# 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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### Comparing Regression Coefficients from a “log-log” to an Alternative De-meaning Procedure

Consider two regression models: $log(y_i) = \log(x_i)\alpha + \epsilon_i \,\,\,\,\,$ (Model 1), $log(y_i) = (\frac{x_i}{\overline{x}})\beta + \varepsilon_i \,\,\,\,\,\,\,\,$ (Model 2), ...
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### group-mean centering and log differenced variables

I have a country-mean centered explanatory variable (X- country mean) in panel data. The variable itself and the mean are transformed with the natural log. The outcome variable is also made like this. ...
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### Coefficient of variation for log (base 10) transformed data set

I've recently become aware that there are different formulas for calculating the coefficient of variation (CV). It is my understanding that for numeric data this formula is used CV=(SDTEV/MEAN)100 as ...
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### Using Logarithmic Function for Election Polling

Can someone explain why logarithmic function is used in sample sizes of election polling? For example, logarithmic function was used to estimate voting intention for different political parties during ...
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### Shall we use log(diff(x)) or diff(log(x))?

I am starting to learn time series and when detrending I always end up with the same doubt... Generally, I use diff() for, let's say there is an upward trend like ...
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### GLM Using Log-gamma Distribution

My data are skewed. Using log-normal causes a strong left-skew in the residuals. Using Gamma causes a strong right-skew in the residuals. I thought to myself, why not log transform the data and then ...
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### Why do we use the log-derivative trick before Monte Carlo?

I still don't understand how we can approximate the gradient of an expected value... Indeed it's impossible to sample points and then to average the gradients of them as we have only samples... (How ...
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### when should I normalize with $\log(1+x)$ instead of with $\log$?

I've seen people log-normalize data by using the $\log(1+x)$ (np.log1p) method for instance normalizing the price of diamonds in the diamonds dataset using ...
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### Why do we log transform response ratios?

In meta-analysis, it seems a standard practice to take the natural log of the response ratio before evaluating it. My question is why? That is, if I have a treatment mean (Xe) and a control mean of ...
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### Is it possible to log transfer all my variables when doing linear regression?

I am currently handling data where all the variables are right-skewed. I would like to log-transfer all the x and y variables, and if I do, the results are great. But I am making a table for the ...
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### Alternative to plug-in estimation for log-tranformed linear model

I want to estimate a relationship of the form: $$y=ax^b\times\epsilon$$ If I log this model i get: $$\log(y)=\log(a)+b\log(x)+ \log(\epsilon)$$ If I then proceed and estimate this model using a ...
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### Interpretation of a quadratic term on a log transformed target variable

I've done some searching and found several posts related to this, e.g.: In linear regression, when is it appropriate to use the log of an independent variable instead of the actual values? Suppose I ...
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### How to revert the sum of observations that are log transformed

I created the linear model to predict the sum of individual observations in a group. Since I only have the observed data in individual level, I aggregated it by group and trained the model with it. ...
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### How to back transform from log10 ~ log10 regression in order to predict?

I would like to understand the results of this paper (they supply all of their R code and raw data here). The idea is to regress home range on body mass for a range of taxa. For one group of birds, ...
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### Does it make sense to include GDP/capita and Population in the same OLS model

I got good results in my OLS model by using as explanatory variables: GDP/capita = GDP/Population and the Population. Do you think that is an issue to include both in the model (multicollinearity)?
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### Converting log standard deviation in terms of the original units

We run regression specifications of the form, lm(outcome_log_s ~ x1_s + x1_x^2) In which the outcome variable is logged and standardized. We want to be able to ...
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### Why is it okay to take the log (or any other transformation) of the dependent variable? [duplicate]

Why is it common practice to take the log of the dependent variable Y? To be clear, I understand that under appropriate circumstances that taking the log can help normalize the distribution/linearize ...
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### what is the difference between log and ln?

can I write a log in place of ln in statistics? I have seen people telling me that logarithm differs from natural logarithm. Is it correct?
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### When to choose difference versus log ratio for expressing variables relatively?

