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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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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1answer
100 views
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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3answers
86 views
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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1answer
33 views
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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13 views
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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2answers
90 views
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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0answers
11 views
Convert ratios into a standardized effect like Cohen's d
This is my first time working with log data. I have performed a contrast of the difference between two log means and have back-transformed this to give me a ratio of geometric means. I'd like to ...
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1answer
49 views
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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0answers
59 views
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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0answers
21 views
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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1answer
20 views
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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0answers
45 views
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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12 views
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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1answer
57 views
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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1answer
123 views
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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0answers
47 views
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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1answer
33 views
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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0answers
20 views
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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1answer
33 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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0answers
54 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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0answers
8 views
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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1answer
244 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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144 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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1answer
60 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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0answers
43 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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1answer
64 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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0answers
13 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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0answers
20 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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0answers
36 views
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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0answers
40 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
100 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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19 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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0answers
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
89 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. ...
2
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1answer
57 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 ...
2
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1answer
299 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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0answers
54 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
45 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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0answers
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
133 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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0answers
170 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 ...
2
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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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1answer
92 views
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
78 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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1answer
38 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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0answers
72 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
621 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
225 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
558 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
101 views
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 ...
