular') with lrem model - only when transforming data to log

I am trying to run a lmer model on my dataset. My dataset : str(tabfi) ...
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### How to report my log transformed (+1) data?

Say that I have a variable with lots of 0 values that needs log-transforming so I do log(variable+1) to transform it. How do I write that in my methods section as opposed to just 'the data was log-...
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### Interpretation of log-transformed (simple) regression models - confirmation requested

I am ashamed to admit I never questioned this while obtaining my bachelor's in statistics but it's coming up again in grad school and I'm now realizing that I've been using approximations for ...
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### Interpretation of estimates for 2 categorial factors and their interaction

I selected the best fitted gamlss model for my data : gamlss(formula = Ratio ~ PROTECTION * JOUR, nu.formula = ~JOUR, family = BEINF, data = D_E1, trace = FALSE) I want to interpret the output of ...
1 vote
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### Dense network can't learn a horizontally shifted log?

I've lately ran into an interesting problem, trying to teach a dense network a seemingly simple monotonous function- to regress a logarithmic function; When this function was centered around 0 it ...
1 vote
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### Kernel Density Estimation on a Log-Scale: Log Transformation vs. Geometric Space

I’m working on a project where I need to plot a Kernel Density Estimation (KDE) on a log-scale x-axis. I’ve come across two different methods and I’m unsure which one would be more appropriate for my ...
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### Always higher R squared after log transformation

lately I lost access to SPSS and instead of using Python or R, I tend to perform analysis using a free software called Jamovi. The thing is, this software doesn't have the different non-linear ...
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### How to know the sample arithmetic mean and standard deviation if I know the mean and the deviation of the logarithm of the observations

For a sample, I know the sample size, and the mean and standard deviation of the values ​​transformed using the natural logarithm. I need to calculate the mean and standard deviation of the original ...
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1 vote
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### How to transform STDEV of a numerical value to logarithmic value? [closed]

I have the following question: I have the average and STDEV values of variable. To transform this to Log10 scale, I directly apply the logarithm to the average. Can I do the same with the STDEV? ...
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### Interpretation of parameters in loglog-regression with scaled variables

Consider e.g the model $y = e^{\text{trend} + \text{seasonality}} \cdot \prod_{k \in \text{channels}} x_k^{b_k}$ where $i$ constrained $0 < b_k < 1$ (to capture diminishing marginal returns) ...
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### Are there any theoretic or computational criteria to apply log transformation on a sample dataset?

I am developing an R shiny app that contains more than 1,000 variables as choices for the user. It plots a choropleth map and an histogram. However for many of those, the visual information is ...
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### How to find the equation on a log-log scale plot (in R)?

I have plotted about 40 000 polygons (topographic depression dataset data) according to their area and volume (see plot below) by the code below: ...
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1 vote
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### Log specification in regression model

I'm working with a basic linear regression model, and I have a question about the specification of the predictor. Consider this basic regression model: g_{i,t} = \alpha + \beta_1 \ln(...
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