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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How to improve upon my composite index from right skewed data in R

Do you have any advice for creating an index from right skewed-data with several extreme outliers in R. I am new to creating indexes for analysis and could use some advice on how to do it in R. So ...
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Can a “proportionality” metric designed for compositional data analysis be used for non-compositional representations of the data?

I have been diving deep into compositional data analysis. Here is a great thread containing a conversation with Thomas Quinn, who is pushing this type of research in microbiology, about some ...
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25 views

Reasoning for tranforming linear model to log-level

I have a multiple linear regression model and found that my error terms are not normally distributed. When looking at the histogram of the dependent variable, it looks like below. I am not sure how ...
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How to deal with indeterminate values in a linear regression?

I have some experimental data over the time. I need to fit this data to two models in their linearized forms: Model 1: $\ln (a-y)=\ln a-b\ t$ Model 2: $\dfrac{t}{y}=\dfrac{1}{k\ d}+\dfrac{t}{c}$ My ...
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Should I use log transformation for my multiple regression? [duplicate]

My response variable is a bank interest rate, and I have as explanatory variables: a concentration index, the non-payment rate and the basic interest rate of the economy: ...
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Confidence intervals for a log transformed dependent variable

I have a basic OLS regression equation with the dependent variable ($Y$) log transformed and a binary independent variable ($X$). In order to correctly interpret coefficient $\beta$ for the $X$ ...
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why arima uses differencing transform not the log transform to make data stationary?

I am currently working on time series project and i am naive. I would like to ask, there exist strict stationary, differencing stationarity. If i understood correct the first order differencing ...
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Different forms of Stirling's approximation

I have Stirling's approximation in the form: Please could someone explain how this is equivalent to the form: log(n!) = nlog(n) - n for large n?
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47 views

When is Log-Cosh Loss used?

I have seen people speaking of the Log-Cosh Loss that is 2 times differentiable and mimic the Mean Absolute Error goers 0. It is therefore useful for algorithm that need hessian. Hence I'm not sure ...
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What would a suitable justification be to use 'log(exports)' as a dependent variable instead of solely 'exports'? [duplicate]

I am doing a diff-in-diff analysis, looking at whether a regulation had an impact on British pollution-intensive exports. Initially I used 'total exports of pollution-intensive goods' as my dependent ...
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39 views

Summation of Log Probabilities

I am trying to implement the following: where the right part returns a probability between 0 and 1. Regarding the product, the authors of the respective paper note: Due to numerical precision ...
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log likelihood function causes huge differences with similar inputs

I am not sure whether there is a solution to this problem, but here goes. My problem is that in my function, I am taking log of a matrix and then taking its mean, and doing this for two very similar ...
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log-log plot and straight line fit

I think this is a silly question, but I'm using a very simple data to be fit using a power law equation. If I use a non linear fit (log-log line), I got some parameters that don't correspond if I ...
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what is the distribution of the log of a normal distribution? [duplicate]

if you exponentiate a normal distribution, Y=exp{X} where X is a normally distributed random variable (RV), then Y is log-normally distributed. What is the ...
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23 views

Augmented Dickey-Fuller test interpretation before and after log transform the data

I have apply the stationarity test to a stock's adjusted price by using the Augmented Dickey Fuller Test with the program R. That is the output from ...
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1answer
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Why to use log while calculating probability of an email being spam?

I worked on a basic spam email project (Naive Bayes classifier with Laplace smoothing). In source code, to calculate probabilities of spam or ham, log of the final result is being used. Why is it ...
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How to interpret different shapes of a log-log graph?

I have a number vs size plot for two species. I'm trying to figure out through some basic plotting what shapes it could take-up. I suspected some sort of hump shaped curve where size peaks at ...
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Confidence Intervals: Passing to logarithm

So one of my problems says to take an answer from the previous part of the problem and "pass it to logarithm" to find a different one and interpret it. Basically, we had to find a CI for $2^{\alpha_2}...
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Regression analysis: Log-transformation to meet assumptions?

For my master's thesis I'm exploring the relationship between attitude towards the advertismenent (Aad), brand types (boutiques and high street) and willingness to recommend (willing or not). ...
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What is the expected value of x log(x) of the gamma distribution?

