The logarithm of a number is the power to which the base must be raised to get the number.

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Interpretation of log(1 + var) transformed predictor

Interpretation of log transformed predictor neatly explains how to interpret a log transformed predictor in OLS. Does the interpretation change if there are 0s in ...
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1answer
28 views

Large Increase in Naive Bayes Accuracy results in decrease precision?

I am trying to classify (37 possible classes) a dataset that has 9 features and 900,000 occurrences. I have tried a couple different algorithms but the one that gave the lowest logarithmic loss was ...
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24 views

Log linear model interpretation - % Contributions?

I know that for log-lin models the interpretation for the coefficiente is this one, that is: Coefficientsâ‹…100 have a semi-elasticity interpretation: for a 1 unit change in x, you get b*100% change in ...
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269 views

How to transform negative values to logarithms?

I would like to know how to transform negative values to Log(), since I have heteroskedastic data. I read that it works with the formula ...
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1answer
42 views

Should I use the mean difference or mean ratio for a t-test?

I have a quantitative variable (medication dose) that is paired: dose of medication before surgery and after surgery for 76 patients. I was under the impression that I should calculate the mean of ...
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61 views

How to backtransform data that has been log transformed in order to report raw values for ease of interpretation?

I have run some lme4 analyses on reaction time data in R, with RT being the main outcome variable of interest, which I first log transformed due to non-normality ...
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22 views

Natural logarithm transfomation and zeroes [duplicate]

I am using Stata 13 to estimate a simple regression. Given a rather positive skew of a few of my covariates, I figured to ln-transform the variables. However, I have a substantial amount of zeroes in ...
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0answers
28 views

How to treat missing values in a regression?

I have used the logarithmic form of wage as my independent variable in Stata. However, it contains missing values. Should I replace these with 0 or let them be?
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82 views

Log Transformation

I am planning to run a 2x2x3 repeated measures ANOVA on reaction time data pre and post treatment. However, my data is skewed and I wanted to do a log transformation but have few questions. Can I ...
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13 views

Meaning of growth of log-transformed variables [duplicate]

I am dealing with the transformation of the variables for my master thesis (a panel dataset with a xtabond2 model). The analysis focuses on growth rates, so my co-director told me to transform the ...
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1answer
66 views

Cohen's D: Should I use raw data, log transformed data or back transformed data?

I am a doctor and right now I am doing medical research. I have some questions about cohen's d. I try to research it on the internet but it seems there is not much answer to this question. My project ...
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0answers
35 views

Interpreting level-level models with units in %

I have a model where the dependent variable is GDP growth in (%). I regress this on a my variable of interest, wine sales ($). Do I have a level-level model? Growth = a + Bwine + u How do I ...
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0answers
24 views

Interpretation of log transformed coefficients, OLS regression [duplicate]

I have a question about how to interpret or use the result of an OLS regression w a log transformed DV. Due to non-normal distribution of the Dependent variable, I used a log10 transformation to coax ...
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0answers
24 views

lin- log model with unbalanced time series

I want to compute the following regression: lm(y~x+log(TAF) from observation nr. 100 to observation nr.300, where x is a controll variable. Now the problem is ...
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1answer
184 views

Interpretation of marginal effects in Logit Model with log$\times$independent variable

I am totally confused by statistics and I would be glad if you could help me. I have a difficulties to interpret marginal effects in logit model, if my independent variable is log transformed. I ...
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0answers
29 views

Why small values produce undulating densities when ploting logarithm of a loguniform prior (in R)?

I am using a program that draws random values in a log-uniform distribution let say between 1 and 100. When I plot the density of the produced values with R it looks like a log-uniform distribution ...
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6 views

Medians of logged fold changes.

