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

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32 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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42 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 ...
0
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0answers
22 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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0answers
12 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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0answers
16 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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0answers
10 views

How to compare regression coefficient of log transformed and level data?

I am estimating a model in the form $\log y=a+b \log x_1+cx_2$. I understand that $b$ represents the elasticity of $y$ with respect to $x_1$, while $c$ is a semielasticity. The question is, if I ...
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0answers
15 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
61 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
36 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 ...
6
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4answers
298 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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0answers
17 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
36 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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0answers
22 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
153 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
32 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 ...
0
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0answers
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 + ...
3
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1answer
56 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
61 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
72 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 ...
1
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0answers
55 views

multiplicative model in r

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 + ...
-1
votes
1answer
610 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
99 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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0answers
284 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
154 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
130 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
74 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
34 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 ...
0
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1answer
94 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 ...
1
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0answers
44 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 ...
0
votes
1answer
88 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 ...
1
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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?
2
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1answer
69 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
150 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
256 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 ...
0
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0answers
28 views

What is data augmented by the additive inverse?

I am reading Biclustering of expression data (Cheng and Church, 2000) The paper is about the Cheng and Church biclustering algorithm and its main metric, the mean squared residue (MSR). It is said ...
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0answers
48 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
votes
1answer
319 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 ...
0
votes
1answer
67 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.
4
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0answers
63 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 ...
1
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1answer
260 views

interpreting the coefficient on a logged independent variable from a probit model

I am using a double model with log transformed independent variables and have calculated average partial effects. Now I am now not sure how to interpret the coefficients; particularly those from the ...
0
votes
1answer
113 views

Best way to estimate a regression with reaction times

I have reactions times in a no-normal distribution, so I am using logarithms. Which can be the best way to estimate a regression? Later, I would like to plot the results according to the age of my ...
1
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0answers
167 views

Linear-logarithmic Regression in MATLAB with two input arguments - which model to assume?

Look at the following plot and ignore the solid lines please (just look at the dotted/dashed ones). ONE curve is described by the following parameters and ONE fixed value for the second input ...
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4answers
2k views

Is it correct to use 'Ln' instead of 'ln' for natural logarithm?

In some research papers, authors use 'Ln' for natural logarithm instead of 'ln'. Is it correct?
2
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2answers
231 views

Use logarithmic or linear values when performing correlation and ANOVA?

The data was collected using a logarithmic scale: scores (explanatory variable) are collected with values from 0-5. A score of 3 is 10x the value of a score of 2. I wasn't sure if using either the ...
1
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0answers
78 views

Log Transformation in Growth Mixture Model (Mplus user)

I am using parallel process growth mixture modeling to estimate bidirectional longitudinal dynamics between pain (0-100 theoretical range of values) and sleep measures (0-20 theoretical range of ...
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1answer
154 views

Interpret interactions and logarithms in linear regression

I'm currently playing around with linear regression in R, and I've come up with a regression that fits data quite well. I'm just having some problems with interpreting the coefficients of my model. I ...
0
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1answer
112 views

Doubt in derivative of logarithm

This seem to silly but I wanted to confirm if the derivative of the log-likelihood $\hskip 2 pt l(x_i)$. The derivative of $$\frac{d (\sum_{i=1}^{M} log(x_i))}{dx} = \frac{1}{x_i} \sum_{i=1}^{M} ...
4
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2answers
167 views

Taking the log of variables

Just before I start the question I would like you all to know that I have checked the other threads on taking the log of variables but I still think I have a question that hasn't been touched on yet. ...
2
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1answer
102 views

Estimating the effects of cumulative odds ratios - additive or exponential?

I have run some regression models that examine the effect of variable X (a 15 point continuous scale) on Y (a binary variable - not perform/perform a particular behaviour) using logistic regression. ...