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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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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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31 views

Am I Log Normalizing correctly?

I am sorry if this is a stupid question, but I have searched the other questions about log normalization found other sources on it all of which assume a level of understanding that I don't have. I ...
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42 views

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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96 views

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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24 views

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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52 views

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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27 views

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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28 views

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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8 views

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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19 views

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 ...
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34 views

Prediction intervals of a log return time series when converting back to levels

I am having a problem when calculating prediction intervals of an ARIMA model of a log return transformed time series. Assume I have the following point estimates for $h \in \{1, 2, 3\}$ where $y_{t+...
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1answer
71 views

A different proof for KL divergence non-negativity

KL divergence's non-negativity can be proved in many ways. One could use the inequality $\log x \leq x - 1$ as a main step in the proof, another one could leverage the property of concave of the ...
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17 views

Poisson bias adjustment

So I was hoping someone could help me make sense of this problem. I came across this paper that discusses how the FSL probabilistic DTT may yield bias tractography relating to the physical distances ...
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30 views

Scatterplot bounded by parabola

I have frequency data for several variables. Each type can take on one of two variants: ...
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1answer
56 views

Removing Variance in Time Series After Applying Log Transformation

I'm trying to look at natural gas prices from 2003-2018. The issue is after applying log transformation and then diffrencing data by 1, I still seem to get an increase in variance from mid 2014-2018. ...
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1answer
53 views

How can I interpret natural logarithm transformed value in the binary regression result

I have the binominal regression output result using R programming and x3 below is the natural logarithm of the data which is large. The x3 before imposing the natural logarithm has the following ...
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1answer
167 views

Impulse response: Interpreting shock and response for log-variables

I have a question related to the interpretation of Impulse Response Function (IRF) functions. Assume we do have two time-series that have been both log-transformed and are stationary. When applying a ...
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53 views

The average change interpretation when the dependent variable is in logarithm

Suppose the regression model is $\text{wage} = \beta_1x_1 + u$. The conditional expectation function is $\operatorname{E}[\text{wage} \mid x_1] = \beta_1x_1$. Then, we interpet $\beta_1$ as the change ...
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1answer
41 views

Is there a name for the distribution whose PDF is -ln(x) on its support [0, 1)?

If so, what is its name? If not, how/where can information about it be found?
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24 views

How could the size of the beta coefficients change order after log-transforming outcome variable?

I had a mixed effects model where the residuals were not normally distributed, so I log-transformed the DV to meet the assumption. There is one fixed effect with 3 categorical levels (L1, L2, L3). ...
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2answers
61 views

Regression with log transformation of dependent variable that has negative values

I am working with a dataset that contains: a dependent variable (DV) taking both positive and negative values a binary independent variable (IV). And I'm interested in the following specification: ...
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114 views

Logarithmic Transform of proportions (Weber's law)

Given we have a function as follows (context is the Weber-Fechner law): $$\frac{\Delta x}{x} = C \tag 1$$ Plotting here $\Delta x$ as a function of $x,$ this is clearly a linear function with a ...
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1answer
34 views

Is it ever convenient to maximize different functions of the likelihood than the logarithm?

We all know that it's often much more convenient to maximize the log-likelihood rather than the likelihood to get a parameter estimate, since it amounts to the same thing by the fact that the ...
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Log-Log in panel data for multiple regression

I'm using a model, for an article, with 6 independent variables. I used the logarithmic transformation of the dependent variable (Y) and 2 of the 6 independent variables. One of my professors said ...
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1answer
63 views

Backpropagation in a logarithmic layer of a regression NN

A "logarithmic neuron" is defined as follows [1]: Which for inputs $\left\{ {{x_1},...,{x_n}} \right\}$ yields an output of $z=\prod\limits_{i = 1..n} {x_i^{{w_i}}}$ (in MATLAB, the activation ...
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33 views

Control for over-dispersion. Why do this: take natural log of metric, exponentiate, rank, remove top and bottom 10%

I'm looking at some NHS healthcare data on the number of deaths in England The measure i'm looking at is called the SHMI - it's simply: The number of observed deaths at a hospital / The expected ...
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27 views

Discussing R-squared of log-log model with a non-technical audience

I have been asked to report on the relationship between two right-skew financial variables using R-squared e.g. "market cap explain ?% of the variance in CEO compensation". The purpose of the ...
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1answer
335 views

Interpreting RMSE of log-values

I am modelling a regression with a GBM and evaluate by RMSE. My model input & target is log-transformed which results in an RMSE that is also on log-scale. How can i interpret this in an ...
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0answers
133 views

calculate binomial deviance (binomial log-likelihood) in the test dataset

I'm predicting probabilities $P(Y=1)$ using a probability forest (ranger in R). I want to evaluate my predictions $\hat p_i$ in a test dataset by calculating average binomial deviance (log likelihood)....
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1answer
381 views

Predicting probabilities after log-linear regression

I would like to estimate a log-linear regression and examine the results with Stata's marginsplot command. I have transformed my dependent variable into natural logarithm (to make a highly skewed ...
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1answer
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How do I interpret the coefficients of a log-linear regression with quadratic terms?

