# 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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16 views

### 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 ...
11 views

### 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....
31 views

### 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),...
23 views

### 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 ...
13 views

### 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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42 views

### 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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65 views

### 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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64 views

### 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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1 vote
17 views

### 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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### How to interpret log a share in a log-log model

my dependent variable Y is a percentage number and I have transformed it additionally into a logarithmic form. How do you interpret the resulting coefficient on log(I(X^2)) in this log-log model? A 1% ...
1 vote
30 views

### 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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35 views

### 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 ...
17 views

### 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 ...
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### How to talk describe log-transformed values in manuscript text

I'm editing a manuscript that I'm a coauthor on, and we are dealing with essentially log-normal data, so all of our statistical analysis was done using log-transformed values. I'm just trying to find ...
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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
29 views

### 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 ...
23 views

### 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 ...
14 views

### 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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28 views

### 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 ...
58 views

### 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. ...
28 views

### 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 ...
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### why does log scale does not start at 0

I need help in understanding the curve shown in the image. As you can see in the image that I-V curves in (a) is for linear scale and it shows 0 Amps at 0 Volts. But for logarithm scale I-V curves in (...
236 views

### Geometric mean of log10 values

I have the following series of log10 numbers: ...
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### How do I find log likelihood function based on observations

Assuming the regression model Yi = BiXi + E is appropriate. And I have observations : X1...X10, Y1...Y10 How do i find the log likelihood function based on the observed values? Any help is much ...
35 views

### Is a linear regression possible here?

I would like to do a linear regression between my response "weed coverage [%]" and my predictor "soil moisture content[%]". Since the response was not normally distributed and had ...
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### Can we compare coefficients from log-log and log-linear regression?

We have two regressions $$ln(Y) = \alpha_1 + \beta_1 ln(X) + \epsilon \tag{1}\label{1}$$ and $$ln(Y) = \alpha_2 + \beta_2 X + \epsilon \tag{2}\label{2}$$ In the first case, a 1% increase in $X$ ...
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### What to do with 100% datapoints when conducting a Logit transformation

I have a panel dataset of 120 different countries measuring a variable over three periods. This variable indicates the percentage of 1000 respondents in each country that answered yes to the question. ...
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### Should I take the log of data-points in a panel dataset before or after averaging them into a cross-sectional dataset

I have a sample of 120 countries with panel data over a nine-year period. I will be averaging this data for each country to create a cross-sectional dataset of my 120 countries. Certain variables ...
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### Log transformed (+constant) in t-test implication and result

For context, I am evaluating the level of underpricing, measured as (closing price-offer price)/offering price and underpricing suggests that the result of this calculation is positive. My H0 for this ...
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### Interpreting data from a GAM that has data on log scale

I have a data set where I'm comparing territory sizes of animals of different age classes and populations. I use a GAM to fit a model as it seems to work very well when I fit the duration the animal ...
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### Interpreting coefficients of log-difference independent variable on log-difference dependent variable in regression

I have the below OLS model: $ln(a)-ln(b) = B_0 + B_1\cdot(ln(c)-ln(b)) + e$ How would you interpret the coefficient in terms of the values of a, b, and c? Thank you for your help in advance.
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### Equal intervals on log scale

I want to make a plot in which the horizontal axis is log scaled, ranging from 1 to 1000. I want to divide the horizontal axis into $n$ equal intervals, where "equal" means that it appears ...
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### log log interpretation with independent count variable [duplicate]

Would anyone know how I could interpret the log-log regression with age below? ln (Income) = const + 0.30 ln(Age) + ut I don't understand how it is possible to say that if age increases by 1%, income ...
1 vote
44 views

### Log a squared variable or square a logged variable

I'm estimating an OLS log-log model like so: $$ln(y) = \alpha + log(x_1) + \varepsilon$$ and now want to account for non-linearities in the response of $ln(y)$ to $log(x1)$....
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### Winsorizing or taking the logarithm first?

I testing if I can describe the StockPRice with EPS (=earnings per share), BookValuePS an ESGscore. Before I start I winsorized all my variables. Now I want to take the loagrithm of e.g. BookValuePS ...
134 views

### interpret coefficient in log10 - linear model

I have a doubt. I had to normalize the errors transforming the dependent variable into log10, so I have an equation of this form "log (y) = 2.49 - 0.0006X1 + 0.0328X2", also the variable X2 ...
55 views

### margins when using a log link. problems with the "expression" option

I am trying to reproduce the output of the margins command in Stata after running an xtgee regression with logarithmic link and ...
38 views

### Interpret log transformed interaction term in Fine-Gray survival model

I have a competing risk survival model with a log transformed interaction term and I am not sure how to interpret and report these results. I'm evaluating the effect of a treatment and the effect ...
95 views

### Back transforming from a log-transformed and subsequently standardized (outcome) variable

Due to skewness of my data I've performed a natural log transformation of my outcome variables, dealing with scores of 0 by adding 1 to all measurements. Then, to be able to compare relationships ...
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### When do we need to log transform predictors for logistic regression model? [duplicate]

I am interested in knowing when we should log-transform the predictors for the logistic regression model? My predictors are highly skewed but I read about some materials online that we don't need to ...
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1 vote
49 views

### Confidence intervals for log-log regression in Python

I've attempted to build a simple regression model with the following data points: where x is some metric related to a product, and y is the sales of that product over a year. The aim being I'd like to ...
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69 views

### Forecasting with log transformed data and then taking the exponential of my predictions [duplicate]

I am aware a similar question was asked here Interpreting forecast predictions of log transformed data. But I would like a deeper comment/answer. I have a time series and want to make forecast. I ...
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### Can log-transform to TS reduce forecast accuracy vs non-transformed TS

I have to apply a SARIMAX model to over 300 TS. Many of them have increasing volatility which can be addressed by aplying log to the TS. Problem is that also many TSs don't have this problem. Is it ok ...
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### Very high intercept in log-normal linear regression in R

I ran multiple linear regression in R. I have a skewed Y variable and log transforming it gives better results. I didn't transform any of the x variables. Thus, in order to interpret the coefficients ...
67 views

### How to derive sales contribution in a log-log regression media mix model?

I am working on a media mix model to determine how different media channels impact sales. Since there is a non-linear relationship between sales and media spend, I needed to apply a log transformation ...
1 vote
162 views

### Normal distribution vs Lognormal distribution for residuals in Bayesian linear models

When should I use normal distributions for residuals, and when should I use lognormal distribution in Bayesian linear regression? For example, if I want to create a regression model for chemical ...
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