All Questions
Tagged with variance correlation
131 questions
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Variance of weighted average of 𝑛 correlated random variables
This answer explains how to calculate the variance of an average of n correlated random variables. How can I do it for a weighted average of n correlated random variables? My random variables are ...
- 11
0
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1
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22
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Intraclass correlation -- which one?
I have data collected from an employee survey, in which employees are asked to rate various aspects of their work experience (like engagement, collaboration, and teamwork). Each row is a record of an ...
- 103
13
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3
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999
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What does it mean for observations to be uncorrelated and have constant variance?
I am learning about linear regression from the textbook Elements of Statistical Learning by Friedman, Tibshirani, and Hastie. In this section they suppose we have a set of training data $(x_1, y_1), \...
- 343
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114
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Derive the expectation and variance of squared sample correlation: delta-method or else?
I would like to obtain the expectation and variance of the squared Pearson sample correlation ($\operatorname{E}(R_{lk}^2)$ and $V(R_{lk}^2)$) between two random variables $l$ and $k$ following a ...
- 215
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55
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Consequences of ignoring correlation on standard error
I want to know the mathematical reason why between-individual standard error is under-estimated, and conversely, why within-individual standard error is overestimated if we fail to take correlation ...
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29
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Why does the ICC differ when comparing multilevel models with using log transformations of the outcome variable in R using lme4?
I'm currently working on a multilevel modeling project in R utilizing the lme4 package. The primary aim of the research is to assess the relative importance of between-family and within-family ...
- 41
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11
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How to use ICC with given data
I have data with columns like this:
ENTITY Avg_Score_1 N_obs_1 Avg_Score_2 N_obs_2
With sample values:
001 | 0.997 | 900 | 1.13 | 905
002 | 0.890 | 250 | 0.96 | 251
For about 1000 unique ENTITY values,...
Jbell
1
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1
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76
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How to quantify the similarity between three sets of complex numbers? [closed]
I have multiple groups of measurements, each containing three sets of complex numbers (impedances of the same thing measured under three conditions). The Nyquist plots belows shows two of such groups.
...
- 121
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30
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Equivalence between two expressions for autocorrelation
Have that
$$
\text{Corr}(X_t,X_{t+h}) = \frac{\text{Cov}(X_t,X_{t+h})}{\sqrt{\text{Var}(X_t)\text{Var}(X_{t+h})}}
$$
and
$$
\rho(h) = \frac{\gamma_X(h)}{\gamma_X(0)}.
$$
Those are both ways to express ...
- 207
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How can I reduce correlation between two independents variable?
Edvard, the evaluator in sample B, does not know Richard, the target subject in sample A. However, the two, independently, give the same answer/Likert value (1-5) to 30% of the questionnaire items. It ...
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2
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814
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Variance of sample autocorrelation (Ljung-Box)
The Ljung-Box and Box-Pierce tests make use of the sample autocorrelation
$$ r_k = \frac {\sum_{t=k+1}^n a_ta_{t-k}} {\sum_{t=1}^n a_t^2}$$
and the Ljung-Box test exploits the result that
$$Var(r_k) = ...
- 34.8k
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0
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140
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How to extract the unique variance of a variable
Is there any procedure to quickly obtain the variance that is unique to a variable among a correlated group of variables?
For example a star's temperature mass and volume are related (3 variables), ...
- 93
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45
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How do you express the variogram $\gamma(h)$ in terms of correlation taking into account also the nugget
let's say that I have a spatial random field $z(\textbf{x})$ with $\textbf{x}$ the spatial coordinate. I can define the semi-variogram as:
$\gamma(h)=\frac{1}{2}E[(z(\textbf{x+h})-z(\textbf{x}))^2]$
...
- 111
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1
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186
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Should we standardize the numerator or the denominator of a rate ratio if their variance are different?
I have a disease rate calculated for people aged <50 (early-onset) and aged 50+ (late-onset), for every US county. The rate ratio is the early-onset rate divided by the late-onset rate for every ...
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33
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Deriving a standard deviation of a random variable using correlated other random variables
Consider three random variables: $$u_1, u_2, u_3 \;\; with \;\; E[u_j]=0 \;\; and\;\; Var[u_j]=\sigma^2_j\;\;for\;\;j=1,2,3$$
Here, we know the values $\sigma_1,\;\sigma_2$ and $\rho_{13},\;\rho_{23}$...
- 441
1
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0
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98
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When would correlation between two variables not exist?
If we have two random variables $X$ and $Y$, then $\text{corr}(X,Y)=\dfrac{
\text{cov}(X,Y)
}{
\sqrt{
\text{var}(X)\text{var}(Y)
}
}$.
