Questions tagged [units]

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

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How does scaling the dependent variable affect the coefficients and more?

Consider the regression model visit_t=β_1+β_2log⁡(pub_t)+β_3 price_t+β_4 win_t+β_5 temp_t+ε_t where visit is measured in 1,000s. What happens to the coefficient beta 1, beta 2, the sum of squared ...
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PCA statistical units

I have a school project where I'm required to use a factor analysis. I chose this dataset from FiveThirtyEight about police killings. I want to characterize the places where people have been killed so ...
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Contextual levels with 1:1 clustered observational units

Imagine a study that, from a design perspective, has both repeated measures and hierarchical structures. The ratio of observational units at level -3 to level-2 is 1:1(For example, "only one &...
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Effect of units on shape of normal distribution

TL;DR: Is the shape of a bell curve / normal distribution idependent of the units chosen to represent a certain variable? More detail: I was playing around with some data from this paper in excel: ...
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Can ratio data have negative values?

I get the concept of a "true zero" value, but I'm not sure why this implies that there cannot be any negative values—at least that's what most sources say that I found only, with only few ...
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What issues arise when you perform stats on scores attributed to concepts/objects rather than people? (2-way independent ANOVA example)

• Pianos have 5 different types of black note, and 7 different types of white note, on them. • A famous music psychology paper examined the effects of note colour (black vs white) and instrument (...
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How do the units of the SIR model cancel out?

I was having trouble trying to understand the parameters of the simplest SIR model. If beta is the effective contact rate and s is the percentage of people who are susceptible, then how do the units ...
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Units of measurement and the t-statistic

Consider a case in which we want to examine the effect of house value on homeupkeep expenditure using linear regression model, where dependent variable y is the upkeepexpense and ...
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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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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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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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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 was ...
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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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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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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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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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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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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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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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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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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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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 ...
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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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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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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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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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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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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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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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2 votes
1 answer
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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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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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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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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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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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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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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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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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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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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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1 vote
1 answer
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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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7 votes
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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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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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2 votes
2 answers
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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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4 votes
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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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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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6 votes
2 answers
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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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3 votes
2 answers
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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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1 vote
1 answer
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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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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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3 votes
1 answer
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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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