# 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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13 views

### Back transformation of mixed models

Need your help: I did my thesis about influence of parenteral nutrition on the liver with repeated measurements and missing data (retrospective aspect) so I used mixed models for statistical analysis. ...
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### Questions about log-log regression model including dummy variables [closed]

I have the following regression, where xi are continuous variables and d_i are dummy variables (four types in total): log(y)=-0.017-0.76log(x1)+0.21log(x2)+0.06d_1+0.33d_2+0.41d_3 Here are my ...
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### Unbounded function with finite integral [migrated]

I am facing the following condition in order to apply a theorem in a paper: $$\int_{\mathbb{R}}\left[\phi^{\prime}\left(|x|^2 / 2\right)\right]^4(1+|x|)^{-\nu_2} d x<\infty.$$ It is stated the if ...
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1 vote
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### Does log-transforming a slightly-skewed y variable make any sense?

I'm separately analyzing 5 subsets of my data and running multiple linear regressions with the same outcome variable in each. (I am also running a single regression with all the subsets and using the ...
1 vote
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### Log scale on two axis vs 1 vs none

I would appreciate some advice on the most appropriate way of displaying the behaviour between two variables: # of subscribers in the first month and # activity (combination of actions) I'm not sure ...
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### Log of a log-transformed variable

I have been suggested to use the log of a log-transformed independent variable (i.e., log(log healthcare expenditure)). I am not sure how would this make sense. Is this a standard practice (in the ...
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### Why using log transformation of target variable helps regression return positive values?

I am working on a linear regression model predicting the quantity of goods to order in the future. However, with some items, the model return negative values (despite the fact that all target values ...
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### Both quadratic and linear term are insignificant

I am trying to fit a model which has age as a control variable and mental health score as my dependent variable. I centered the age because 0 is not meaningful in my analysis. I tried age, age^2, log(...
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### negative values after log transformation

I need to find input demand for several food crops. Here I used profit function approach to find price elasticities. It is a time series data analysis. However, I have to normalize and find real ...
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### Interpretation of log-linear regression

The regression is $$\ln y = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + \varepsilon$$ I know there is an approximation, but what about the exact interpretation of $\beta_1$ in non-log terms of $y$? This ...
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### Log linear transformation in diff-in-diff (did_multiplegt)

I have a panel dataset of firms that take a treatment in different time periods and which may also stop being treated, or may not be treated at all. I am using the did_multiplegt in Stata. I want to ...
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### Log-Transform Values in the range of -400 to 400. Would adding a large constant matter for log-transform? [duplicate]

My data consists of score values in the range of -400 to 400. I am thinking of log-transforming them, but is it statistically wise for me to make 400 as a constant? ...
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### What can I say on scatter plots generated with log transformed variables? [closed]

Please imagine we got scatter plots revealing a (1)rising straight line (/), (2)horizontal line (-), or (3)u-shape line (U), after log-transforming (a)one of two variables, or (b)both variables. So, ...
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### Log-log linear model interpretation, when does the approximation not hold?

I read in the following post: Interpreting Log-Transformed Percentages in OLS that In a log-log model, such as $\log(y) = b_0 + b_1 \log(x)$, I know that with OLS the standard interpretation is a &...
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### Running a regression of sorts with data in different forms - logs, levels, percentages

This is my first question on StackExchange, and while I've looked at other posts related to similar things, I haven't found a fully satisfactory answer. My thesis is looking at some macroeconomic ...
1 vote
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### Does the P value need to be "back- transformed" after logging one variable in Regression analyse?

I have a data series, sediment concentration in water Vs Time. The data is not normal but I want to use regression and so have logged the sediment concentration (log10(x)). The residual and fit to ...
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### Question Concerning the Invariance of a Log-Transformed Normal Random Variable under Reciprocal Transformations

So I just started looking through through E.J. Gumbel's "Statistics of Extremes" (1958) and I came across a rather strange problem that I had never seen before. The problem is phrased as ...
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### log(x * constant) transformation

I am a conservation biologist and I am creating a new index to classify species extinction risk. The index ranges from one to zero, with scores closer to one representing a higher extinction risk. Due ...
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### dataset in log & lin-lin regression function vs. dataset not in log & log-log regression function: Why different results in R?

I've discovered by chance that R produces different results when using a dataset which has been first transformed by the natural logarithm and then loaded into R for analysis and when the dataset is ...
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### How do I interpret these results? [duplicate]

I have some data and have performed a long rank test using the survminer package in R: survdiff(Surv(survivaltime, status) ~ gene, data = data) I am effectively ...
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### How to adjust for lognormal distribution in linear regression when dependent variable is a ratio?

I am working on a model that uses a dependent variable (Damage ratio) that is a ratio composed of two other variables (Flood damage / market value). One of those variables follows lognormal ...
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### regression log transformation output with smaller than 1 unit increase

I have a question. I did a simple regression with the depended variable being logged log(x) = a + by Now that I have my outcome I am aware of how to transform it to a percentage change in the ...
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### How to interpret log likelihood [duplicate]

I am using negative binomial regression on panel data. I would appreciate help interpreting part of my regression table. The log likelihood is very low (~-7000) and doesn't change that much- does that ...
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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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### Is ln(y+Δy) == β0 + β1(X+ΔX) in log-linear/non-linear regression?