This correlation will not be defined if either variable has an ...
- 67.1k
1
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1
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174
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Variance of average of 𝑛 correlated random variable where 𝑛 is random variable also
I have a sum of n correlated variables $\sum_{i=1}^n X_i$ and would like to estimate the variance of the sum. I do it with two different methods.
Firstly, I can decompose sum as multiplication of the ...
- 117
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2
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186
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How do I calculate the weighted variance, $\sigma^2$, of a set of $N$ random variables considering their correlation $\rho$? [duplicate]
In a finance textbook of mine, there is an equation for calculating the variance $\sigma^2$ of a portfolio of two risky assets (i.e. random variables) $X$ and $Y$ by considering the correlation $\rho$ ...
1
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0
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43
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How to compute the variance for this process?
I have a sequences of random iid non-correlated positive integers sampled from some (unknown) distribution $\boldsymbol X=[n_1,n_2,...,n_N]$.
From it, I built another sequence in the following way:
$$ ...
- 673
2
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1
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121
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Meaning of "average correlation" in Var$(\bar X)$
From some process I got a series of values. I want to compute the variance of the mean from this series. The series is built with contiguous sub-series. In each sub-series the values are correlated. ...
- 673
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0
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104
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Asymptotic variance of identically distributed but non-independent random variables
I have a question in computing the asymptotic variance of a sequence of random variables that is identically distributed but are not independent. Suppose we have a sequence of i.i.d. random variables $...
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2
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521
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Why do we use $R^2$ instead of $R$ in linear regression?
$R^2$ equals the "amount of variance explained by the model".
However, we rarely use variance in descriptive statistics. We say a sample's weight is 78 ± 13 kg, which is $\bar x$ ± $\sigma$ (...
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0
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26
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Power calculation to check if multiple predictive models are correlated
Say there is a classification setting so that $$ { \{(x_1,y_1),(x_2,y_2), ..., (x_n,y_n)\} } $$ is a set of $n$ observations, and then there is a set of $m$ estimators (models) that take an individual ...
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1
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355
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R function to compute variance of average of correlated random variables
I want to calculate the variance of the average of n correlated variables. I found a formula for that in Borenstein et al. (2009) Introduction to Meta-Analysis.
$$\operatorname{Var}\left(\frac{1}{m}\...
- 151
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55
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Variance of the sum of N correlated random variables with equal variance [duplicate]
According to this Wikipedia article,
In general, the variance of the sum of $n$ variables is the sum of their covariances.
So if the variables have equal variance ${\sigma}^2$ and the average ...
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174
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How can population variance be estimated from a bivariate sample?
Let's assume a bivariate population with a correlation $\rho$ and a common $\sigma$ so that $\Sigma = \sigma^2 \begin{pmatrix}1 & \rho \\ \rho & 1\end{pmatrix}$.
I would like to know the ...
- 351
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28
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Proving non-correlation with very disperse distributions
I'm fairly new to statistics and came up with a problem.
I have a sample with a variation coefficient CV = 0.517 for variable x, and I want to prove this variable is not correlated with a second ...
- 235
2
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1
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369
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Correlation matrix for 2d normal variables with components constrained by $y_1 + y_2 = x_1 + x_2$
I'm following this tutorial on Canonical Correlation Analysis, and had a question about an example from that tutorial.
Question:
On Page 4 of that document, the following example is given:
"...
- 23
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52
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Correlation Based Models vs Covariance Based Models
I am trying to better understand why some models are "covariance based" vs. why some other models are "correlation based".
1) For example, a Multivariate Normal Distribution ...
1
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1
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88
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What is the new sample size of a within study summary effect for outcomes with different sample sizes?
I am performing a meta-analysis and want to compute a summary effect (i.e. weighted mean) for studies that report data on more than one effect size. The same participants are involved, however the ...
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11
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2
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2k
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How to estimate the variance of correlated observations?
Assume we have n observations $x_i$ (i from 1 to n), each from the a normal distribution with mean 0 and some variance component: $X_i \sim N(0, \sigma^2)$. The random variables $X_i$s have some (let'...
- 21.9k
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Comparing variances of multiple correlated variables
I am trying to find a way to compare the variances of multiple variables in the same sample. More specifically, I have a sample of 118 participants who completed eight items (on the same 0-100 ...
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3
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1
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78
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Let $X, Y$ be independent RVs given the variances and no means what is correlation coefficient of $X$ and $Z=2X+Y$?