So I have a set of measurements from several studies consisting of fold changes between log2-transformed values between two groups, each calculated using the formula ...
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1answer
83 views

Advantages of taking the logarithm to minimize the likelihood

In regression/classification problem, we are often interested in minimizing a cost function with respect to the parameters of the model. In many cases, the cost function is the negative likelihood. To ...
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47 views

Why not just use log for regression if it improves r-squared?

theoretical question here: Say I have a model, $y = \beta_0 + \beta_1 x + u$ and it gives an $R^2$ of 0.02 Suppose, I re-estimate the model with $y = \beta_0 + \beta_1\log(x) + u$ which gives an ...
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49 views

What happens if I square the variable in my log in OLS regression?

Say I have a model: ln y = B0 + B1(x1) + B2 ln(x2) + u and the B2 estimate I get is 0.5 If I change the model to be ln y = B0 + B1(x1) + B2 ln(x2^2) + u the estimate will change to 0.25, but why ...
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49 views

mean of log or log of mean

I'm interested in how indiviudals are influenced, by other individuals they are connected to. So mean values of connected individuals are included in a linar regression model. Some of my variables are ...
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161 views

Percent change interpretation in log-transformed regression: Percent change from what?

I am dealing with a regression model where both the DV and IV are log-transformed. I have found this explanation of how to interpret the effects (both in the Cross-Validated hyperlink and in ...
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35 views

Interpreting standardized log coefficients in OLS

I used the log for my dependent variable as well as for some independent variables. Then I standardized all variables. Now I'm not sure how to interpret the coefficients. Are the log and non loged ...
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35 views

log transformation decreased model fit?

I just wondered why logged income (independent variable) decreased my model fit for OLS regression. My income distribution is skewed to the right and I am trying to transform the data. I separately ...
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78 views

Interpretation of impulse response functions with variables in logs

I am looking at the relationship of several macroeconomic variables, all in natural logs, using Vector Error Correction (VECM) models and Impulse Response Functions with a standard Cholesky-type ...
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3answers
78 views

What is the statistical logic behind using logarithms in analyzing threshold elevations?

In my field, a lot of experiments are done comparing performance between a baseline condition, and a more difficult condition. Typically, thresholds are measured at each of these two conditions, and a ...
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1answer
105 views

Log form of variables and descriptive measures

Because of larger values of variables, I did a log- transformation in my dataset. Now I want to give a descriptive table regarding my variables like mean, max, min, median, skewness, kurtosis. Can I ...
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624 views

What are the formulas for exponential, logarithmic, and polynomial trendlines?

In creating linear trendline, I used the following formulas: $$y=mx+b$$ $$m = \frac{n\sum(xy)-\sum x \sum y}{n\sum x^2 - (\sum x)^2}$$ $$b = \frac{\sum y- m \sum x}{n}$$ and this for the R-squared: ...
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29 views

Interpretation of logged term in logit (generalizing previous answers)

I have a logistic regression model, where one of my variables is logged. It is of the following form: $\ln(\frac{p}{1-p}) = B_1\ln(X) + B_2Y + ... + \epsilon$ , where $\epsilon$ is an error term. I ...
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1answer
42 views

Value of logarithmic form

I'm having trouble grasping the viability/value of log'ing a dataset. This post mentioned that it's used to normalize (read: shrink extremes of) a dataset and make it easier to fit a curve. But, ...
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31 views

Semi partial correlation importance variables

I have some SAS code that is used to calculate the importance of variables using semi-partial correlations: ...
2
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1answer
304 views

do logs modify the correlation between two variables?

I am applying logs to two very skewed variables and then doing the correlation. Before logs the correlation is 0.49 and after logs it is 0.9. I thought the logs only change the scale. How is this ...
2
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1answer
37 views

Interpreting a logarithmic difference as an error

This is a fairly simple question but I can't figure out which one is the correct approach. In astronomy it is usual to report age values via their base 10 logarithms instead of the actual value. So a ...
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20 views

How to account for data taken at $t=0$ when using $\log(t)$ in the model? [duplicate]

I have a data set with four observations consisting of the variable $Y$ measured at time $t_0=0$ and at times $t_1, t_2$ and $t_3$. I would like to fit the following model: $$\log(y_j) = \alpha + ...
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1answer
74 views

Looking for a layman's explanation of how to manually calculate log odds?