I came across the following in explaining the log-linear regression model. Given the model $\log(Y_i) = β_0 + β_1X_i + u_i$ The expected value of $\log(Y)$ given $X$ is $β_0 + β_1X$. So far, so good. ...
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### Robust regression after log-log transformation

I’m considering to do a robust regression after the dependent variable and two of the independent variables have undergone a log (ln) transformation. (Because of economic reasons.) The remainder of ...
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### Can I compare model output from GARCH and EGARCH when the EGARCH is log conditional variance?

I have used the rugarch package in R to construct a sGARCH and an eGARCH model, but have ...
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### Back-transformation of confidence intervals

I have read that I can simply back-transform my confidence intervals from my (mixed) linear models, which seems very handy for model interpretation. What I don't understand is why log-transforming the ...
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### Regression with independent variables as percentages [duplicate]

I'm trying to run a regression analysis where my dependent is number of deaths and some of my independent variables are things like: poverty rate (Ex - 0.16, 0.09), incarceration rates (Ex 0.0042, 0....
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### Log Transformation to treat outliers

I am trying to replicate a research paper as part of my Applied Econometrics course, and I came across a particularly vague statement in the reference paper. "Following Malmendier and Tate (2005),...
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### Which method of logarithmic transformation is correct to use in linear model?

I try to do a simple linear model with logarithmic transformation of y values. I found that depending on which method I use the results differ and I don't ...
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### Comparing RMSE/MSE of original data and log10-values of the same data

I want to see if my models work better on the original data or on log10 transformed data. But how can I do this? Normally I train the model, calculate the RMSE/MSE on the test data and compare these ...
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### How to handle a highly right skewed dataset without 'hurting' it too much?

I have a freemium mobile app usage dataset. I want to perform a regression with the average spending per month (continuous) as a dependent, and if they came via referral program (binary) as the ...
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### E(log(x)) to E(x) [duplicate]

Sorry if this is a straightforward question, but I have tried digging into econometrics book and cannot find anything about it. I worked on a model with ...
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### Should I use a two-tailed t-test to generate p-values?

I have a data set similar to the one below. The real data set has 89 values in each column. I'm looking at the expression of RNA between two different treatments (treatment $X$ and treatment $Y$). <...
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### Taking the logarithm of observational errors

I have a set of observational measurements, each with their unique +/- observational error. I need to take the logarithm of this set of data. My question is, to include the error bars in the logarithm ...
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### Is there an intuitive way to present or interpret log earnings when plotting predictive probabilities?

I am running a regression analysis that shows how earnings have changed across cohorts. I log my outcome (earnings) as it is the standard practice in my field. To ease the interpretability of log ...
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### Interpreting Impulse Response Function after first differences of logarithm transformation

I created an impulse response function from a VAR model. I used data transformed by taking the first difference of logarithms. I am now in trouble with giving a substantive interpretation of the scale ...
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### Can a natural logged control variable drastically change a regression?

Hello I am writing my undergraduate accounting & finance dissertation so my statistical knowledge is quite basic. So one of my OLS regressions has Firm value as the dependent and CSR as the ...
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### log transformation with the self-reported health score variables

With self-reported health scores (as a dependent variable) - such as CES-D for depression which typically ranges from 0 to 60, I was wondering whether log-transforming these scores would allow me to ...
1 vote
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### How to justify logarithmically scaled frequency for tf in tf-idf?

I am studying tf-idf (term frequency - inverse document frequency). The original logic for tf was straightforward: count of term t / number of total terms in the document. However, I came across the ...
1 vote
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### Estimating the log-space sigma (std) parameter of a lognormal distribution from its regular-space mean and variance

validaters, I've spent a lot of time on this issue and I can't figure it out yet. So, a lognormal distribution is being defined as follow: X=e^(μ + σ Z), where Z is ...
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### How to interpret linear regression with log10 dependent variable

I have run a linear regression in R where independent variable = X and dependent variable = log10(Y). The results indicate that r2 = 0.11 and p = 0.04. Now how can I calculate the percentage of ...
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### Formal way to test what kind of differencing is necessary?

I'm working on a project that concerns time series data for South-Africa. My series has 34 explanatory variables and only (!) 30 yearly observations. The analysis is meant to be high-dimensional, ...
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### Get Standard Deviation and Variance of log 10 data in Excel

In Excel, my data is between 0.000001 and 0.005 and treated as "logarithmic" so I transformed by log 10 (log10(x)) which are all negative. The Excel Var.P() and Stdev.p() functions can only ...
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### X intercept of a log-log linear model in R using lm ()

A linear regression on dependent and predictor variable was run on simulated data after log transformation. ...
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### Log-Log model errors are not normal

I am trying to model sales as a function of various variables (debt, number of employees, competitors etc.). For this I have transformed both dependent and independent variables using natural ...
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### is the % difference between 2 log numbers the same as for the corresponding real numbers?

I am editing a report that has a table showing average treatment effects expressed as [log(kg/ha)] - its about growing maize. The authors have compared treatment and control values of 7.42 and 7.10 ...