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Questions tagged [units]

units of measurement. Use this tag also for dimensional analysis.

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27 views

How do units match up in variance in Poisson and normal distribution?

I was reading about variance, and learnt that variance does indeed have units. Also, since it is essentially average squared deviation, it would be unit2. Taking an example from temperature use case: ...
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25 views

How to interprete a scaled response variable as an unscaled response variable?

I'm new to R and I'm having trouble to interpret the estimates of my scaled response variable. I used (scale) function to standardize all my variables (1 response ...
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1answer
40 views

Standardizing versus percentile rank with survey data

I am currently working with survey data, collected across different locations, but with slightly different units of measurement. For example, on questions such as "What is your level of education", ...
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1answer
67 views

Changing units in linear regression

A linear model: $y_{i}=\alpha +\beta x_{i}+u_{i}$ was estimated using least squares and the following estimate was calculated: $\widehat{\beta }=\frac{\sum (x_{i}-\overline{x})y_{i}}{\sum (x_{i}-\...
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0answers
171 views

Probability density function units of the log-normal distribution

In a discussion on this forum lognormal distribution, standard-deviation and (physical) units the cumulative distribution function (PDF) of the lognormal distribution was analysed. The conclusion ...
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1answer
76 views

What are the units of a medcouple?

Let's say I have a distribution of some weights in kg. I want to estimate the skewness of this distribution using a robust statistic, the medcouple [ G. Brys; M. Hubert; A. Struyf (2004). A robust ...
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1answer
142 views

Multiple regression of variables with different units

I'm new in statistical modelling and using R, so please excuse my mistake for this question. I want to make multiple regression model with these variables: Revenue (in million USD) as dependent ...
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0answers
28 views

Linear unit-transformation (say, from liters to milliliters) of response variable in simple regression

The setting Consider the simple regression model: \begin{equation} y_i=\hat{\beta}_0 + \hat{\beta}_1 x_i + \hat{\epsilon}_i \end{equation} Now, suppose I want to apply a linear transformation to ...
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1answer
295 views

Units in Principal Component Analysis

If I have a data set with 6 variables (A, B, C, D) all measured in different units (eg. m, kg, s, K) and I perform principal component analysis to transform this into two Principal Axes, how do I ...
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1answer
25 views

Interpreting regression results for different units of measure

Could you kindly help me with interpreting the results from the Probit model for different units of measure of the covariates? Consider the Probit Model $$ Y=1\{X\beta+\epsilon \geq 0\} $$ with $\...
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1answer
127 views

Sampling Methods/Monte Carlo method and Log-normal distribution

I found a problem from some notes i found online, here is a screenshot: I am trying to understand this question, it seems this function they define as the LIP() function is basically the quartile/...
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736 views

Can a ratio level variable have negative values?

According to Stevens (1946) ratio level variables require an absolute zero. The implication, I believe, is that 0 = an absence of the thing being measured. As such, can ratio level scales have ...
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1answer
88 views

What do “scales” refer to when comparing correlation matrix to covariance matrix?

In one post it was written that: You tend to use the covariance matrix when the variable scales are similar and the correlation matrix when variables are on different scales. What does scale ...
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1answer
81 views

Dimensional analysis for a qdf/quantile function correspondng to the pdf/CDF (income distribution example)

This question is a duplicate of a question I previously asked, here: Dimensional analysis for a qdf/quantile function corresponing to the pdf/CDF (size distribution of income example). I believe I ...
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2answers
69 views

Can I use a dataset even if the observations of a variable are not in the same unit?

I am using a dataset where a variable is "height". However, when I read about the construction of the dataset, it seems that some observations in the dataset are labelled in centimetres and others in ...
2
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1answer
325 views

What are the units of entropy of a normal distribution?

