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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Transformed independent variable into natural log results in a quadratic relationship [closed]

I'm a beginner in running regressions and I have this problem: I'm trying to regress the share of expenditure on alcohol and tobacco to total income on total income and a few other independent ...
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How to determine the best fitted model by AIC between lm(y~x),lm(log(y)~x), drc(y~x) in R

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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 ...
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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 ...
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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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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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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 ...
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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 ...
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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 ...
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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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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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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: \begin{equation} g_{i,t} = \alpha + \beta_1 \ln(...
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interpretation of loglog regression

It is common econometric disciplines to model an baseline + incremental quantity due to treatment. E.g baseline sales + incremental sales(due to marketing). It is common to deploy loglog models to ...
pete lewis's user avatar
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Can you do a log transformation for excess kurtosis, or is that mainly used for skewness?

I am planning on doing a regression analysis on STATA on the financial performance of private equity funds. On my descriptive statistics, I saw higher levels of kurtosis and skewness. I decreased ...
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How can I back transform the residuals of a decomposed time series , where I used log(x+c) transformation on the original data?

I did a time series decomposition on a series of Twitter activity data into trend, seasonal and residual component. I checked the distribution of the residuals when fitting a linear model to the time ...
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Reducing Variance in Estimating the Exponential Average of Random Variables

Imagine we have a random variable called X, and the function form of the probability density for X is unknown. Now, I'm interested in finding the average value of the exponential of X, denoted as E[...
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GLM with log link vs linear regression with logarithmic transformation parameter estimation

I am trying to calculate the parameter estimates of GLM with log link and normal distribution and the linear regression with logarithmic transformation. For the first I get the total derivative of the ...
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Log Transforming variables already in percentage [duplicate]

I'm running a regression analysis and I'd like to know if log transforming a percentage value is ok. My y-values are already in percentages and my x-values in absolute numbers. But I'd like to know by ...
Allan's user avatar
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Should I use log transformation on Target Encoding values ​to avoid heteroscedasticity?

The dataset I'm working with contains categorical variables with several classes. To do its pre-processing I chose to use Target Encoder. With numerical variables I used MinMaxScaler. When training ...
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How do I interpret an independent variable which is a log(%)? [duplicate]

My linear regression is: School's average test score ~ log(%FSM) %FSM = the percentage of pupils at the school who are eligible for free school meals (an indicator of low socio-economic status). The ...
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Interpreting linear mixed effect model results with log transformed dependent variable and log transformed predictor w/ normal predictors as well

I have a linear mixed effect model that I built using longitudinal country level data to help me predict TB incidence based on country level diabetes prevalence, HIV incidence, prevalence of ...
TBResearch's user avatar
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What does it mean if both log-log and semi log y transforms both linearise my data

I am running some least squares linear regression on nonlinear data. I considered linearising by taking the log of both the IV's and DV and also by only taking the log of the DV. Both linearise the ...
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How to use partial correlation on compositional (counts) data? (e.g., as described in Erb et al. 2020)

I've read through this paper: https://www.sciencedirect.com/science/article/pii/S2590197420300082 Which introduced me to the concept of partial correlation. I typically use Proportionality when ...
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Method of moments for the Logarithmic/Log-Series distribution

I'm looking for some more insights in applying the method of moments for the Logaritmic (or also called Log-Series) distribution. The Logarithmic distribution only has one distribution parameter $0 &...
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Interquartile range when back-transformed mean on log-scale is not equal to median on normal scale

I have 2x10 observations that follow a non-normal distribution. They are perfectly distributed on log-scale. From what I've learned, the back-transformation of the mean on log-scale should be a "...
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Interpreting log-transformed ARIMA Coefficients in R

I am fitting an ARIMA model to do interrupted time series analysis on cancer rates. I have log-transformed the data for fitting for stability and because this is typical with cancer rates, but I am ...
Todd Burus's user avatar
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In R Limma's `normalizeMedianValues` function, why is its operations preceded with a log transformation followed by an exponential transformation?

In the function normalizeMedianValues in the package limma, column counts are normalised such that their column medians are ...
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