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 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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44 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
46 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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29 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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23 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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19 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
84 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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25 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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4 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
76 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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39 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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42 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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47 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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107 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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29 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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31 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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54 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
72 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
82 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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4answers
492 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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28 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
40 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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27 views

Semi partial correlation importance variables

I have some SAS code that is used to calculate the importance of variables using semi-partial correlations: ...
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1answer
244 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 ...
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1answer
34 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
65 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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74 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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94 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
129 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
696 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
311 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
178 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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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
86 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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44 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
99 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
50 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
101 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
42 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?
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1answer
81 views

Log-scaled chart for visualizing extreme range

I need a simple bar chart or the like. I am not a statistician by any means, but this chart is supposed to accurately represent FileIO in MB/s compared to the theoretical peak of a specific drive. ...
1
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1answer
211 views

Understanding stationarity with Inflation

I am looking at the link between inflation and insolvencies for an econometrics project. I have the raw quarterly insolvency data and raw quarterly CPI data for the UK (roughly 100 samples) from ...
2
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2answers
323 views

Reporting regression statistics after logarithmic transformation

I'm a bit troubled about how to report linear regression statistics after log transformation of the dependent variable. I suppose I should report the transformed coefficient, but would they be easily ...
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55 views

Use of log of an independent variable and its implications

I am currently analyzing the relationship between Google Search frequency and the CDS market. I used a monthly backward rolling regression to determine the 30 search queries which have the biggest ...
2
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1answer
453 views

Interaction term in a linear log model

I am using a linear-log model to test whether overseas development assistance and remittances positively affect FDI in cases of good governance and financial market development. Let's say I want to ...
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1answer
78 views

Expectation operator and logarithmic function

$$\frac{1}{C_t}=E_t\left[\beta \frac{1}{C_{t+1}} \right]R_{t+1}$$ How to log linearise the function? $C_{t+1}$ is the stochastic term; $\beta$ is known.
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68 views

Avoiding large variances when taking the logs of small values

I have two random variables $(X$ and $Y)$ that are always positive. The assumption I'm making is that their logs follow normal distributions (i.e., $N(\overline{\log(X)},s^2_{\log(X)})$ and ...