I have a random process that follows a normal distribution. It's parameters are mean = 35 units, std.dev. = 8 units. I've seen from the wiki entry for the normal distribution that there is a formula ...
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146 views

Change of units in linear regression [duplicate]

Take the following sample linear regression equation: $$ \hat{y} = 20 + 50X $$ I understand how a change of units in X that consists of simple scalar multiplication would alter the regression ...
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1answer
7k views

The unit of Root Mean Square Error (RMSE)

What is the unit of root mean square error (RMSE)? For example if we get an RMSE of 47 from a regression model, what does it tell in terms of unit?
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204 views

How to define general covariance with a dirac delta with correct units

I want to define the covariance of a variable, say $X$, which is the integral over $Y(t)$: $$ {\rm Cov}[X,X'] = \int\int {\rm Cov} [aY(t), a'Y(t')] dt dt'.$$ Just as an example, let the variable $...
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1answer
251 views

in calculating Kalman gain, what if state and measurement space have different units?

My understanding is that the Kalman gain for a regular multivariate filter is computed as $$ K = \bar P H^T S^{-1} \\ S = H \bar P H^T + R $$ $K$ being the Kalman gain, $\bar P$ being the prior ...
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1answer
802 views

What are the units of a convolution?

The convolution of $f$ and $g$ is defined as $ (f * g )(t) \, \stackrel{\mathrm{def}}{=}\ \int_{-\infty}^\infty f(\tau)\, g(t - \tau) \, d\tau $. Let's say that $f(t)$ and $g(t)$ have units of, say, ...
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0answers
32 views

Convert LP3 parameters following a unit change

The USGS uses a Log Pearson Type 3 (LP3) distribution to model flood frequency based on cubic feet per second (cfs) annual maximum flow data (AMAX). The result for a gauging station is the three ...
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1answer
48 views

Compare relationships independent of units

I am trying to compare multiple columns of data with different units graphically. If I z-score the whole dataset am I introducing any error? Can I safely compare from column to column? Eg ...
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1answer
200 views

Is there a way to reconstitute the unit of measurement in PCA?

I have a data set composed of changes in financial asset prices. Because they are on different levels, e.g., one asset is trading in the 100s, the other in the 5s, the change their prices have vastly ...
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2answers
363 views

Inconsistency in unit on gradient descent equation

The update algorithm for gradient descent is $$\theta_j = \theta_j - \alpha \frac{\partial}{\partial \theta_j}J(\theta)$$ $ \frac{\partial}{\partial \theta_j}J(\theta)$ have the unit of cost per ...
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0answers
45 views

Units of measurement when going back from regression to theory

This is a fundamental question I have, and so far I have not found a convincing answer. My theory is this: $$ w_{ijt} = \theta_{jt} a_{ij} $$ where $w_{ijt}$ is wage of worker $i$ in occupation $j$ ...
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1answer
93 views

Are units of the parameter important when considering Fisher information?

This is a follow-up question to one I asked on Math.SE: What are the measurement units of Fisher information? (Dimensional Analysis) When doing calculations with Fisher information in practice, ...
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1answer
1k views

Is the multiple of a lognormally distributed variable also lognormally distributed?

If $X$ is distributed normally $N(\mu,\sigma^2)$ then the variable $Y = \exp(X)$ is lognormally distributed. If the variable $Y$ is multiplied by some constant $C$: $$D = CY$$ Is the variable $D$ ...
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2answers
190 views

Which is the dimension (or units) of the predicted random effects?

Consider a simple panel data (or multilevel model) with random effects. For context, consider a wage regression, where the dependent variable $ln(y_{it})$ is the natural log of wage, where the wage is ...
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3answers
387 views

How to predict orders when unit of measure is different across and within months

I have to predict the order quantity for a 6 month time period. The products are available in different unit of measurement and i dont the relationship between the measures i.e i dont know the ...
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1answer
65 views

Do I really need to put unit on the graphic?