I have a regression equation of this kind: $$\log {y} = a + bx + cx^2 + \epsilon$$ where $a$ is the intercept, $b$ and $c$ are the coefficients of $x$ and $x^2,$ and $\epsilon$ is the error. How do ...
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1answer
71 views

Maximum likelihood estimation and $\log(0)$

I am thinking I can't be the only one encountering this. I am trying to do maximum likelihood estimation on a probit model, i.e. trying to find the most optimal fit for three parameters in my case ...
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1answer
14 views

multiple regression log transformed how do i see initial values

I log transformed my dependent variable and all 5 independent variables to get a better fit. The dependent variable is sale price in dollars. Before I logged it, the intercept and all coefficients ...
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2answers
345 views

How can I interpret intercept when my dependent variable is in log form?

My model consists of both log independent and dependent variables, and percentage share, as well as number of people and etc. My dependent variable is log(GPD per capita in USD), my statistic package ...
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1answer
33 views

Log-transformations and concave functions

Consider a linear equation $O = SW$ with $O \in \mathbb{R}^{g \times n}, S \in \mathbb{R}^{g \times k}, W \in \mathbb{R}^{k \times n}$, with $g \gg n, g \gg k, k < n$. $W$ is a frequency matrix and ...
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1answer
436 views

Correcting log-transformation bias in a linear model

I am using a log-transformation for my response variable in order to get a linear relationship between it and the explanatory variable. I have split my data to training set (70%) and evaluation set (...
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1answer
32 views

Log-log specified regression coefficients don't agree with level-level specification

I've got a bunch of data on charities and I'm doing a study on the effectiveness of fundraising in the sector. I've got two regressions. The first is $$\text{revenue} = \beta_0 + \beta_1\text{...
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1answer
21 views

Need some enlightment about how log affects the mean of the data?

So, I have some data regarding the views by videos on youtube. I took the log of the data and compared the mean of both variables. Why did the categories change so much when log was applied (first ...
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1answer
49 views

Advice on choosing a likelihood distribution for data in logaritmic units

I have a Bayesian model to fit a set of parameters given some observables (flux from astronomical objects). Since many users will prefer to define the priors using logarithmic units and I could remove ...
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19 views

Back transform the integral of a log-log model?

One of my colleagues has an issue with back transforming the integral of model back to its original units. His model has a log transformed Y as a function of a log transformed X predictor. He can ...
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1answer
26 views

Definition of nonarithmetic law

I came across the term nonarithmetic, but I don't now what that means. It is a condition for a Proposition of a Paper I am reading. There it is said: Assume that the law of $\ln A_0$ is nonarithmetic....
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1answer
41 views

Difference vs log-difference: do they behave similarly?

Consider two positively-valued time series, $\{X(t),Y(t)>0|t\geq0\}$. Now consider two transformations: $$ U(t) = Y(t) - \beta X(t),\\ V(t) = \ln{[Y(t)]} - \ln{[\beta X(t)]}, $$ with $\beta>0$ ...
3
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1answer
114 views

x is correlated with y but log(x) is uncorrelated with log(y)

I ran an experiment where I experimentally (randomly) manipulated $x$ to find out the effect on $y$. Both variables tend to have power law distributions, and this was indeed the case. I ran some ...
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19 views

transformation of a market index data

This is excess return data, and from the result it can be shown that there is a negative skewness. ...
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1answer
34 views

Slope of a graph [closed]

I am plotting some data which should have a positive slope but instead, it has a negative slope (because the values were decreasing with time). Is there anything to transform the data to have a ...
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0answers
18 views

How do i retransform my unstandardized coefficient?

I have preformed one of my first multiple linear regressions in SPSS, and i am unsure how to proceed. My dependant variable was not normally distributed, so i transformed it with log10(x+1), since ...
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1answer
218 views

What is the use of the log of the sum of exponents in machine learning

I want to understand why somebody would use log sum exponent trick. I am reading this blog. But I don't really understand the first paragraph. It says Let's say we have an n-dimensional ...