Let $w(x) = x \log{x}$ $x \sim Gamma(\alpha = 3.7, \lambda = 1)$ Find $E[w(x)]$ I have set up the following integral: $\int_0^{\infty} x\log{x} \frac{\lambda^{\alpha}}{\Gamma(\alpha)} x^{\alpha -1}...
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Regression: Is it bad practice to use log difference as approximation for % difference when changes are large?

I'm running a vector autoregression model with quarterly IPOs as one of the variables. Since the number of IPOs isn't stationary, I took the log first difference to make it stationary. However, I ...
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Predicting y from the log y as the dependent variable using panel data

Assume that we have the pooled OLS as the follows: $$\widehat{\log(y)} = \hat{\beta_0} + \hat{\beta_1}x_1 + ...+\hat{\beta_k}x_k$$ In order to calculate $\hat{y}$, Wooldridge suggests that $$\hat{y}...
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245 views

Help with log2 transformation of normalized data

I have a dataset that I normalize so that the average equals 1. If I then log2 transform the dataset, should the average of the log2 data equal 0? For example: 1, 1, 1. The average of the dataset is ...
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Tractability of Expectations: log expectation vs expectation log

I'm working my way through a paper about bounds on the mutual information [1]. However, I have some issues in understanding claims they make about the tractability of the different bounds. Given: $ ...
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Log-transforming a mean - what to do with SD?

I am doing a meta-analysis of means. I have gathered means, SD and N from a set of studies. I do not have access to the raw data of the means. After doing an Anderson-Darling test, I found that the ...
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Reporting the average log-probability the model assigns to some examples

I am currently studying Deep Learning by Goodfellow, Bengio, and Courville. In chapter 5.1.2 The Performance Measure, $P$, the authors say the following: To evaluate the abilities of a machine ...
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How to present Confidence Interval for Log-Transformed Means & Mean Difference?

After trying to read on this topic, I still have some clarifications remaining. Context: Comparing between 2 arms (categorical), measuring microbiological plate-counted bacteria concentration (...
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Prove that the likelihood function L(θ|x) is equivalent to maximizing log L(θ|x) where log is the natural logarithm [closed]

In other words, why $\text{argmax} \text{ } L(\theta) = \text{argmax} \text{ } \text{log} \text{ } L(\theta)$ ?
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How to fit CDF on LogLog plot?

I build CDF of differences for Gold Pice. As series of day-diff multipliers. For both increase as green (>1) and decrease as red (<1) diffs. ...
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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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Interpreting standard errors of linear regression with logged dependent variable

I'm running a linear regression with a logged dependent variable. This is the only variable in the model that is logged. For interpretation, I've exponentiated the coefficients, subtracted one, and ...
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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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Modelling exchange rates: how to log transform percentage changes?

I'm trying to model an exchange rate to test for extreme values. However, I have percentage changes from day to day. Given some changes are negative, I can't take the logarithm. Any idea how I could ...
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1answer
587 views

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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log regression - what is the last variable in this equation? it wasn't defined can this be the error term?

Can someone help me understand what ∆η_it is?
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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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36 views

Can I fit a Poisson model to ln transformed data? [closed]

This is my first question in stats Stack Exchange and I would say that it is an easy one, but hard to find around! I have a set of fish counts which should follow a Poisson Distribution (right ? ). ...
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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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139 views

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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459 views

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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Log-Log regression and cost function

I have made a very siple linear regression model having used log-log tranformation for the y and one of the independent variables: log(y)=B0+log(X1)B1+X2B2 where B0 is the intercept and B1,B2 the ...
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186 views

For lognormal distribution which one is preferred? Log 10 or Ln or Log 2?

I want to perform a linear regression analysis. The distributions of data for all continuous variables are not normal. The tail of graph is to the right and thre highest point of graph is due to 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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Why is the expected gradient of a density not parallel to the expected gradient of the log density?

I'm confused by a seemingly counter-intuitive property of the interaction between distributions, log transforms, expectations and gradients. Suppose I have some distribution over random variable $x$ ...
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log values in coxph model?

I have a data frame of gene expression values (sequencing). When I do CPM-normalization without doing log2, I get much "better" (lower) p-values compared to when I do log2-CPM. What is the ...
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125 views

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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39 views

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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