I would like to add unit on this graphic: As stated in many sources, I should place as much of the required information within the figure itself. Unit is a (very) important information so therefore I ...
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1answer
38 views

Statistic calculation (Conversion from one unit to another)

I could get the mean using the formulae but not the value of SD and IQR from using the formulae. What is the problem?
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1answer
942 views

Comparing Standard Deviations with Different Units

Given: the standard deviation is 15.5 cents per gallon in one set of quoted prices and a standard deviation of $5.5 per barrel in another set of quoted prices. There are 33.5 gallons in 1 barrel. ...
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1answer
3k views

If I divide my data by its mean, does it still have a unit?

When dividing a timeseries by its mean value so that its mean becomes 1, does the resulting data still have a unit or is it unitless?
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1answer
562 views

What are the tests to measure agreement between two methods of measurement when the unit of measurement is different between the two methods?

Bland-Altman plot measure the agreement between two different methods which measures the same variable. As far as I understand Bland-Altman can measure only if the two methods have the same unit of ...
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2answers
541 views

Changing the units for an independent variable in a Poisson model

I'm trying to model a dose-response relationship between the incidence of cancer (dependent variable, counts) and the radiation dose (independent variable in gray). Can I change the unit of the ...
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1answer
1k views

lognormal distribution, standard-deviation and (physical) units

I have a distribution of microparticles that follows a lognormal distribution. The cumulative distribution function thus is given by: $$ F_X(x;\mu,\sigma) = \frac12 \operatorname{erfc}\!\left(-\frac{\...
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0answers
429 views

Z-score calculation for a single variable with readings in multiple units

I ran into little trouble transforming a set of data I need for analysis. I have been trying to analyze results of a lab test as Z-scores. I have an output field with a reading and unit field. Data ...
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2answers
275 views

Getting the units right for the Pareto distribution of wealth: x = people, dollars, dollars per person?

When people talk about the 80-20 rule in the context of wealth, it is usually expressed, verbally, by stating that the 20 percent of the people with the highest wealth get 80 percent of the wealth, ...
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2answers
203 views

What is a dimensionless indicator?

What is a dimensionless indicator? I assume it refers to the fact that it is consistent in the way that it doesn't vary disproportionately at the variation of its factors.
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1answer
43 views

Consideration of type/unit errors relevant in statistics and correlation studies?

In http://www.academia.edu/1067827/Defence_of_Empirical_Evidence, Paul Cockshott argues that "type error" must be considered. So, the type of the average cost of the unit of oil is dollars/barrel, ...
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1answer
58 views

Re-expression units conversion

I was arguing with my Stats teacher today in class because we were stuck on the topic of re-expression. She decided to give me extra credit if I could prove to her, using the internet, something ...
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1answer
2k views

The organization as a unit of analysis and sampling issue

I'm doing a quantitative study entitled "Technology Transfer and Competitive Advantages in Oil and Gas Companies". In my study, the unit of analysis is the organization and there are only 9 oil and ...
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1answer
150 views

What rules should guide scaling variables to maximise interpretation, particularly within a regression context?

Context: In this previous question @adhesh asked about the benefits of coding a binary variable zero-one rather than one-two. I realised when I wrote this answer that I had quite a lot to say about ...
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7answers
38k views

Why is gender typically coded 0/1 rather than 1/2, for example?

I understand the logic of coding for data analysis. My question below is on the use of a specific code. Is there a reason why gender is often coded as 0 for female and 1 for male? Why is this coding ...
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2answers
220 views

How a strong trend could be mean-reverting?

I'm testing ADF, PP and KPSS unit tests with tseries library. I get strange result with ADF and PP. I have this vector: x <- rnorm(1000) obviously this ...
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4answers
18k views

Why do demographers give rates per 100,000 people?

It seems universal that demographic statistics are given in terms of 100,000 population per year. For instance, suicide rates, homicide rates, disability-adjusted life year, the list goes on. Why? ...
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1answer
242 views

Generating survival times in days or in years

When generating survival times to simulate Cox proportional hazards models, does it matter to generate them in days or in years? In theory, I guess it does not matter. But in practice? Is there a ...