Oftentimes I wish to express one time series (say) relative to a second one. The two obvious candidate approaches are to take their difference or their ratio. Whereas the difference is symmetric with ...
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### Is $\ln\{E[f(x)]\}$ equal to $E\{\ln[f(x)]\}$? [duplicate]

Is the logarithm of an expectation the same as the expectation of the logarithm?
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### The interpretation of the economic significance in level-log and log-level models

I have the following two models. The first is a level-log model, and the second is a log-level model. These models are two separate regressions and are estimated independently. Assume that α=0.036 ...
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### Interpretation of a log-level regression in its 'level' form

Is it conventional to interpret a least-squares regression with a log-transformed dependent variable (log-linear least-squares model) in its "level" form? In other words, running a model with the ...
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### Solving an equation with logarithms of negative numbers

I'm modelling a bunch of non-homogeneous poisson processes. I'm impossing on them a linear-log functional form. you end up with two parameters, theta1 and theta0 for each estimated process. The ...
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### Why do we use natural logarithm in categorical outcome variables

I'm reading a chapter on categorical outcome variables (chi-square & log linear analysis) and the author, in an effort of fitting a linear model, said that because the outcome variable is a ...
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### Back transforming the intercept of double log normal distribution

I apologise if this is a duplicate, i couldn't find a thread that seem to be talking about the same thing. I have a dataset with a bunch of duration of varying lengths in seconds, i log-transformed ...
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### Interpretation of log(1+x) variable with y in percentage

In std regression analysis, I'm wondering what the correct interpretation of a log (1+x) variable is when my y is in percentages. My x variable takes on values from 0-4, with the the majority of the ...
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### Log-Log Regression - Dummy Variable

I have following regression: logCPI = 1,2922 - 0,3525*logGDP + 0,4239*logImport + 0,2115*logNEER + 0,6291*logWAGE + 0,0121*dummy How should I interpret last variable (dummy variable)? The regression ...
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### Interpret a multiple linear regression when Y is log transformed [duplicate]

I have the following multiple linear regression model: Log(y) = B0 + B1X1 + B2X2 + B3x3 + e. X1 is a dummy that can take 0 = male and 1 = female and X2 and X3 are continuous variables. I am not ...
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### Back-Transformation for Ln(X+1) of zero rich data

I have seen and read several similar questions, but mine pertains specifically to zero rich data. I will be back transforming my data based on a first order Taylor series approximation. As outlined ...
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### Fitting a logarithmic trendline on already logged values

This is the situation. I am running trials with a population simulator, which produces various outputs (y), with the variance of these outputs being dependent on the number of clones (x) (recursions) ...
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### Interpret model estimates after log transformation [duplicate]

I asked this question before, but maybe on the wrong audience at math.stackexchange.com. So, sorry for the redundancy. I sat up a mixed-effects linear model with the dependent variable log-...
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### Am I Log Normalizing correctly?

I have searched the other questions about log normalization and all assume a level of understanding that I don't have. I have some ecological data and I am told that it needs to be log transformed. ...
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### Transforming back after a log transformation with subtraction

I needed help with back transforming my data. My initial data was positively skewed so I had to log transform it, after which I did my statistical test. One of my regression test required for my ...
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### Comparing log normal and propensity multiple imputation models using confidence intervals

I am imputing income data with information about individuals characteristics and I am comparing the following multiple imputation models: Regression method using logarithm of income. Propensity score ...
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### Need help understanding what a natural log transformation is actually doing and why specific transformations are required for linear regression [duplicate]

I’m taking an online “Intro to AI” course for which I’m doing some azure machine learning labs. This course is largely about how to apply azure ML solutions and, while there is an “essential math for ...
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### Converting log transformed and differenced time series back into original in R

I have built a Garch model in R based on taking a log transformation and a one order difference on the original time series. I would like to know how develop a forecast based on the Garch model for ...
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### Interpreting GLM with logged variable

For my logistic regression model I have: glm(reconv ~ -1 + log(precon) + log(age), data = crime, family=binomial) With the following co-efficients outputted from ...
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### Can I log-transform realized volatility in a co-integration setting

I'm writing my master's thesis and looking to see if there exists fractional co-integration between the volatility of some large stock-indices. My estimates of realized volatility are based on the ...
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### How to calculate growth rate from a semi-log plot?

In the following plot, if we model the population growth as a linear function of time, what would be a good estimate of the linear growth rate? I don't know if it's the slope or the intercept!
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### Using log odds ratio to compare bigram frequency between 2 profiles

I was reading an article where the author proposed using the log odds ratio calculation to compare the relative frequency of bigrams between 2 websites. From my understanding the odds ratios are used ...
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### Bound for type of correlation measure

Assume you have a finite, discrete probability distribution for a joint random variable and such that $P(X=i,Y=j) = p_{i,j}$ for $i \in \{1, \dots, |X|\},j \in \{1, \dots, |Y|\}$. The marginal ...
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### Why don't my GWAS QQPlots look the same?

I am trying to create a QQPlot of 100 log-transformed p values from a GWAS study. The idea is that taking the -log(p) will magnify the smallest p values to make them easier to see. (reference) I was ...