Questions tagged [units]
units of measurement. Use this tag also for dimensional analysis.
61 questions
3
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1
answer
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Interpret PCA components as a predicting variable in a regression model
I'm struggling to find an answer to this question but I have used the principal components of a PCA as predictors in a regression model and I know want to interpret their effect. Let's say I ran a PCA ...
3
votes
1
answer
48
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Dimensional analysis of a simple linear regression coefficient
I was asking ChatGPT about the intuition behind the beta coefficient and, after some back and forth, it came with an interesting response. It said that we can use dimensional analysis to improve our ...
0
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0
answers
21
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Meta-analysis of odds ratio for continuous variables, how to interpret the decrease or increase per unit?
So, I am doing a meta-analysis of odds ratios to find out the risk factors for a certain medical outcome. One of those risk factors would be (simplified) the time spent in the operation room. My ...
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7
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1
answer
123
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What are the units of a binomial variable's standard deviation?
I recall that a standard deviation is in the same units as the random variable, which is useful.
However, when deriving the standard deviation of a binomial variable, how do we resolve the units of ...
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3
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1
answer
50
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If I do a PCA on centered only variables (of the same unit), does it mean that the principal components created expresses themselves with that unit?
This question might look very trivial, but PCA is still nebulous to me.
If I have a set of individuals described by 10 variables: $A, B, C, D, E, F, G, H, I, J$, all quantitative and having the same ...
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0
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37
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How should I write the units for MSE in its formula and in a plot axis?
I am trying to write a paper for IEEE and would like to know if for MSE, which can have any units, it correct to write "MSE (error^2)" in its formula (i.e. MSE (error^2) = ) and in a plot ...
10
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3
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3k
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Can statistical units measured per thousand inhabitants be bigger than 1000?
I found some data on the number of self-employed people per one thousand inhabitants in Europe here. However, in the year 2020, for instance, some statistical units have over one thousand self-...
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13
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4
answers
2k
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How should variables in statistics be understood?
I had a slightly basic question about variables (particularly in statistics).
We would say that “height” is a variable. In my mind, “height” does not just represent different values, like 2, 45, or 75....
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-1
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1
answer
52
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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 ...
0
votes
2
answers
338
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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:
...
- 101
3
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1
answer
3k
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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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2
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1
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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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1
vote
1
answer
88
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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 ...
0
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0
answers
1k
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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 ...
2
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1
answer
170
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How to interpret 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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0
votes
1
answer
531
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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", ...
0
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1
answer
949
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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}-\...
- 825
3
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0
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1k
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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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1
vote
1
answer
372
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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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1
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1
answer
4k
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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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1
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0
answers
39
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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 ...
- 11
2
votes
1
answer
3k
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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 ...
- 143
1
vote
1
answer
78
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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 $\...
- 976
2
votes
1
answer
476
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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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3
votes
1
answer
4k
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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 ...
- 101
2
votes
1
answer
341
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 ...
- 4,129
-1
votes
1
answer
135
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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 ...
- 3,267
1
vote
2
answers
134
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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 ...
3
votes
2
answers
2k
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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 ...
- 695
2
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0
answers
229
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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 ...
- 203
9
votes
1
answer
27k
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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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1
vote
0
answers
445
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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 $...
- 203
4
votes
1
answer
760
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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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3
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1
answer
3k
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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, ...
- 3,132
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vote
0
answers
39
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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
53
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
...
- 779
2
votes
1
answer
299
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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9
votes
2
answers
850
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 ...
- 91
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0
answers
48
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 $j$ ...
- 2,746
2
votes
1
answer
186
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, ...
- 6,509
6
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1
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4k
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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 $D$ ...
- 1,235
6
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2
answers
254
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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 ...
- 2,746
1
vote
3
answers
641
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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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1
answer
70
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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 ...
- 339
1
vote
1
answer
115
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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?
- 11
1
vote
1
answer
2k
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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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1
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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?
- 505
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1
answer
1k
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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 ...
- 21
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votes
2
answers
723
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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 ...
- 133
4
votes
1
answer
2k
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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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