Let $X, Y$ be independent RV given the variance and no means what is correlation coefficient of $X$ and $Z=2X+Y$?
Given $var(X)=3, var(Y)=4$ and $\mathbf{E}[X]$ and $\mathbf{E}[Y]$ are not known, let $...
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33
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Correlation of Subsets - When the population correlation is known
Suppose I have a population of N pairs of (X,Y). I know the correlation of the population is Z. I now break the population into two unequal sets (n1 + n2 = N and n1 <> n2). If I calculate the ...
2
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1
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196
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Variance of the Product of Correlated Random Variables?
I would like to multiply two correlated random variables, but I'm getting a negative variance. Please point out where I'm wrong.
Variable1 and ...
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2
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2
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126
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"Dependency" definition
Origin Lab has in their fitting parameter's statistics "Dependency". Each parameter has a dependency. It's not like the covariance between 2 parameters. I thought it could be defined from ...
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5
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2
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1k
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Finding correlation coefficient of $X$ and $XY$
Let $X$ and $Y$ be independent random variables with nonzero variances. I'm looking to find the correlation coefficient $\rho$ of $Z=XY$ and $X$ in terms of the means and variances of $X$ and $Y$, i.e....
- 221
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Best model for various bad situations
"What type of predictive model would best handle a wide variety of data issues.
Extreme heteroscedasticity
bi or tri modal distribution’s
heavily correlated predictors…
Saw this as an Amazon ...
- 503
2
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1
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129
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When using Linear Models with random covariates, is it the pearson correlation that determines the reduction of the residual variance?
Typically, if you have normally distributed dependent variable Y with variance $\sigma_Y^2$ a treatment indicator and a random covariate that is also normally distributed, then when fitting a linear ...
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0
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1k
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How do you interpret generalized variance?
Per Wiki, generalized variance is the determinant of a covariance matrix: https://en.wikipedia.org/wiki/Generalized_variance
I have heard that if the determinant is small, there is strong correlation ...
- 3,263
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1
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3k
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How to combine standard errors for correlated variables
What is the formula for calculating the standard error of a quantity (A) that is the ratio of 2 quantities (A = B/C) if B and C are correlated?
According to page 2 of http://www.met.rdg.ac.uk/~...
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2
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675
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If two predictors are uncorrelated, is the variance explained by multiple regression the sum of variance explained by both linear regressions?
Pretty much what it says in the title. I don't know too much about statistics and I worry I'm getting this wrong.
There are variables $X$ and $Y$, they are uncorrelated by design, because one has ...
9
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4
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5k
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Why highly correlated means higher variance?
I am reading the book Introduction to Statistical Learning and on page 183, the book states that
Since the mean of many highly correlated quantities has higher variance than does the mean of many ...
- 93
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67
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What is the difference between covariance and correlation? [closed]
I am analysing stock returns and whether they move in the same or opposite directions across different regions, investment styles or company sizes.
Which of the covariance or the correlation gives ...
- 29
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232
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Why does the correlation between decision trees have to be positive?
In the book "Elements of statistical learning" we have that the variance of a the random forest is given by
$V(\frac{1}{n} \sum X_i)= \rho \sigma^2+ \frac{1-\rho}{n}\sigma^2$
where $\rho$ is the ...
- 303
1
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0
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53
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How is the variance of correlated outputs int LOOCV higher than K-fold?
In addition to this question I want to know how the "outputs" in a leave-one-out CV have a higher variance.
I understand the answer provided that says that when elements of each sample are highly ...
- 329
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29
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Can I determine what the correlation matrix is if I have regression coefficients and standard errors?
I am trying to reverse engineer a manuscript and was wondering if I can get a correlation matrix or the covariance-variance matrix from values reported in a paper. Can I use the reported regression ...
- 662
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2
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3k
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Linear Mixed Effects Model Variances
Consider the following model:
\begin{equation}
Y_i = X_i\beta + Z_ib_i + \varepsilon_i,
\end{equation}
where $b_i \sim N(0, D)$, and $\varepsilon_i \sim N(0, R_i(\gamma))$.
The variance of $Y_i$ ...
- 843
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0
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20
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What conclusions can we draw from different correlations between IQ scores between subjects belonging in different groups?
I was reading a presentation where research was quoted according to which children and parents who live together have IQs that are correlated with a correlation coefficient of 0.42 while children and ...
- 245
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76
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If the coefficient of determination is a measure based on variance, then what about standard deviation instead?
Background: I've been teaching a very simple course of introductory Statistics for a few years now and we cover linear correlation and the Correlation Coefficient ($r$). I want to introduce the ...