I will start that I am not as math oriented as I would like to and could use a layman's / non-staticians explanation walk through of how to calculate the log odds. I am reading Hosmer, Lemeshow, and ...
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0answers
78 views

Using log of dependent variable as regressor

I am running a regime switching (hidden) Markov model, and I found out that if I construct the following model, it gives very interesting and useful state switches: $ y = \alpha_{S_t} + \beta_{S_t}\ ...
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0answers
105 views

PSM, Diff-in-Diff and Neg-logged income variable? How to interpret estimates?

I am estimating a difference-in-difference based on propensity score matching. The "treatment"-variable defines whether a household registered for a public insurance which was only active for two ...
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0answers
96 views

multiplicative model in r [duplicate]

I have to estimate a model forecasting the sales (as stock units) for AXE deoderants.I want to apply the multiplier specification on this model. The model should look like this: log(Sales) = b0 + ...
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1answer
2k views

What are the advantages of using log GDP per capita versus simple GDP per capita when analyzing economic growth? [duplicate]

I have quite a lot to learn regarding analysis and economics, one thing I have noticed is that when analyzing growth, log is used quite often, why is this so?
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2answers
143 views

Maximum Likelihood estimator of population variance and its derivation process

I have 2 questions about maximum likelihood and using it to calculate variance: Question #1: The question is about finding the derivative of the score function with respect to the parameter $ ...
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1answer
777 views

Multi-class logarithmic loss function per class

In a multi-classification problem, we define the logarithmic loss function $F$ in terms of the logarithmic loss function per label $F_i$ as: $$ F = -\frac{1}{N}\sum_{i}^{N}\sum_{j}^{M}y_{ij} \cdot ...
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1answer
400 views

Interpreting Log-Transformed Percentages in OLS

In a log-log model, such as $\log(y) = b_0 + b_1 \log(x)$, I know that with OLS the standard interpretation is a "1% increase in x is associated with a $b_1$% increase in y." I have three related ...
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2answers
211 views

Approximation of logarithm of standard normal CDF for x<0

Does anyone know of an approximation for the logarithm of the standard normal CDF for x<0? I need to implement an algorithm that very quickly calculates it. The straightforward way, of course, is ...
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0answers
16 views

A few questions about using logarithms in regression equations [duplicate]

I have a simple regression equation where log(salary) = b0 + b1*log(sales). How would you interpret b1 in this model?
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1answer
92 views

Why can certain variables in a multiple regression not be included in logarithmic form?

I have a multiple regression equation where log(salary) = b0 + b1(ceotenure). What is the purpose of putting the dependent variable in logarithmic form? How would you interpret the change in y for a ...
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0answers
48 views

What to do with coefficients of log-transformed predictors in meta regression of effect sizes?

I am preparing data for a meta-analysis regression of effect sizes, in which I will study the determinants of effect size for a specific variable across several studies. I have some studies in my ...
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1answer
106 views

Log and natural log

I have few seemingly simple questions. I am working on time series data and applying vector error correction model. I find different results when I transform the data into LOG and LN. Which one is ...
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0answers
58 views

Metropolis Hastings when acceptance rate is not a probability

I need to implement a Metropolis Hastings where the acceptance probability $\alpha$ is not a probability but a logarithm of a score. The logarithm of a score is a negative float. In original ...
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1answer
113 views

dealing with exponentials in python - infinities and overflows [duplicate]

In a machine learning algorithm that I'm using, I need to get the exponential values of something in one of the steps. This is the step that I'm dealing with right now: I've already got all the ...
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1answer
45 views

Regression and link function

Suppose we have $E (\log (Y)) = a+bx $ vs $\log (E (Y)) = a+bx $. Can $\exp (b) $ in both cases be interpreted as a geometric mean?